STACKS

lannini

Foundation

DEmnno nno iocrtioii nspEtrs

OF EmERGEnCV mEDICHL FHULITIES
in RURHL nORTHERn [RllFORniR

S. C. Daberkaui and G. H. King

Giannini Foundation Research Report No. 329

March 1980

Division of Agricultural Sciences
ZZZ^Z^iZ^ UNIVERSITY OF CALIFORNIA

•4

University of California, Davis
Department of Agricultural Economics
in Cooperation with
Economic Development Division
Economics, Statistics and Cooperatives Service
U.S. Department of Agriculture

DEMAND AND LOCATION ASPECTS OF EMERGENCY MEDICAL
FACILITIES IN RURAL NORTHERN CALIFORNIA

S. G. Daberkow and G, A. King

FORET-JORn

Most research of the Agricultural Experiment fetation Is directed to
efficient use of resources In the production and marketing of agricultural
commodities. This study Illustrates that some of the same techniques can
he applied In other areas as well — In this case to the analvsls of delivery
of services to people In rural areas.

This is an analysis of efficient provision of emerpencv medical services
In a six-county area of Northern California, comnrlslnp most o^ the Superior
California Health Planning Area. The California Department of Health has
set goals for provision of such care, hut has not piven full consideration
to the cost and location of facilities. The results are presented as a
contribution to a more comprehensive analysis of the costs and benefits o^
provision of emergencv medical services. The methodolopv and a brief review
of findings of this study are Riven in Daberkow and King (1977). The
authors express their appreciation to the several reviewers of the manuscript
for their suggestions and to the typists ^or their assistance in preparing
the final copv.

TABLE OF CONTENTS

Page

I. INTRODUCTION 1

The Problem 1

Objectives of the Study 3

II. FRAMEWORK OF ANALYSIS 6

General Considerations 6

Operational Model 7

III. PRODUCTION OF EMERGENCY HEALTH SERVICES 11

Legislative Perspective H

Characteristics of EMS in Rural Areas 12

EMS Production Activities 1^

Theoretical Cost Functions 19

Empirical Cost Functions 21

IV. DEMAND FOR EMERGENCY HEALTH SERVICES 27

Theoretical Aspects 27

EMS Utilization in the Study Area 30

Estimates of EMS Usage Per 1,000 Residents 39

Resident Population Demand Points 41

Nonresident Population Estimates: Recreation Popula-

lation and Transient Population 49

Estimate of EMS Usage Per 1,000 Population-Days. ... 54

V. LOCATION OF FACILITIES 55

Response Time Standards - Resident Population 57

Response Time Standards - Peak Month Demand 65

Service Time Standards 66

Page

VI. FINANCIAL ANALYSIS OF EMS FACILITIES AND FUNDING

ALTERNATIVES 66

Revenue Structure 69

Funding Alternatives for Low Volume EMS Facilities. . . 73

Subsidy Schemes 74

Volunteer Systems 77

VII. SUMMARY AND CONCLUSIONS 78

Uses of the Model 78

Extensions of the Analysis 82

Conclusions 85

LITERATURE CITED. 83

APPENDIX A - Cost Data 92

APPENDIX B - Resident Population Estimates by Demand Point. . 104

APPENDIX C - Nonresident Population Estimates by Demand Point 109

iii

LIST OF TABLES

Table Page

1 Typical Allocations of Functions Among the Elements

of an Ambulance Service System 15

2 Number of Operators, Trips per Operator, Ambulances
per Operator and Trips per Ambulance by Type of

Ambulance Service, California, 1969 25

3 Distribution of Ambulance Calls by Medical Diagnosis

for Three Study Areas 31

4 Emergency Room Arrivals, True Emergencies, Percent
of True Emergencies by Selected Categories, Arrivals
by Ambulance and Arrivals by Auto for Hospitals in
the Study Area, 1972

9 Study Area Demand Points and 23 Potential Facility
Sites

10 Population by City and Area Represented by City, 1970

11 Location and Number of Expected EMS Calls by Demand
Point

13 Present Location of EMS Facilities as Possible Sites:
Results for Selected Response Times (Based on Annual
Demand Estimates)

Number of Emergency Room Visits to Study Area Hospi-
tals for 1971, 1972, and 1973 33

Selected Data from the 1968 Ambulance Survey for the

Study Area Counties and State 37

Relationship Between Total Ambulance Calls and Total

Resident Population by County, 1968, For All Counties

and Rural Counties Only ^0

Number of Study Area Rural and Urban Places by County
and Size Range

46
48

12 Response Time Standards: Comparison of Selected
Parameters for the Optimal and Present Location
Patterns of EMS Facilities (Annual Demand) 58

Table Page

14 Optimal Location of EMS Facilities: Results for
Selected Response Times (Based on Annual Demand

Estimates) 62

15 Present Location of EMS Facilities as Possible Sites:
Results for Selected Response Times (Based on Peak

Month Demand) g7

16 Optimal Location of EMS Facilities: Results for

Selected Response Times (Based on Peak Month Demand) 68

17 Financial Analysis of the 15 Facilities Entering
Optimal Program with 40-minute Response Time (Annual

Demand Model) 71

18 Financial Analysis of the 22 Facilities Entering the
Optimal Solution with a 27-Minute Response Time

Standard (Based on the Annual Demand Model) .... 72

LIST OF FIGURES

Figure

1 Sequence of Events Following an Emergency 17

2 Hypothetical Short and Long Run Cost Curves For Firms

of Different Capacities 22

3 Discontinuities Associated With Adding Number of
Ambulances For Firms I and II 22

4 Derivation of a One-, Two-, and Three-Ambulance EMS
Facility Total Cost Function 23

5 Spatial Distribution of the Demand Points in the Study

Area 43

6 Facilities and Demand Points Associated with Those
Facilities Using the 13-Minute Response Time Standard
(Present System Servicing Annual Demand) 61

7 Relationship Between Response Time, Total Regional
Cost, and Percentage of Population Served Within

Selected Response Times (Optimal System) 63

8 Facilities and Demand Points Associated with Those
Facilities Using the 40-Minute Response Time Standard
(Optimal System) 64

DEMAND AND LOCATION ASPECTS OF EMERGENCY MEDICAL
FACILITIES IN RURAL NORTHERN CALIFORNIA

1/ 2/
S. G. Daberkow- and G. A. King-

I. INTRODUCTION

The Problem

Emergency Medical Services [EMS], a subsystem of the general health
care sector, has been of Increasing concern to legislators and governmental
agencies. Willemain [1974, p. 4] has presented the goals of an EMS sub-
system in terms readily recognizable by economists:

The goals of the EMS system are to prevent death, disa-
bility and suffering in persons with injury or acute illness.
The allocation of public resources should be systematically
directed to these ends; ideally, the EMS planner should be
able to assess the impact of proposed combinations of money,
people, facilities and equipment in terms of death, disability
and suffering. In other words, the best planning requires
input-output relationships linking resource allocations to
patient outcomes.

Unfortunately, the input-output relationships referred to by Willemain
are unavailable. Thus, this study will concentrate on the input side of EWB
delivery while exploring the resource allocation problem in a theoretical
framework. The empirical results hopefully will be useful to health

1/ Agricultural Economist, Economic Development Division, ESCS, U.S.D.A.

2f Professor of Agricultural Economics and Agricultural Economist in the
Experiment Station and on the Glannlni Foundation, University of California,
Davis.

planners and pollcy-nahers vrho nust deal with standards for UlS delivery and

the costs associated with those standards. The theoretical framework is

intended to provide insip.hts into the WlS resource allocation process and

the need for future research.

The 1P7'1 State E!!S Plan [California Department of Health, 1974, p. 5]

lists several specific goals, which vjill be used to provide boundaries for

this study. Amonp, the froals listed are the following:

To create an emergency ipedical services system consistinp
of an organized pattern of readiness and response services
based on private and public agreements and areawide operational
procedures, including:

a) Contractual or direct public provision arrangements with
certified emergency medical transportation services pro-
viding a 2A-hour zoned deployment of sufficient numbers
and types of vehicles and crews in relation to emergency
medical facilities to meet the needs within the systems
area.

b) Policies and procedures ensuring that necessary em.ergency
medical services will be rendered to all patients requiring
such services without prior inquiry as to ability to pay.

c) Programs of public education and inform.ation which take
into account the needs of visitors, as well as residents
of the area, to know or be able to learn imm.ed lately the
means of obtaining emergency m.edical services....

d) Assessment of the costs and benefits of alternative
designs for the statewide system and recommendations for
allocating available financial resources so as to ensure
optimal system development and availability of quality
service.

An operational interpretation of these objectives is needed. In terns
of an economic model, the consumption and production aspects of EMS must be
identified. Assumptions about the demand for EliS will be discussed as well
as the production and distribution of EMS to satisfy the demand. Although

the state f»oals listed above are admirable, the costs associated with

these goals have never been quantified. One objective of this study, therefore,

is to quantify these costs.

Objectives of the Study

The specific Intent of this study Is to analyze MS delivery in a rural
environment. In 1P74 California was divided into 12 regions for health
planninp purposes. One of these repions — Superior California — provides
the rural environment needed for this study. The sparsely settled moun-
tainous areas surrounding small population clusters in the foothills of the
upper Sacramento Valley are typical of rural population distributions.
The Superior California Comprehensive Health Planning Aeency, currently
knovTn as a Health Systems Apency, provides health planninp expertise to the
region, and therefore represents an established administrative unit involved
In the n!S planninp process. Although the apency does not at present have a
lepal mandate to oversee the delivery of P'S, it m.ay soon have the respon-
sibility to approve or deny applications for the establishment of additional
EMS facilities within the region. Hence, the planning bod}'' will then be
concerned with all aspects of EMS in a rural area.

The goals quoted above em-phaslze that the provision of PIS
should be baf;ed on need. The need for health care is defined by the medical
profession; whereas tlie demand for health care is the translation of needs
into the action of seeking medical services.

The state goals also emphasize that the provision of EIIS should not
be based on abillty-to-pay — that is, price and income are not to influence

the rationing of EMS among consumers. Thus, the demand for EMS is assumed

to be perfectly Inelastic with respect to price and Income in this study.

Due to the heavy influx of recreationists and transients into the

study area, particular attention will be paid to quantification of seasonal

population changes. The following quote is indicative of the problem [Area

II Regional Medical Program, 1972, p. 4];

An additional factor which serves to increase the pressure
on over-taxed health facilities and services is the impact of
the resort and recreation traffic. The presence of recreational
facilities in mountain and lake areas attract tourists, campers,
and visitors. More than six million persons visited 29 state
parks in Northeastern California and 1,750,000 registered at
3 National Parks within the target area during 1969-70. Week-
end populations may Increase many fold during recreation seasons
compounding the load on health care resources.

The deployment of EMS facilities refers to their size, number, and
location. Size of facility is defined as the annual number of calls
served by each facility. Since the "consumption" of EMS occurs at the
point of production [Jeffers, et at., 1971], availability (i.e. location)
of EMS is crucial. The deployment analysis in this study uses a least-cost
algorithm to find the size, number, and location of EMS facilities subject
to a constraint that the demand for EMS be satisfied. As is the case in
most location analyses, this study specifies that the demand for E>S and the
potential EMS facility sites be located at discrete points.

Quality of service, of course, involves value judgments making quanti-
fication difficult, but the process is further complicated by the necessity
of describing EMS delivery as a system of several components. Personnel
training, transport equipment, and communication equipment are all part
of the EMS system. When referring to quality, personnel training levels
and equipment type should be specified. Some guidance to quality

specification is offered by state rep;ulations such as those coverintt the
training of drivers and attendants. For purposes of this analysis it is
assumed that the level of training of medical personnel and the aualitv of
the communication equipment is adequate for anv spatial arrangement o^
facilities. A further analysis might examine the trade-offs among training,
communication equipment and facility location as reflected by the mortality
and morbidity of patients entering the EMS system.

Goal (d) above is concerned with assessing the costs and benefits
of alternative EMS system designs. The several TJ'S system designs analvzed
in this study are under alternative time constraints placed on the location
algorithm. Response tine, or the time between the notification of an
emergencv and the arrival of an ambulance at the scene is often used as a
measure of the effectiveness of an EMS system. This effectiveness measure
assumes that tine-to-treatment has an important effect upon morbiditv and
mortality. A response time of 10 to .30 minutes has been used as a standard
in urban areas. In a rural area, however, response time may be over an
hour. As would be expected, a very fast response time requires additional
facilities or ambulances or both, which, of course. Increase the cost of an
EMS system. The optimal size, number, and location of EMS facilities will
be found under various time constraints. As the time constraint is changed,
the algorithm determines the total annual cost for the regional E^'S system
as well as the deployment zones or the demand points served by each EMS
facility.

This study concentrates on the cost or production aspects of ET^S.
The reduction in death, disability, and suffering is a direct benefit of an

Eltr system. From a societal viexTpoint or for the resource allocation
process, benefits from an E-ff system must be weighed apainst costs.
TTnfortunately, the benefits or patient outcor.es associated vith EJ!S
resource allocation decisions have been neither well-documented by the
medical profession nor accurately quantified by economists. Furthermore, a
problem, arises when an EMS facility is established to serve a community
vrhich nay not have the ability to pay for such a system. In more succinct
terns; who pavs the costs, and who receives the benefits?

This report first presents a framework for the analysis, (giving an
overview of the study area and the location model in Section II. The next
tv.'o sectlonr. (Ill and IV) provide a detailed treatment of the production of
and demand for enerjTiency health services. Those who are Interested mainly
in tb.e empirical results, nay turn directly to Section V vAere the location
rnttern.'=: are presented under alternative tine constraints. A discussion of
t;i«^ financial feasibility of emergency facilities is friven in Section ^.'T,
followed by a brief summary of flndinrs and sugc'estions for further v.'ork in
Section VII.

II. FRAMEITORK OF ANALYSIS

General Considerations
A problen faced by a liealtli planninj^ ap;ency is
anliulance service to a f'iven population. Two basic
arc: (1) health services should be provided to all
services and (2) health services should be provided
cost) as possiMe [Cordes, 1975]. Two standards of

to provide emergency
premises in this study
persons needing these
as efficiently (least-
effectiveness used

throughout this study are response time and service time , where response
time is time elapsed between the time a call is received and the arrival of
the ambulance at the emergency scene, and service time is the time from the
dispatch of the ambulance to the transfer of the patient to a hospital. The
former standard emphasizes a rapid response of vehicle and trained crew to an
individual in need of acute care; the latter, a rapid transport of the
patient to a hospital emergency room.

The major objectives of this research are: (1) to minimize total
costs of providing ambulance service under different standards of
effectiveness, (2) to determine the trade-off between costs and standards of
effectiveness, and (3) to analyze the financial feasibility of providing EMS
as standards of effectiveness and facility usage change.

Operational Model

Economic literature on the location of firms and/or production is
quite extensive. The theoretical work of Lefeber [1958], Isard [1956],
Kuenne [1963], and Takayama and Judge [1971] should be acknowledged as
should a large number of applied studies (e.g., Weinschenck, et al.t
[1969]). More recent work has concentrated on the location problems within
the public sector (Miller and King [1971] and Revelle, et at. [1970]).

As to solution procedures, a relatively new class of algorithms, known
as tree-searching or combinatorial programming, can be applied to location
problems which exhibit certain characteristics.—^ Typically, these problems

1/ These problems are sometimes called location-allocation problems.
They have the following general structure (Scott [1970], p. 118): "Suppose
that there are given (a) a set of n points distributed in the plane; (b) a
numerical weight to be attached to each point; and (c) a set of m Indivisible
centroids without predetermined locations; then the location-allocation
problem in its most general form is to find locations for the m centroids and
an allocation of each point, or fraction of a point, to some centroid so as
to optimize an objective function." In this study, m, the number of centroids
or facilities. Is also part of the solution rather than given.

minimize either assembly and processing or processing and distribution costs
where supply or demand, respectively, is predetermined. These models can
be used for locating commodity processing facilities, warehouses, hospitals,
clinics, schools, airports, transport terminals, police stations, or fire
stations (e.g., Chaiken and Larson [1972]). If the processing facility's
total cost function is linear with a positive intercept, the problem becomes
the classic fixed charges transportation problem (Hadley [1962], p. 136;
Scott [1970], p. 128). Such a function Implies declining average facility
cost.

Additional constraints (such as travel time or distance) are often
added to these models to meet various goals defined by a planning body
concerned with the provisions of the particular good or service. Such a
system of facilities, however, may not be economically self-supporting
solely by user fees. The reader is referred to Hirsch [1970] for a com-
prehensive discussion of demand and supply aspects of publicly provided
goods and services.

Algorithms used to solve location problems range from complete
enumeration, such as the Stollsteimer [1963] model, to the more systematic
examination of a combinatorial tree,— ^ The latter approach Includes the
branch and bound algorithm, backtrack programming and discrete dynamic
programming (see Scott [1970] Ch. 2 for an Introduction to these tech-
niques). Manne [1964] utilized dynamic programming to solve the location-
allocation problem "based on the fact that the total cost of processing

Ij Integer programming is another alternative but its application seems
limited to small, well-behaved problems.

and distribution form a hypercube with regard to all possible combinations
of locations" (Weinschenck, et al.^ [1969], p. 47). This technique is
also known as "steepest ascent one point move algorithm," or SAOPMA
Manne notes, however, that the algorithm may give a local rather than a
global optimum. An example of backtrack programming used as a location
algorithm is not known; however, the solution technique is similar to
that of branch and bound programming utilized in this study. All of these
techniques can solve very general location problems including those with
some nonlinearities. Their major drawback has been the inability to handle
large problems, either because of computer storage requirements or solution
times,—''

This study utilizes a modified branch and bound algorithm to solve
the fixed-charges transportation problem noted above. The algorithm was
proposed by Efroyrason and Ray [1966]. Khumawala [1970, 1972] improved
the efficiency of the original algorithm. On the CDC 7600 computer, located
at the Lawrence Laboratory, Berkeley, California, this algorithm was found
to be operational for moderately large location problems. (Extensive
testing of the capacity and time requirements of the algorithm is reported
by Khumawala, [1970]). The basic idea is to solve a sequence of linear pro-
gramming problems (not necessarily meeting the integer restriction) that
give progressively improved lower bounds on the value of the objective
function of the mixed integer programming problem. The algorithm terminates

1/ Another category of solution algorithms, not discussed here, are known
as heuristic methods and defined as (Scott, [1970], p. 39): "... algorithms
[which] represent sets of rules which produce solutions to given problems, but
which do not necessarily produce the best possible solutions."

when the lowest value for an integer solution is reached. The mathematical
model is as follows:

n m

Minimize Z = Z E C X + Z f y (1)
iGN, j=l i=l ^ ^

Subject to: Z ^ = 1 j = 1, 2 n (2)

ieN.
J

0 < Z X < n y 1 = 1, 2 m (3)

Yj. - 0, 1 i = 1, 2, m (4)

where:

= total cost of satisfying the entire demand for EMS services
at demand point j from facility i

tj^j = ($ cost per patient per mile) (miles from i to j)

= cost per patient which is independent of distance (e.g., linen

supplies, equipment use, etc.)
Dj = demand for EMS (ambulance service) at demand point j (patients)
X^^ = the fraction of the demand at point j which is met by a facility

at i

= fixed charge for establishing and maintaining a facility at i
y^ = 1 if a facility is established at i; 0 if not
n = total number of demand points
m = total number of potential EMS facility sites

" the set of demand points which can be served by a facility at 1

«» the number of demand points which can be served by a facility at i
Nj = the set of EMS facilities which can serve demand point j.

The objective function (equation 1) indicates the mixed integer programming
nature of the problem since is continuous and y^ is a binary variable.
Equation 2 ensures that total demand at each demand point is exactly satis-
fied, while equation 3 ensures that a facility i is open before it can serve
demand point j.

III. PRODUCTION OF EMERGENCY HEALTH SERVICES

Legislative Perspective

Several factors are responsible for generating interest recently in
EMS as an important component of health care planning. In the context of
rapidly rising prices of medical care in general, attention has been drawn
to the extreme costliness of emergency medical care. Furthermore, emergency
medical care is an unevenly distributed service, for many geographical areas
have acute medical manpower shortages [Matthews, 1973]. It is particularly
in rural areas where emergency facility services are deficient. Another
factor focusing attention on EMS is that its use as an entry point into the
health care system seems to be growing at a disproportionate rate. There
has even been an increased use of EMS for other than true emergencies.

As the awareness of EMS problems increased, several government agencies
have become involved, and since the mid -I960' s several pieces of legislation
have significantly affected EMS. The 1966 Traffic Safety Act charged the
National Traffic Safety Administration with making highways safer. One

outcome was the development of standards for emergency care systems by the
U.S. Department of Transportation. In California it is the Office of
Traffic Safety that coordinates EMS for the Department of Transportatltm.

Government units most concerned with emergency medical care are the
various health agencies. At the federal level, the U.S. Department of
Health, Education, and Welfare (HEW) has responsibility for emergency care
via the Health Services and Mental Health Administration. The California
State Department of Health has the Bureau of Emergency Medical Services to
facilitate planning and coordination procedures as well as set goals and
standards for the state EMS plan. Comprehensive Health Planning (CHP)
agencies (currently called Health Systems Agencies or HSA's) are perhaps the
most significant local bodies engaged in emergency health care planning.
CUP agencies were created under the Partnership for Health Act in 1967;
HSA's were created under the National Planning and Resource Development
Act of 1974. These agencies have the responsibility and power to approve or
deny various additions or deletions to the current medical care system
within their jurisdiction. They also attempt to coordinate planning of the
diverse interests within the medical care industry. The most EMS-specific
legislation is the Emergency Medical Services Systems Development Act of
1973 which at the federal level is carried out by HEW. The Act is designed
to foster EMS demonstration projects throughout the U.S., with particular
regard for rural areas.

Characteristics of EMS in Rural Areas
In 1968, the National Highway Safety Bureau released a study by
Dunlop and Associates [1968] entitled Eaonomios of Highway Emergency

Ambulance Services ^ which was one of the most comprehensive studies of
ambulance services in the U.S. The report undertook two tasks [p. 9]: "(1)
to describe the present status of emergency ambulance service across the
country, their problems and their ability to continue to provide emergency
services, and (2) to develop methods and guideline information helpful to
individuals at all levels of government in planning new or expanded services.
Types of ambulance purveyors were identified by their principal source of
revenue. Commercial or private purveyors are supported by the users of the
ambulance system; municipal or county units may be wholly or partially
supported by taxes; volunteer groups are dependent upon donations of time,
equipment, supplies, and monies. Funeral home-sponsored ambulances and
volunteer groups are the most common in the nation's rural areas. The
prevalence of volunteer services in rural areas appears to be a direct
result of low aggregate demand for emergency medical services and the high
costs of providing quality emergency care comparable to that of urban areas.
Sparsely populated areas not only generate fewer calls but increased
distances lead to less effective service. The Dunlop report Indicated that
80 percent of the ambulance services had less than 500 calls per year. The
report further notes the high cost of high-quality (24 hours per day)
emergency care: annual costs per ambulance in 1968 were estimated to be
between $60,000 and $65,000. Much of this (50-90 percent) is fixed cost
with personnel accounting for 60 percent of the fixed cost and housing and
depreciation, most of the remainder. Personnel training and recruitment
are of major concern to emergency care purveyors. Training standards for
emergency medical care personnel are currently undergoing revision, with the

likely result that more schooling will be required (see the 197A California
EMS plan). In addition, the ambulance industry has traditionally paid only
minimum wages to drivers and attendants; as a consequence, recruitment
and rapid personnel turnover are problems. Revenue collection is another
area of concern with delinquent or tardy payments by individuals and insti-
tutions (welfare and insurance agencies) apparently a common occurence.
Areas with a large transient population during all or parts of the year tend
to have more noncollections. The seasonal demand for emergency medical care
also tends to strain a system designed to accommodate only resident needs.

The public's lack of awareness of proper usage of an anergency care
system also causes concern and adds to costs. When calls are made for non-
urgent causes, resources are diverted from their best use, increasing the
cost of the system.

In rural areas where private emergency medical care purveyors do
operate and also in several urban areas, they frequently ask for a res-
traint on competition in order to ensure a stable demand. Thus, local
governments have resorted to exclusive contracts, zoning, regulated monopo-
lies, franchising, or outright subsidies to guarantee that emergency service
will be present for their constituents.

EMS Production Activities
Table 1 presents an abstraction of a basic Ef^S unit, combining labor,
equipment, and facilities to produce ambulance calls. These inputs are
used to perform a variety of tasks, such as transportation, communication,
medical care and clerical work. The allocation of functions varies among

TABLE 1 — Typical Allocations of Functions Among the Elements of
an Ambulance Service System

System
elements

System Functions

Transportation

Medical
care

Communications

Records &
support

Labor

Drivers

Attendants

Dispatchers

Clerks

Equipment

Facilities

Ambulances

Garages ,
workshops

Stretchers ,
resuscitators ,
etc.

Radios, phones,
teletypes, etc.

Dispatch
center

Office &

data reduction

equipment

Offices,

bunkhouses,

etc.

Source: Dunlop and Associates, Inc. [1968]

the elements of the system, but basically management specifies policies and
procedures that define the functions and Interactions of the system
el eraent s .

The emphasis of this study is on the transportation function of an
EMS system and, in particular, the time of response of the system.
In order to analyze the transport function in isolation, the remaining
functions, particularly the medical care and communications functions,
are specified at certain levels of quality. As formulated, the analysis
(size, number, and location of facilities) is performed under the assump-
tion that the level of training of the medical personnel and the quality
of communication is adequate for any spatial arrangement of EMS facili-
ties. The specification of the level of training of the medical personnel
and the quantity and cost of the communication equipment assumed for any
EMS facility proposed in this analysis is given in Appendix A.

The dynamics of EMS, pertaining to the transportation function, is

illustrated in Figure 1. The traditional view in the medical profession

is that total waiting should be minimized [Waller, et al.^ 196A]. For this

reason, the health planner Imposes standards on total waiting time,

minimizing time after the call is received (i.e., minimizing response time).

The following passage from the 1975 California State Plan for Emeryenay

Medical Services (p. 132) exemplifies this goal:

In emergency situations, time is a crucial factor for
securing assistance, to protect the patient from further
preventable deterioration, and to promote optimum clinical
disposition. A maximum response time pattern is critical in
determining whether adequate assistance for medical emer-
gencies can be achieved.

Figure 1 Sequence of Events Following an Emergency

Emergency
occurs

Call
received

Ambulance
dispatched

Arrival at
the scene

Departure from
the scene

* * * *

Arrival at
hospital

Depart
hospital

Arrival at
station

Delay
time

Travel
to the
scene

Treatment
at the
scene

Travel
to the
hospital

Transfer
patient

Return
to station

Dispatch
~ delay

Travel
delay

Response time

Total waiting time

Service time

Round-trip time

Source: Stevenson (1974)

The maximum response time for transport should be met for
95 percent of the requests occurring in that ambulance service
area. Maximum response time may vary with population density
levels as shown below:

Dens ity

Maximum Response Time

High
Med ium
Low

10 minutes or less
20 minutes or less
30 minutes or less

Service time also may be used as a criterion or standard. Particularly
in rural areas where medical training of ambulance personnel may be minimal,
it is crucial that the time between ambulance dispatch and patient transfer
to a hospital be minimized.

To place the emphasis on response time in perspective, mention should

be made of other research that has suggested alternative goals. Herlihy

[1973] concluded that in rural areas an adequate communication system would

yield a greater marginal return than would reduced response time, because a

significant number of patients have to wait to receive medical attention

after being transported to a hospital. Plaas et at. [197A p. 17] note the

lag between the occurrence of an emergency and detection time, and make the

following observation:

...the response time of an ambulance to the scene may
not be of critical Importance. Indeed, if there is an hour's
delay between when the incident occurs and when a call for
help is made, and by some innovation response time is reduced
from 30 minutes to 20 minutes, then the actual reduction from
the time of the incident to the time of the first professional
care is not 33 percent but 11 percent. It may thus be more
useful to investigate whether some investment in remote area
communications is more beneficial than an investment in more
ambulances.

Nevertheless, for the analysis here, response and service time will be
considered critical to the allocation of health resources.

Theoretical Cost Functions
The firm producing EMS faces a relationship between the Inputs or
factors of production and the resulting output measured in terms of ambu-
lance calls. This relationship (i.e., the production function) and the cost
conditions affecting the inputs determine the firm's cost function. For
this study, the distinction between long-run and short-run cost functions is
of interest. As typically defined, the long run Implies that all factors
are variable; while in the short-run plant size is assumed constant. The
long-run cost function is defined to be associated with the lowest cost of
production for plants of differing size. Logan [1962 p. 12] refers to the
long-run cost function as an economies of scale curve and describes that
function as follows:

The economies of scale curve, then, is simply the locus
of costs "expected from the operations of plants of various
sizes, when ope-mtions ave ovganized as efficiently as possible

under the given aonditions ."—^ Such a cost function has a
variety of uses with the prime value to the firm being one
of showing the expected relative operating cost of one size
of plant against the cost of another size. The cost function
then becomes a planning device for the producer in deter-
mining the size of a prospective new plant.

The usefulness of a long-run cost function is in terms of its plan-
ning properties, for it allows the firm to analyze a variety of plant sizes
and determine which size of plant is appropriate for the expected future
demand .

A long-run average cost function which slopes downward and to the right
exhibits economies of scale. Reasons given for economies of scale include

1/ Bressler, R. G., Jr., "Research Determination of Economies of
Scale7" Joiccnal of Farm Eaonomios, XXVIII (August 1945), p. 526.

technical forces, management, marketing economies, etc. The most obvious
reason for economies of scale In the production of EMS Is the large "fixed"
cost relative to the variable costs as well as the Indivisibilities of
certain Inputs such as ambulance vehicles. "Certain equipment may not be
'economically available' to smaller plants, since Its operation would be at
considerably less than Its capacity" [Logan, p. 19].

The use of the term "fixed" costs In the last paragraph may seem
Inconsistent with the long-run concept, but the Inclusion of a long-run
"fixed" cost represents "the minimum average annual long-run cost of es-
tablishing and maintaining a plant" [Stollstelmer , 1962, p. 636] or, as

French, et al,^ [1956, p. 572] state: ,

...the fixed base represents the long-run average rate
of returns above variable costs that are required to maintain
and replace the capital goods. Returns in any particular
short-run period need not cover these costs, but over the
long run they must average this amount if the firm is to
continue in business.

Throughout this study, each EMS facility is assumed to have a
long-run total cost function, which is linear with a positive inter-
cept. Figure 2 Illustrates this form. The LRTC is an "envelope" curve to
the linear short-run total cost curves (SRTC^) , Cost curves SRTC^,
SRTCjj, and SRTC^^^ reach a technical capacity constraint at q^^, q^, and
q^, respectively. The right-hand side of Figure 2 shows the companion long-
and short-run average cost curves. The LRTC curve is drawn here to coincide
with SRTC curve of the smallest plant. The analytical framework to be
presented later requires this assumption.

A final aspect of EMS facility cost functions deals with the concept

of discontinuities. Logan [1962 p. 35] discusses this point as follows:

While short- and long-run cost functions are generally
represented by continuous curves, in reality cost functions
often exhibit discontinuities. Such discontinuities generally
result from indivisibilities of factors of production. In
other words, inputs are added by discrete units instead of
as a continuous flow.

Cost functions of EMS facilities tend to exhibit such discontinuities.
The most severe example of indivisibility arises when an additional ambu-
lance must be added to a facility. Figure 3 illustrates a total cost
step function where an ambulance is added at various intervals. Thus
the long-run total cost curve may take on a "jagged" appearance because
of these discontinuities [Logan, p. 39]. The long-run total cost curve
used in the analysis approximates this "jagged" function in a linear
fashion as shown in Figure 3.

Empirical Cost Function
Dunlop [1968] presents one way— queueing theory— of apprpxJmating
the total cost step function alluded to above. (See Plaas, et al,^ Vol. I,
[1974] for an annotated bibliography of other queueing methods.) By
assuming a Poisson distribution for the arrival rate of ambulance calls
for a given service time and by requiring that at least one ambulance be
available at least 90 percent of the time when a call arrives, Dunlop Is
able to show how many calls per year a one-ambulance and a two-ambulance
system can serve. Figure A shows the theoretical step function derived
from the Dunlop model if service times of one and one-half hour and one-half
hour are assumed for one- and two-ambulance systems. A one-ambulance system

Figure 2 Hypothetical Short and Long Run Cost Curves
for Firms of Different Capacities

Figure 3 Discontinuities Associated with Adding Numbers
of Ambulances for Firms I and II

SRTC|,

Number of Calls Per Year

FIGURE A— Derivation of a One-, Two-, and Three-Ambulance EMS Facility Total Cost Function

Three-ambulance service (Total Cost = $150,000 + $10 per call)-

One ambulance

Two ambulances

•Two-ambulance service (Total Cost
$10 per call)

$120,000 +

fA=l

P = 1
fC = 1 call
|d = 1 call

call requires 1-1/2 hour service time
call requires 1/2 hour service time

requires 1-1/2 hour service time
requires 1/2 hour service time

Assume Poisson arrival rate and 90 percent availability

One-ambulance service (Total Cost = $70,000 + $10 per call)

Calls per Year (000 's)

can handle between 613 and 1,927 calls per year depending on length of
service time. A two-ambulance system is able to serve between 3,066 and
9,417 calls per year also depending on the service time.

Some data are available which indicate the actual, rather than
theoretical, number of calls per ambulance per year. Table 2 indirectly
reflects at least four factors influencing the number of calls per year per
ambulance: the area demand for ambulance service, variation in service
time, type of service, and number of ambulances per service. A shorter
service time, characteristic of a more densely settled area, enables both
a one- and two-ambulance system to serve more calls per year. Terrain,
climatic conditions, type of roads, and distance to a hospital all in-
fluence service time and thus could cause wide variation among ambulance
operators which otherwise are similar. Data are rot available to distin-
guish between one, two, three, or more ambulance systems. Therefore, the
data in Table 2 are average indications of the actual number of calls per
ambulance. The Ambulance Survey [Dunlop, 1968, p. 128] notes that "In the
'rural' counties, 86 percent of the services averaged less than 50 calls
per month." The Implication is that many ambulance services have a large
amount of excess capacity (or insufficient demand relative to resources
available), at least compared to the queueing model results presented above.
For example, the volunteer fire departments which are typically found in
rural areas, had an average of 102.3 calls per ambulance in 1969 while the
commercial operators, which are often in urban areas, averaged 805.3 calls
per ambulance in the same year.

TABLE 2 — Number of Operators, Trips per Operator, Ambulances per Operator and
Trips per Ambulance by Type of Ambulance Service, California, 1969

Ambulances Trips Trips

per per per

Type of service Operators operator operator ambulance

number

Commercial

177

2.4

2,738

805.3

Funeral director

3.4

906

266.5

Private or nonprofit hospital

1.9

434

228.4

Local tax supported hospital

4.1

3,838

936.1

Volunteer fire department

1.3

133

102.3

Municipal, district or other fire department

1.8

811

455.5

Police department

3.4

3,714

1,092.4

Voluntary organizations or other local
government services

4.1

7,975

1,945.1

Total

331

2.98

2,245

547

Source: 1968 Ambulance Survey. [California Department of Transportation, 1970]

Since the location model used in this study is essentially a planning
device, the potential EMS facilities were assumed uncapacltated,— ^ which
necessitated the estimation of a long-run total cost function. Output of an
EMS facility is measured in terms of ambulance calls per unit of time. The
long-run total cost function for an EMS facility was estimated to be a
linear function with a positive intercept. The intercept was Interpreted
as the long-run cost of establishing and maintaining a facility. The
annual fixed cost of a 24 -hour per day, 365 days per year EMS (one ambu-
lance) service, manned with adequately trained crews and supporting clerical

staff, and stocked with appropriate communication and transport equipment

was estimated to be $70,000 (see Appendix A).- The estimates were derived
from an update of the Dunlop study as well as data from the California
Ambulance Association (personal interview, 1975). The aggregate variable
cost of linens, bandages, ambulance maintenance, etc., was estimated at
$10 per call. The over-the-road cost of ambulance vehicles (gas, oil,
tires, etc.) was estimated at $0.10 per mile per patient. Although the
algorithm is designed to handle facility costs (fixed) which may vary by

\l Facilities were not limited in the number of calls each could
serve per year.

11 This model implicitly assumes an ambulance will always be available
at a potential facility, thereby neglecting probabilistic aspects of ambulance
call arrival rates and ambulance service times. Using queueing theory notation,
this implies an M/M/" or M/G/" system (Wagner, p. 865-866). Thus the facili-
ties are commonly assumed to be uncapacitated and a post optimization analysis
determines the number of ambulances necessary at each facility to keep expected
(in a statistical sense) response time below a given standard. (See Bell and
Allen [1969] for a discussion of the number of ambulances necessary at a given
location.) An M/G/<» queueing model, for a one-ambulance facility servicing
2,012 calls per year (the largest number reported in this study), using a mean
monthly arrival rate and having a one-hour average service time would exhibit
a probability of 0.19 for a call having to wait.

location, there Is little justification for doing so; it was assumed,
therefore, that the fixed facility costs were equal at all potential
facility sites.

IV. DEMAND FOR EMERGENCY HEALTH SERVICES

Theoretical Aspects

Economists typically hypothesize that the quantity demanded for a
particular good or service is a function of several variables including the
price of the good or service, the price of other goods and services, income
and/or financial reserves, and the collective preferences of the population.
Furthermore, the number and location of people influence the spatial in-
tensity of demand for goods and services in a particular area.

When considering medical care, health planners, health agencies,

and health professionals tend to use the word "need" rather than demand.

Jeffers, et al, [1971, p. 46] use the following definition of need;

That quantity of medical services which expert medical
opinion believes ought to be consumed over a relevant time
period in order for its members to remain or become as "healthy"
as is permitted by existing medical knowledge.

The definition of need says nothing about the "restraining" variables
noted in the demand function. Hence, there is a gap between need estimates
and the actual consumption of a good or service. Not only are the restraining
variables of price (including the extent of insurance coverage), income,
tastes, and preferences responsible for this gap, but also consumer ig-
norance, inertia, fear of pain, and other psychological barriers to medical
care consumption. For purposes of this study, the demand rather than need

concept is utilized. This approach is pragmatic because of: (1) the
difficulty of the medical profession in establishing an adequate measure of
need, (2) the obvious discrepancy between need standards^^ and actual
consumption by the population under consideration, and (3) the fact that
available data measure only the actual usage or consumption of medical
services.

The demand for EMS is conceptually less complex than for all medical
2/

services.— In a true life threatening situation in which medical atten-
tion is not postponable, the influence of prices or ability-to-pay diminishes.
The influence of prices and ability- to-pay upon the consumption of emergency
ambulance service is, therefore, hypothesized to be minimal. Population
size and consumer preferences then become the dominant determinants of
demand.—^

From the definition of EMS used in the California State Plan for

Emergenay Medical Services (1974, p. 2), it is seen that the consumption

of EMS is really the consumption of several interrelated elements:

Emergency Medical Services (EMS) are those communications,
transportation, medical and related services rendered in response
to the perceived individual need for immediate medical care in
order to ameliorate or prevent suffering and disability and
reduce the incidence of death.

1/ See Daberkow [1976] for attempts to evaluate various need indicators
for EMS in the study area.

2/ Daberkow [1976] presents a review of health care demand models in
general .

2_/ A number of other variables have been suggested to impact aggregate
EMS demand including age distribution, education, health insurance coverage,
type of employment, health status and various socioeconomic characteristics
of the population as well as the availability of ambulance services (i.e.
supply) and alternative medical care resources (i.e. doctors and proximity
to hospitals). See Daberkow (1976, Ch. 5).

The service of an ambulance provider embodies most of these functions. The

ambulance provider usually serves as a communication link between the

ambulance and hospital as well as between the ambulance and accident site.

The ambulance provider also is involved in the transport of victims from the

accident site or demand point to the nearest medical facility, usually a

hospital. The ambulance driver and attendant can legally provide only

limited medical attention to stabilize the patient's condition.

The State Plan for Emergency Medical Services [1974, p. 2] also

defines a medical emergency:

A medical emergency is a situation in which there is a
perceived physiological need for iranediate medical care, based
on an injury or other unforeseen acute physiceil or mental
disorder which apparently threatens life or function. It is
recognized that many of the patients using anergency rooms and
departments do not fall within this definition. The resolu-
tion to this problem is through triage (sorting according
to the apparent urgency of the need presented) , which is
essentially a clinical determination and must be made by a
qualified individual.

The assumption throughout this study will be that each medical
anergency generates a need for emergency medical service. The question
arises as to whether this need is translated into demand for EMS. The
definition of a medical emergency, given above, recognizes that not all
perceived medical emergencies are life-threatening. Hence hospital emergency
rooms receive patients who do not have a clinical life- threatening emergency
but only a self-perceived emergency. It has also been suggested that the
hospital emergency room is sometimes used as an entry point into the medical
system. This is particularly true of travelers, new residents, and tran-
sient workers who are unfamiliar with the location of physicians or other
medical personnel in the area.

The demand for emergency care can be separated into two categories:
(1) the demand for emergency room services and (2) the demand for ambu-
lance services. The latter requires that some form of communication and
transport be performed, whereas the former requires only medical attention.
Demand for ambulance services implies a life-threatening situation in
most instances, with the exception of routine transfers.

Emergency ambulance calls are generated from two basic causes: (1)
accidents and (2) acute illnesses. Several studies have attempted
to disaggregate these two categories (Table 3). These studies (Waller,
et at [1966], Aldrich [1971], and Deems [1973]) show the variety of cir-
cumstances in which ambulances are used and indicate differing relative
frequencies of specific emergency situations among areas of the U.S.— ^
The studies use different classification schemes, but some generalizations
about accidents seem appropriate. Traffic accidents account for nearly
one-third of the calls in the first two studies and 10 percent in the
remaining study. All accidents (traffic plus other) include nearly one-half
of all calls in the first two studies but only 30 percent in the remaining
study; the remainder of calls in each study were primarily for illnesses,

EMS Utilization in the Study Area
Data on EMS utilization for the study area are taken from three
sources: (1) 1972 Regional Mediaal Vvogram Survey [Superior California

\J Dry runs are not included in the Waller et dl [1966] study.

TABLE 3 — Distribution of Ambulance Calls by Medical
Diagnosis for Three Studies

The Waller Yolo County, California Study

Diagnosis

Cardiovascular & respiratory
disease

Traffic accidents

Other accidents

Poisoning and suicide

Acute & chronic alchoholism

Psychiatric

Acute abdomen

Obstetrical

Other

Unknown

Total

Percent of
total calls

20.1
33.1
13.1
1.6
3.7
2.0
4.0
1.1
8.0
12.5

100.0

The Aldrich Los Angeles, California Study

Diagnosis
Auto accidents
Other accidents
Cardiac
Poisoning
Other illness
Dry runs

Total

Percent of
total calls

26.6
21.0

4.9

3.5
34.3

9.9

100.0

The Deems Atlanta, Georgia Study

I^ercent of

Diagnosis

total calls

Drug intoxication

7.1

Obstetric

3.7

Auto-related trauma

9.1

Other trauma

24.0

Cardiovascular

10.2

Other medical

20.6

Dry runs

25.3

Total

100.0

Source: Waller et . al. study [1966]; Aldrich et. al. study 11971]; Deems study [1973].

Comprehensive Health Planning Agency, 1974]; (2) 19?S California State Plan
for EMS [California Dept. of Health 1975]; and (3) 1968 Arrbulanae Survey
[California Department of Transportation 1970], These data reflect utiliza-
tion by residents as well as non-residents who are passing through the area
(transients) as well as those who are visiting the recreation sites in the
area. The following section relates total EMS usage to the resident popu-
lation of the area while the subsequent section addresses the problem of
seasonal fluctuations in the area's population.

Total emergency room arrivals, true emergencies, arrivals and emer-
gencies per 1,000 residents, percent of true emergencies by selected
categories, number of arrivals by ambulance and number of arrivals by
auto for hospitals in the study area during 1972 are shown in Table A.
It should be stressed that much of these data are estimates by hospital
personnel and therefore are subject to vagaries associated with lack of
recall and inadequate, incomplete, or nonexistent records.

As would be expected, total emergency room arrivals are highest for
the two most populous counties — Butte and Shasta. The resident per capita
emergency room arrival ratio is quite varied among the hospital service
areas, ranging from 345.9 arrivals per 1,000 residents in the Oroville
hospital service area to 93.6 arrivals per 1,000 residents in the Gridley
hospital service area. Emergency room arrivals can be divided into two
groups by qualified medical personnel: those patients with true emer-
gencies and those in need of only primary care. The percentage of total
arrivals which were considered true anergencies by hospital personnel
ranged from 100 percent at the Biggs-Gridley and Butte County hospitals to

TABLE 4— Emergency Room Arrivals. True RmerRenclps . Percent of Trijp EmcrRenclp-^ by Selected CateRorleB. Arrivals l.y Ambulance and
Arrivals by Atito for Hoepitala In the Study Area, 1972

County and Hospital

Total H.S.A.-' True_eme r fienci e n H.S.A. Pet. true

emerRency arrivals Percent emerRenclea emergencies by

room per 1,000 of total Number per 1,000 s elect ed cau s es Percent by Percent by

arr Iva 1 n res Ident s arr iva ls re sidents Auto Tra u ma Heart _ Auto Nu mber Am bul ance Number

_County emer g^ enc^ _ rooni arrlval a

County Anbulance
arrlvala per
1,000 realdenta

number

percent number number

percent

percent number

Butt e County

Chlco Comunlty Hemorinl Hospital , a c t \
N.T. Enlow Hospital

5,100
5,956

223.8

55
40

2,805
2,382

105.0

10
25

25
45

10
5

Feather River Hospital (Paradise H.S.A.)

3.150

198.1

473

29.7

BlgRg-Grldley Memorial Hospital (Grldley H.S.A.)

1,376

93.6

100

1,376

93.6

Butte County Conwunlty Hospital (Orovllle H S A )
Hedlcal Center Hospital

1,463
8,914

345.9

ino

1,463
2,139

120.0

0
60

26
0

0
24

Glenn County

2,063

1.375

(8.7

Glenn General Hospital (UUlowa H.S.A.)

3,438

221.8

1,375

88.7

Shasta County

21,707

4,008

50.8

Hegmrlal Hospital

Shasta General Hospital (Redding H.S.A.)
Herry Hospital

6,236
18,000

337 .0

60
50

1,742
9,000

177.2

40
35

10
30

Mayers Memorial Hospital (Fall River Mills H.S.A.)

1,971

281.6

512

73.1

Tehana County

4,547

752

25.5

Corning Memorial Hospital (Corning H.S.A.)

1,466

178.8

1,100

134.1

St. Elizabeth Coimunlty Hospital (Red Bluff H.S.A.)

3,884

182.3

2,000

93.9

Trinity County

Trinity General Hospital (UeavervlUe H.S.A.)

1,220

162.7

610

81.3

Source: Superior California Comprehensive Health Planning Aasoclatlon. [1974]

a/ Hospital Service Area

b/ Dashes indicate data not reported

a low of 15 percent at Paradise. The per capita true emergency arrivals is
highest at the Redding hospital service area (177.2) and lowest at the
Gridley hospital service area (29.7). Traffic accidents account for
60 percent of the true emergencies at the Oroville Medical Center and
Fall River Mills hospitals. Over 60 percent of the true emergencies were
from trauma cases at Biggs-Gr idley hospital. Heart cases accounted for
up to 30 percent of true emergencies in the study area hospitals.

Most arrivals at hospital emergency rooms are by private automobile.
Ambulance arrivals range from 14 percent of total arrivals in Tehama County
to a high of 40 percent in Glenn County. The fact that the majority of
emergency room arrivals use automobiles has implications for the ambulance
system in the study area. Without loiowing the state average percentage of
private auto emergency room arrivals, comments about the study area are
speculative. If the study area has an unusually large percentage of
emergency room patients who arrive by auto, it may be that EMS resources
are inadequate, the public is unaware of ambulance availability, or perhaps
a majority of emergency room patients do not require or are assumed not to
require ambulance transport. One should also recall that the Table 4
data represent estimates for 1972 only, and information on the variation
in these data are not available.

One source of EMS usage data over several years is available. The
California Department of Health [1974] has collected data on hospital
emergency room visits for 1971, 1972, and 1973 (see Table 5). The report,
however, notes that the data come from several sources and, therefore, are
not uniform across all hospitals. Of special concern is the possible

TABLE 5 — Number of Emergency Room Visits to Study Area Hospitals
for 1971, 1972, and 1973

County and Hospital

1971

Visits in Year

1972

1973

Visits per
1,000 H.S.A.-
residents, 1972

Butte County

N.T. Enloe Memorial Hospital
Chico Community Hospital

(Chico H.S.A.)

Feather River Hospital (Paradise H.S.A.)
Biggs-Gridley Memorial Hospital (Gridley H.S.A.)
Medical Center Hospital of Oroville (Oroville H.S.A.)

Glen County

Glenn General Hospital (Willows H.S.A.)

Shasta County

Mayers Memorial Hospital (Fall River Mills H.S.A.)

Shasta General Hospital
Mercy Hospital
Memorial Hospital

(Redding H.S.A.)

Tehama County

Corning Memorial Hospital (Corning H.S.A.)

St. Elizabeth Community Hospital (Red Bluff H.S.A.)

Trinity County

Trinity General Hospital (Weaverville H.S.A.)

5.2
2.2

1.7
4.0
8.9

3.2

1.3

4.8
12.8

numbers in l,000*s

1.3

10.0

3.4

0.5

0.5
18.6
1.6

1.5
3.5

1.5

10.4
8.6

3.5
4.4
16.0

5.5

0.9

0.2
20.1
7.7

2.0
5.1

1.5

No.

234.8^^

138.4
265.3
333.3

219.4

71.4

287.9^^

182.9
164.3

200.0

Source: California Department of Health, 1975.
aj Hospital service areas,
b/ Chico H.S.A.
c/ Redding H.S.A.

inclusion of outpatient visits In the count of emergency room visits.
Table 5, however, gives some indication of the instability of usage data.
The variability of the data from year to year is quite severe (e.g.. Redding
hospital service area and Chico hospital service area) . These data make
future demand projections somewhat speculative. As an illustration of the
problems of using different data sources, the last column of Table 5
shows 1972 emergency room visits per 1,000 residents which is comparable
to the second column of Table 4. Surprisingly, the EMS usage in a majority
of the hospital service areas was comparable between data sources. The
Gridley and Fall River Mills hospital service areas, however, exhibited
radically different per capita usage patterns between data sources. This
inconsistency should encourage a more uniform approach to data collection.

A third data source is the 1968 Ambulance Survey [California Depart-
ment of Transportation, 1970]. This study reports the results of a survey
of approximately 80 percent of the ambulance providers in California.
Table 6 presents selected study area counties and state-wide ambulance
utilization data from that report. The number of ambulance trips and
number of true emergency ambulance trips have been adjusted for those
ambulance providers who did not respond. Butte and Shasta counties reported
the study area's highest ambulance utilization rate, with 35.2 and 35.4
ambulance trips per 1,000 residents, respectively, Tehama County's utili-
zation rate was the lowest among the study area counties.

Ambulance trips can be divided into four categories: (1) patients
transported to a hospital, (2) patients treated at the scene with no
transport, (3) routine transfers, and (4) dry runs. The 1968 Ambulance

TABLE 6 — Selected Data From the 1968 Ambulance Survey for the Study Area Counties and State

True Emergency Trips

County

Ambulance Trips

Total per 1,000
residents

Ambulance Trips

Trips Per

1,000

residents

Dry Runs

Traffic
accidents

Non-residents

Resident Usage/
1,000 residents

number

percent

number

percent 1

number

percent number

percent

number

Butte County

3,473

35.2

881

8.9

100

28 247

106

7.9

Glenn County

596

31.9

141

7.5

-jJ

68 96

3.6

Shasta County

2,807

35.4

1,169

14.8

63 740

343

10.42

Tehama County

584

20.1

176

6.1

55 97

4.5

Trinity County

237

26.0

160

17.6

34 54

14.3

California

839,135

42.6

46.7

391,977

19.9

43, U7

33 129,352

31,358

18.3

Source: California Department of Public Health in contract with the California Department of Transportation, California Ambulance
Survey Final Report , 1970.

a^/ Dashes indicate data not reported.

Survey tried to ascertain the number of true emergency ambulance trips
(categories one and two) in each county during 1968. The percentage of
true emergencies and the number of emergency trips per 1,000 1968 residents
are also given in Table 6. The highest percent of ambulance trips for true
emergencies occurred in Trinity County (68 percent). The state ratios for
total ambulance trips and emergency trips per 1,000 residents are consider-
ably higher than for any of the study area counties. The question arises
as to why the utilization rate of EMS in the study area is below the
average for the state. One might hypothesize that in rural areas, EMS
resources are not readily available or not located in a manner allowing
easy accessibility to resources.

Table 6 also presents data on emergency ambulance trips which were
dry runs, emergency trips for traffic accidents, and emergency trips for
nonresidents. Other than Trinity County, which had only three percent
dry runs, the study area counties were close to the state average. Glenn,
Tehama, and Shasta counties recorded over 50 percent of their true emer-
gency calls being due to traffic accidents. Butte and Trinity Counties
were much closer to the state average of 33 percent.

Table 6 also indicates the estimate of ambulance use by nonresi-
dents. Although the ambulance survey report does not specifically reveal
how these or other data were verified, it is assumed that these percentages
were estimated by ambulance providers. The estimates range from 12 percent
in Butte County to 52 percent in Glenn County while the state average is
8 percent. Obviously, in the study area counties, especially Glenn, EMS
usage is influenced by nonresidents. But, those counties with the highest

number of true emergency trips per 1,000 residents were least affected by
nonresidents. The last column of Table 6 represents true emergency trips
per 1,000 residents with the influence of nonresidents removed. The
variability of EMS utilization is not reduced by the adjustment. Trinity
and Shasta counties have the leading utilization rates for residents among
the study area counties.

Estimates of EMS Usage Per 1,000 Residents

A popular measure or "rule of thumb" for estimating EMS resource
usage is in terms of visits or trips per area resident per time period.
For example, Stevenson [1971] estimated that 35 emergencies per year are
generated by every 1,000 people. This estimate is fairly constant for
urban populations of less than 500,000, but for places of greater size
the ratio is much more variable. The California 1968 Ambulance Survey
suggested that for the U.S. in general one emergency per day Is generated
per 10,000 people. For California, the report stated that one emergency
per day per 20,000 people is more appropriate. The Dunlop study [1967]
reported that for populations of 10,000 or less, every 1,000 people gen-
erated approximately 17 calls per year. Obviously, these latter two es-
timates differ substantially from the former two.

Table 7 summarizes the results of an analysis relating 1968 county
resident population to 1968 total ambulance calls. The results are given
for all California counties and for rural counties only. The standard
linear model was tested with and without a constant term. When the constant
term was included. It was not significant at the .05 level. For the state

TABLE 7 — Relationship Between Total Ambulance Calls

and Total Resident Population by County, 1968,
for All Counties and Rural Counties Only

Analysis

Constant

Resident
population-

Degree

of
freedom

All Counties

with constant

constant suppressed

Rural Counties
(with less than
125,000 population)

with constant

constant suppressed

-2,361.4
(-1.26)

-44.24
(-.25)

49.24
(27.19)

48.46
(28.4)

30.1
(9.47)

29.5
(14.8)

.93
.93

.74
.74

Source: Daberkow (1976)

a/ Population variable is significantly different from zero at the 5 percent
level in all equations.

W t value is given in parentheses.

as a whole, there are between 48 and 50 ambulance calls generated per 1,000
residents. For rural counties, this estimate drops to between 29 and 30
ambulance calls per 1,000 residents, depending upon which model is used
but the coefficient of determination declines when only rural counties
are analyzed. For purposes of the location model the estimate of 29.5
calls per 1,000 residents is used.

Resident Population Demand Points

An objective of this study is to analyze the delivery of EMS in a
rural environment. Northern California provides such a rural setting.
Heavy dependence upon agriculture and forestry, sparsely populated
hinterland, and small population clusters scattered unevenly over the
area characterize the region designated as the Northern California Health
Service Area. The upper end of the Sacramento Valley lies within this
area, as do the foothills and mountains of both the Coastal and Sierra
ranges bordering the Valley. Discrete geographic points have been
chosen to represent geographic areas in the study area. The geographic
points represent sources of demand for EMS, and the logical choices
for these demand points are population clusters of larger towns and
cities. To model the location of population perfectly, each person or
household would represent a source of demand. For tractability and
statistical reasons, however, the demand points are taken as aggregations
of people or households (i.e., towns). Rural areas are particularly
hard to model because of the spatially irregular population distribution.
The demand points used in this study represent a wide variety of

population distributions within varying geographic shapes. The
geographic areas represented by the demand points vary in size (i.e.,
square miles), population and concentration of that population around the
demand point.

Density (people per square mile) is not an adequate measure of the
population distribution between areas surrounding demand points because
of the variation in population and square miles of these areas. For
example, a large population cluster in a large area may have the same
density as a small area with a small population. If the former area has
all of its population concentrated near the demand point, while in the
latter case the population is uniformly distributed over the countryside,
then density is not a good comparison of population distribution between
the two areas. Therefore, concentration (the percent of the area's
population residing in the town designated as a demand point or the
percent of the area's population within one mile of the demand point) is
a more descriptive measure of population distribution.

The study area (Figure 5) is basically rural with large and small
population clusters scattered throughout the area. Table 8 indicates the
number of rural and urban places by population category and by county for
the study area. These 130 places reflect an approximate spatial location
and intensity of demand. Obviously, the rural farm population Is dispersed
throughout the study area and is not included in these clusters of poptilation.

To further reduce these 130 places to a tract Ible number of demand
points, urban and rural places which have a zip code were considered
viable demand points. The assumption was that areas designated by zip

Figure 5 Spatial distribution of the demand points in the study area.

TABLE 8 — Number of Study Area Rural and Urban Places by County and Size Range

Population Butte Glenn Shasta Tehama Trinity Total

Rural Places

0-99 13 5 14 7 13 52

100-199 4 3 9 5 2 23

200-399 9 5 5 2 1 22

400-599 1 0 0 0 0 1

600-799 1 1 3 0 0 5

800-999 0 0 2 11 4

1,000-1,499 1 0 2 0 1 4

1,500-1,999 .-1 0 0 0' 0 1

2,000-2,499 0 ' 0 2 0 0 2.

Urban Places

2,500-2,999 0 1 0 0 0 1

3,000-3,999 -1 0. 0- l' 2?

4,000-4,999 3 1 1 - 5

5,000-5,999 0 1 ' 1

6,000-6,999 1 - . . • - 1

7,000-7,999 1 1 • r2

8,000-8,999 0 '0

9,000-9,999 0 ' 0

10,000-14,999 1 1 2

>15,000 1 ' 1 2_

Total 38 16 41 17 . 18 130

Source: California Department of Transportation, City and Unincorporated Place Names (1971).

code had a sufficiently large population to qualify as a demand point.
In addition, several geographically separated places were included even
though they did not have zip codes. Appendix B lists the demand points
and their respective resident populations as well as the Census enumeration
districts which surround each demand point. The population associated
with each demand point is derived from the 1970 U.S. Census district population
estimates or from the California Department of Transportation, California
City and Unincorporated Place Names [1971]. The boundaries for the area
represented by each demand point follow the Census enumeration district
boundaries. Each demand point is associated with a particular hospital
serving that point; the collection of demand points served by a hospital
define a hospital service area.

Due to computer capacity limitations and a shift in the boundaries of
the health planning area during the study, the study area was restricted
to the counties of Butte, Glenn, Shasta, Tehama, and Trinity plus parts
of Siskiyou, Lassen, and Modoc. Table 9 presents the demand points
actually used in the analysis. The 72 demand points were assumed to
be an adequate representation of the location of population clusters.

Table 9 also indicates the sites chosen to be potential EMS facility
sites. The selection of these potential sites follows two general guide-
lines. First, all cities which are currently served by an EMS facility
are automatically included as potential EMS facility locations. Second,
the geographic dispersion of demand points may be so sparse that a
potential facility must be allowable in that area regardless of the size
of the city Involved.

TABLE 9 — Study Area Demand Points and 23 Potential Facility Sites

Bangor

37.

McArthur

Berry Creek

38.

Millville

Biees*

39.

Montgomery Creek

Butte Meadows*

40.

Oak Run

Chico*

41.

Old Station*

Durham*

42.

Palo Cedro

Feather Falls

43.

Platine*

Forbestown

44.

Project City

Forest Ranch

45.

10.

Gridley*

46.

Shinpl ptown

11.

Nord

47.

Summit City

12.

Oroville*

48.

Whiskey town*

13.

Palermo

49.

Whitmorp

14.

Paradise*

50.

Dunsmuir *

15.

Richardson Springs

51.

Live Oak

16.

Richvale

52.

Cornln p^*

17.

Sterling City

53.

Gerber

18.

Yankee Hill*

54.

Los Mo linos*

19.

Princeton*

55.

Mati f" on

20.

Artois

56.

Minpral *

21.

Elk Creek*

57.

Pa QVfin t"fl

22.

Glenn

58.

Pa VHP Q PTPplf

23.

Hamilton City*

59.

Proberta

24.

Orland*

60.

Red Bluff*

25.

Willows*

61.

Tehama

26.

Bieber*

62 .

Vina

27.

Adin*

63.

Rip Rflr

28.

Anderson

64.

Biimf" Rflnrh*

11 L. XVCH.1 L^ 11

29.

Bella Vista*

65.

30.

Burney

66.

Forest C^ pn*

31.

Castella

67.

Havf ork*

32.

Oo .

Hyampom

33.

Enterprise

69.

Junction City

34.

Fall River Mills*

70.

Lewis ton

35.

Igo

71.

Trinity Center*

36.

Lakehead

72.

Weaverville*

*Potential facility sites.

To assess the degree to which the study area's population is repre-
sented by discrete demand points. Table 10 was constructed showing
19 of the 72 demand points which are large enough (i.e., greater than
1,000 population) to have a satisfactory population estimate in the
1970 Census of Population. Table 10 presents the census estimate for the
resident population of the selected demand point (town), the total
population of the surrounding area which is represented by that demand
point (see Appendix B for enumeration districts that make up the sur-
rounding area), and the percent of the total population which is within
the city limits of the demand point under consideration.

The large percentages in the last column indicate that a high degree
of an area's population is represented by the demand point in question.
The percentages range from 37.3 percent to 100 percent. The overall
average was 70.5 percent. Thus, on the average, about 30 percent of an
area's population is outside of the 19 demand point's limits. Little can
be said for the distribution of this population without more detailed
information on house locations within large rural census tracts.

The 19 demand points represent 198,818 of the study area population
of 244,062, with 45,244 not represented. If other demand points given in
Table 9 are assumed to represent 70.5 percent of these 45,244 people,
then 13,347 or 5.5 percent of the study area's total population is not
represented by specified demand points. Due to lack of detailed resi-
dence information, these people are assumed to be represented by the
demand points given in Table 9. The use of discrete demand requires the
assumption that distances between potential EMS facilities and the
various demand points are average distances.

TABLE 10 — Population by City and Area Represented by City, 1970

U.S. Census Area population

Demand point

population

of city (1970)

assumed to be repre-
sented by the city

City /Area
Population

number

percent

Chico^''

32,818

40,193

81.7

Oroville^''

15,864

21,060

75.3

Palermo

1,966

5,270

37.3

Paradise

14,598

100.0

Gridley

3,534

7,808

45.3

Biggs

1,115

2,084

53.5

Live Oak

2,645

4,811

55.0

Or land

2,884

6,602

43.7

Willows

4,085

6,010

68.0

Burney

2,190

2,633

83.2

Anderson

5,492

14,164

38.8

Cottonwood

1,288

2,574

50.0

Project City-

3,792

7 031

S'^ Q

Enterprise

11,416

11,486

99.4

Redding^''

21,541

27,181

79.3

Dunsmuir

2,214

2,819

78.5

Red Bluff

7,676

14,497

52.9

Corning

3,573

6,508

54.9

Weaverville

1,489

100.0

Total

140,180

198,818

70.5

Source: U.S. Bureau

of The Census (1972)

a./ Includes Chico North, Chico West, Chico, and Mulberry

hj Includes Oroville, South Oroville, and Thermalito

cj Includes Project City and Central Valley

d^/ Includes Redding and Bonneyview

Nonresident Population Estimates;
Recreation Population and Transient Population

Northern California experiences a large Influx of people seeking
outdoor recreation. In addition. Interstate 5 serves as a major trans-
portation artery along the West Coast, so large numbers of transients
pass through the area. An attempt must be made to estimate the total
population at risk at a given time; therefore, the non-resident popula-
tion must be added to the resident population.

Available data on the recreation population visiting Northern
California is limited to estimates of visitor-day use at various public
recreation sites. Recreation use data are available from the U.S. Forest
Service, California Parks and Recreation Department, U.S. Department of
the Interior, the National Park Service and from the Pacific Gas and
Electric Company (see Appendix C). The public organizations which
provided the bulk of these data stress that the estimates of recreation
site usage are imprecise since the areas under their responsibility are
very large, and only organized campgrounds and national parks utilize
systematic counting techniques. Private recreation sites are not in-
cluded in the estimates, but second home tracts located within U.S.
Forest boundaries are Included.

The influx of nonresidents into Northern California is a seasonal
phenomenon. According to some health planning authorities [Northern
California Emergency Medical Care Council, personal interview, 1970], the
concentration of nonresidents in Northern California during the summer

months is the critical problem confronting the EMS system. Fortunately,
many of the data sources report recreation use by month as well as by
site. One source, the U.S. Forest Service, however, does not report
monthly use data and, therefore, several assumptions were made about the
seasonal recreation use of forest land. The methods used to estimate
monthly recreation use are described in Appendix C.

Recreation use statistics are commonly quoted in terms of visitor-
days. The U.S. Forest Service defines a visitor-day as one person present
at a site for 12 hours or conversely 12 persons present at one site for
one hour or any combination of people and hours which equals 12. Hence,
visitor-days combine a time dimension with a pure count dimension. The
visitor-day concept is used throughout the study. Furthermore, the re-
sident population was put on a time basis, called resident-days, making
addition with the nonresident population possible. To avoid double
counting, use of recreation sites by the local population was also
taken into account (see Appendix C) .

U.S. Forest Service Data . The federal government owns over one-third of
the land in the study area and the majority of the federally- owned land
is administered by the U.S. Forest Service. The study area includes
parts of the Lassen, Mendocino, Shasta, Six Rivers, Trinity, and Plumas
National Forests. The Forest Service (1972) records recreation use by
various geographical delineations such as counties, forests, and ranger
districts (R.D.). The ranger districts are the smallest areas within a
National Forest for which visitor-day data are available. In a rather
arbitrary manner, the visitor-days are associated with a particular

ranger district. Although this is a gross assumption, no other data are
available to more rationally locate the people involved in outdoor
recreation activities. In some instances, the visitor-days for a par-
ticular ranger district are divided between two or three demand points
due to the proximity of a ranger district to several demand points
(see Appendix Table C-2) . Appendix Table C-5 presents the total number
of visitor-days present at each demand point during 1972. The same table
also presents estimates of monthly recreation use for demand points
located within or near the U.S. Forests. Although specific data are not
available by month, U.S. Forest personnel are aware of the peak usage
months during the year [personal interview, 1974]. In general, recreation
use in the U.S. Forests is minimal during the winter months, with activity
slowly increasing to Memorial Day. Recreation use then normally declines
slightly until a few days before July A. Peak usage occurs between
July 4 and Labor Day. Usage then gradually declines until October 1,
when activity again becomes minimal. This pattern changes for certain
forested areas where skiing and big game hunting account for a significant
amount of the recreation use.

Another component of the nonresident population at risk at any
demand point is the transient population which only passes through a
demand point but does not live there or visit a recreation site. Ob-
viously the transient population is more evident on the major transpor-
tation routes through the study area, such as Interstate 5. An examina-
tion of data in Appendix C, however. Indicates that during the summer
months, transient population Increases significantly on several of the

smaller state highways which pass through the study area. Estimates of
the transient population were made from traffic flow data (see Appendix
C) . A conversion factor of 2.4 persons per vehicle, while not well-
substantiated, is considered an appropriate measure and is used by
transportation agencies for planning purposes (California Department of
Transportation, personal interview, 1974).

Details of the seasonal pattern of demand are given in Appendix C
(see especially Table C-3) . Given the assumptions used in allocating non-
residents to specific demand points, several of these demand points experi-
ence significant fluctuations in population during the year. One criterion
to use in identifying the demand points with greatest variation in popula-
tion is the comparison of resident-days with the total population-days
during the month of peak nonresident influx. August is generally the peak
influx month. Appendix Table C-3 indicates that approximately 20 demand
points have very large increases in nonresident population during August.
The following demand points exhibit a ratio of total population-days to
resident-days greater than 1.5:

Butte County Shasta County Tehama County Trinity County

Butte Meadows
Feather Falls
Yankee Hill

Lakehead
Platina
Whiskeytown
Old Station
Castella

Paskenta
Mineral

Big Bar
Burnt Ranch
Junction City
Lewiston
Trinity Center
Weaverville

The outlying demand points of Butte County are Influenced by the
visitors to the Lassen and Plumas National Forests. The nonresident
Influx into Shasta County is Influenced by the Shasta National Recreation

Area, Whiskeytown National Park, Trinity National Forest and Lassen
National Forest. Tehama County experiences an influx of visitors near
Mineral because of Lassen National Park and Lassen National Forest, while
in the vicinity of Paskenta, the Trinity and Mendocino National Forests
attract a relatively large number of recreationists. Trinity County has
several small communities scattered throughout the Trinity National
Forest. With the influx of transients into the forests during the summer
months, residents comprise a relatively small part of the total popula-
tion at some of the demand points.

The problem of a large influx of a recreation population appears to
affect nearly all demand points to some degree. The implication for EMS
is two-fold. First, many of the smaller communities are not currently
served by any organized form of emergency medical care. Second,
smaller communities exhibit a relatively small demand during a large part
of the year, but during the summer season, demand for EMS may exceed
the EMS resources which are available. The larger conmunities in the
study area also experience an increase in demand for EMS during the
summer months. Most of these demand points, however, already have
existing EMS providers; and, therefore, the problem is one of absorbing
increased demand. Apparently this is accomplished through longer service
and response time or these providers may have excess capacity during
the remainder of the year.

The data from Appendix Table C-3 are used to derive demand estimates
for EMS which include the usage by the nonresidents in the study area.
One problem, of course, is the aforementioned differences among data

sources. Another Is that of an aggregation-type problem. The assumption
used In Appendix Table C-3 was that three populations — residents,
visitors, and transients — can be combined into one population which
collectively expresses demand for EMS.

Estimate of EMS Usage Per 1.000 Population-Days
Appropriate data were not available to estimate accurately the
relation between hospital service area population-days and ambulance
calls. (Ambulance use data are by county for 1968, while population-days
estimates are available by hospital service area for 1972.) As a crude
estimate of this relation, however, one could assume that the ratio of
ambulance calls per resident to hospital emergency room visits per
resident is equal to the ratio of ambulance calls per population-day to
hospital emergency room visits per popul at ion-day .^^ For example,

y Data for point estimates (using ordinary least squares [OLS]
without a constant) of the following ratios were available: (1) hospital
emergency room visits per 1,000 resident population (r^^) ; (2) hospital

emergency room visits per 1,000 population-days (r2); and (3) ambulance

calls per 1,000 residents (r^) . (See Chapter 5 of Daberkow [1976] for

a derivation of the above regression coefficients.) Making the necessary
assumptions about the stability of the ratios over time (due to different
years used in calculating the ratios), the following proportion was
hypothesized:

^3 X

— = — where X = ambulance calls per 1,000 population-days.
1 ^2

In other words, the relation assumes that the ratio of the number of
ambulance calls per 1,000 population-days to hospital emergency room
visits per 1,000 population-days is equal to the ratio of the number of
ambulance calls per 1,000 residents to hospital emergency room visits
per 1,000 residents. Note that r^, r^, and r^ were estimated using

ordinary least squares and were significant at the .05 level. Since r^

is an estimate of R (population parameter), then r is a random variable

with a distribution having mean R and variance a . Therefore, X =

2 3 also has a distribution but it is unknown and, therefore, no statis-
'^l

tical tests of significance can be made.

29.5 ambulance calls/1,000 population
252 emergency room visits/1,000 population

X ambulance calls/1,000 populatlon-days

0.372 emergency room visits/1,000 population-davs

This calculation gives an estimated .0435 ambulance calls per 1,000
population-days. This value was multiplied by the estimated nimber of
population-days at each demand point during the peak recreation month o^
August to derive EMS demand estimates.

The location algorithm requires point estimates of the demand for
ambulance calls at each demand point. Annual EMS demand of 29.5 ambu-
lance calls per 1,000 residents was taken from Table 7, while .0A35
ambulance calls per 1,000 population-days was chosen to represent the
peak month demand (August). Table 11 presents the expected EMS demand
(in total ambulance calls) for each demand point. The regional ponula-
tion was estimated to generate 7,163 calls throughout the year (244,062
residents times 29.5 calls per 1,000 population). Nonresidents generate
additional calls during certain months of the year due to the summer
recreation opportunities available in the area. Residents plus non-
residents generate 666 calls for the entire region during the month of
August (16,061,200 population-days times .0435 calls per 1,000 population-
days). Both the annual demand and peak month demand estimates were
truncated rather than rounded.

V. LOCATION OF FACILITIES

Currently, there are 15 locations serving the EMS demands of the
area. Here, the existing system is compared with optimal locations for

TABLE 11 — Location and Number ol Lxpected LMS Calls by Demand Point

Demand Expected annual Expected peak Demand Expected annual Expected peak.

poitit: demand month demand point demand month demand

1185

105

230

621

155

430

198

T 7

177

417

338

2t
3

207

801

71
/ X

141

1 7

191

1 7

1
X

a
o

427

1
X

■J

Source: See Appendix B and C.

given levels of demand and response and service time standards, T'lmnhasls
Is given to the trade-off In (a) total costs and (b) percentage of
population served as the response time standard Is Increased from 13
minutes (a standard often promulgated for an urban area by health planners)
to 67 minutes.—^ The latter Is considered an upper limit to effective
response time.

Response Time Standards - Resident Population

Given the existing system with 15 EMS facilities and a 13-mlnute

response time, 42 of the 72 demand points cannot be served.— These 42
points represent about 25 percent of the population of the entire area.
As the time standard Is relaxed by Increments of approxlmatelv 13 minutes,
the number of sites needed Is reduced until at a 67-mlnute response time
the number of sites could be reduced from the existing 15 to only 8.
Then the entire population xrauld be served at a cost of about 57 percent
of that for the simulated 13-mlnute situation. Results for these and
other response times are shown in the bottom half of Table 12 for the
present system.

A more detailed listing of demand points served with the present
location pattern of EMS facilities is given in Table 13. The 15 sites

1/ The response times were selected to correspond to the time an
ambulance traveling an average of 45 miles per hour would require to
travel 10, 20, 30, 40, and 50 miles, respectively.

11 The algorithm requires that all demand points be served within
at least 67 minutes. When a smaller response time is Imposed, not all
demand points can be reached within that time. Of course, all demand
points could be served within a piven time standard if an EMS facility
could be established at each demand point. However, this was assumed
to be fiscally infeaslble and, therefore, only 32 of the demand points
were allowed to be potential facility sites.

TABLE 12 — Response Time Standards: Comparison of Selected
Parameters for the Optimal and Present Location
Patterns of EMS Facilities (Annual Demand)

Response

Percentage

time

Total

Demand

of total

standard

Number of

annual

points not

population

(in minutes)

facilities

cost

served

no.

mil. $

no.

pet.

-Optimal System-

2.24

86.2

1.62

97.7

1.13

99.8

0.71

100.0

0.64

100.0

-Present System-

1.13

75.1

1.06

95.5

0.92

98.4

0.71

100.0

0.64

100.0

TABLE 13 — Present Location of EMS Facilities as Possible Sites: Results for Selected
Response Times (Based on Annual Demand Estimates)

Present
EMS fa-
cility
sites

Demand points served by each potential facility site for selected response times

13 minutes

27 minutes

40 minutes 53 minutes

67 minutes

^ . . No.
Demand point ,
... of pa-
mdices ^, ^
tients

^ . No-
Demand point .
... of pa-
indices

tients

J . No.
Demand point -
... of pa-
indices ^. ^
tients

J • ► No.
Demand point ^
. , . of pa-
indices

tients

No .

Demand point ,

■ of pa-
indices

tients

Chlco 5

Grldley 10
Oroville 12

Paradise 14
Elk Creek 21
Orland 24

Breber 26
Adin 27
Fall River Mills 34

Redding 45

Dunsmuir 50
Corning 52

Red Bluff 60

Hayfork 67
Weaverville 72

Total
annual

cost

4,5,6,9,11,15 1,397

3,10,19,22,51 498
1,2,7,8,12,13,16 834

14,17,18 478
21 32
20,23,24,25 446

26 26

27 19
30,34,37,41 160

28,29,33,35,36,38, 2,029

39,40,42,44,45,46,

47,48,49

31,50 99
52,54,57,61,62 347

32,53,55,56,58,59,60 593

43,66,67,68 69
63,64,65,69,70,71,72 136

4,5,6,9,11,15 1,397

3,10,19,22,51 498
1,2,7,8,12,13,16 834

14,17,18 478
21 32
20,23,24,25 446

26,27 45

30,34,37,41 160

28,29,33,35,36, 2,029

38,39,40,42,44,

45,46,47,48,49

31,50 99

52,54,57,61,62 347

32,53,55,56,58, 593
59,60

43,66,67,68 69
63,64,65,69,70, 136
71,72

4,5,6,9,11,15, 1,491
22,23

1,2,3,7,8,10,12, 1,296
13,16,19,51

14,17,18 478
21,25 209

26,27 45

30,34,37,41 160

28,29,33,35,36, 2,029

38,39,40,42,44,

45,46,47,48,49

31,50 99

20.24.52.54.57, 558
61,62

32.53.55.56.58, 593
59,60

43,66,67,68 69
63,64,65,69,70, 136
71,72

4,5,6,9,11,14, 1.899
15,17,62

1,2,3,7,8,10,12, 1,305
13,16,18,19,51

20,21,22,23,24, 722
25,52,57

26,27,30,34,37, 205
41

28,29,33,35,36, 2,029

38,39,40,42,44,

45,46,47,48,49

31,50 99

32,53,54,55,56, 699
58,59,60,61

43,66,67,68 69
63,64,65,69,70, 136
71,72

1,2,3,4,5,6,7,8,9, 3,204

10,11,12,13,14,15,

16.17.18,19,51,62

20,21,22,23,24,25, 732
52,57

26,27,30,34,37,41 205

28,29,33,35,36,38, 2,209

39,40,42,44,45,46,

47,48,49

31,52 99

32,53,54,55,56,58, 699
59,60,61

43,66,67,68 69
63,64,65,69,70,71, 136
72

$1,125,380

$1,055,403

$916,456

$707,178

$641,04 7

Total

annual 7,163
patients

7,163

bemand 1,2,4,7,8,9,11,15,16,17,18,
points 19,22,23,25,28,29,30,32,35,
meeting 36,38,39,40,41,42,43,46,48,
the time 49,54,55,56,57,58,62,63,64,
constraint 66, 68, 70, 71

4,7,8,19,22,36,39,40,
41,43,46,49,55,56,57,
58,63,64,66,68,71

4,39,41,43,46,49,55,
56,64

In existence when the study was undertaken are listed in the first column
of the table. With a 13-minute response time, 42 sites are not served
within the stated time constraint. These points are listed in the last
row of Table 13. Vfhen the response time standard is increased, locations
not served within the required time, of course, decrease, and the number
of facilities needed also decreases. Fipure 6 f»ives the present system
solution for a 13-minute response time standard with areas to be served
encirclinf* the blocked location site.

An optimal location of facilities under these same response time
standards and demand conditions is also given in Table 12. To meet the
13-minute standard, EMS facilities would have to be located at 31 of
the 32 potential sites (see Table 12). However, 22 demand points still
would not be served under this time constraint, or about lA percent of
the area population. One should note that in order to serve 100 percent
of the population within 13 minutes, more than 32 facility sites are
required. The location of sites is piven in Table 14.

The trade-off between response time standards and system cost is
shown in Figure 7 where costs drop sharply as the number of facilities
decreases and response time increases. The percentage of the population
served, however, increases as response time increases. For a 13-
minute response, 86 percent of the population is served, but for a 27-
minute response time and location of 22 facilities, about 98 percent of
the population is served. The location pattern of EMS facilities and
demand points served by those facilities for the 40-minute response time
is given in Figure 8.

Figure 6 Facilities and Demand Points associated with those facilities using the 13 minute response
time standard (present system servicing annual demand)

TABLE 14— Optlul Lootlon of DIS Facilities: Keaulta for Selected
Responae Tlaea (laaed on Annual Deaand Eatlaatea)

tlal
altes

13 Blnutes

Band points served
27 Blnute

by each
s

potential facllit
40 Blnute

y site
s

or selected respon
53 Blnute

se tloies
s

67 ailniirtfa

Deaand point
indices

No.

of pa-
tient a

Deasnd point
Indices

Mo.

of pa—
tienta

Denand point
indices

No.

of pa-
tients

Deaand point
Indices

No.

of pa-
tlenta

Demand point

No.

of pa-
tients

Biggs 3

3,16

Butte Meadows 4

6.9

Chico 5

5,6,9,15

1,371

5,6.9,11,15,23,

1,477

4,5,6,9,11,14,

1,899

Durban 6

15,17,62

Grldley 10

10,51

371

3,10,51

432

Orovllle 12

1,2,7,8,12,13

816

1,2,7,8,12,13,

834

1,2,3,7,8,10,12,

1,266

1,2,3,7,8,10,12,

1 305

1,2,3,7,8,10,12,

1 744

13,16,51

13 16 1R 19 SI

13,14,16,17,18.

Paradlae 14

14,17

469

14 ,17 , 18

478

5,6,14,15,17,18

1,841

Yankee Hill 18

Princeton 19

19,22

Elk Creek 21

Baallton City 23

11,23

5.6.9,11,15,19,

2,344

20,21,22,23,24,

25,52,53,54,57,

Orland 24

194

20.21 22 33 7L

895

59.61.62

25,52,53,54,57,

Willows 25
Bieber 26

20,25

194
26

19,20,22,24,25,
26,27

454
45

19,20,21,22,25,
26,27,34,37

292
109

59 61

Adin 27

Bella Vlata 29

29,38,39,40,42,46,49

159

29.38,39,40,42,

180

26,29,33,35 38

2 012

9lt 90 19 11 IC

2,526

46,49

39,40,42.44145!

38,39,40.42,44,

46.47,48,49

45.46.47,48,49,

Pall River Hills 34
Old Station 41

30,34,37
41

141
19

30,34,37
41

141
19

55,60

26 27 30 34 37 A1

205

26.27,30.34,37,41

205

Platlna 43

Bedding 45

28,33,35,36,44,45,47

1,844

28,33,35,36,44,

1,870

28,29.32,33,35,36,

3,543

45,47,48

38,39,40,42,44.45,

Wilakey Tom 48

46,47.48,49.55,60

Dunsmiir 50

Coming 52

31,50

99
191

31,50

31,36,50
11,23.24,52,54,

116

614

31.36,50

116

31,50

Los Hollnoa 54

53,54,59,61,62

206

57,61,62

Mineral 56
Paskenta 57

56,58

12
17

56,58

4.36,58

Red Bluff 60

32,55,60

514

32,52,53,54,55,

857

32,53,55,59,60

581

Burnt Ranch 64
Porest Glen 66
Hayfork 67
Trinity Center 71

59,60,61

63,64
66

67,68
71

29
6

60
8

63,64
66

67,68

29
6
60

63,64
43,66
67,68

29
9
60

43,66,67,68

Weavervllle 72

65,69,70,72

-65,69,70,71,72

107

63,64,65,69,70

136

63,64.65.69,70,

136

71,72

Total

annual

(2,244,319

region-

$1,615,298

81,128,816

$709,262

$639,678

al cost

Total calla

7,163

Deaand

polota

1,2,7,8,9,15,17,28,30

.32,

7,8,36,39,40,46,47

.49,

not

35,36,38,39,40,46,49.

55,

55,58,68

■eetlng

58,63,68,70

the ti>e

constraint

•

'Since potential facility sites do not exist at all demand points, seversl deaand points cannot be aerved within the tlae constraint. In
tbeae caaea, the deaand pointa are served by the closest potential facility alte.

Figure 7 Relation Between Response Time, Total Regional Cost, and Percentage
of Population Served Within Various Response Times (optimal system)

$2.4

2.0

1.6

1.2

— ' —

/ Percent

1 1 M i

/ V Cost

•

1 I 1 I 1 1

100

13 27 40 53

Response Time in Minutes

e
o

80 »

Figure 8 Facilities and Demand Points associated with those facilities using the 40 minute response time
standard (optimal system)

The standards promulgated in the 1974 California State Plan for
EMS suggest that 90 percent of the population for low density areas
should be within 30 minutes of an EMS facility. The 27-minute response
time standard meets this criterion. The total cost of this system is
$1.6 million.

Response Time Standards - Peak Month Demand
The peak nonresident demand occurs during the summer months, particu-
larly in August. If the goal of the EbiS system is to locate permanent
facilities to meet the peak month demand of residents and nonresidents
at minimum cost, the analysis must be modified. The approach was to
estimate the number of population-days for nonresident population asso-
ciated with the various demand points based on estimated traffic flows
and visits to parks and forests as given in the previous section. Demand
for EMS was assumed to be a function of the number of population-days at
each demand point.

The overall location of facilities did not change substantially
from that given previously; however, the pattern changed for some of the
points. For example, under the 40-minute response constraint. Forest
Glen served Platina on an annual demand basis. Using peak month demand,
however, it is more efficient for Platina to have its own facility with
Hayfork serving Forest Glen. The annual costs were slightly higher due
to travel costs for more patients. Also, there were slight reductions
in the percentage of population served within given response time stan-
dards due to the use of remote recreation areas by nonresidents. The

current location of sites is given in Table 15; the optimal location, in
Table 16.

Service Time Standards
Service time is defined as the total time between notification of
an accident and delivery of the patient to the nearest hospital. Service
standards were arbitrarily set at twice the corresponding response time
standards to evaluate the trade-off between costs and service time. The
general results X\'ere similar to those presented for response time. There
were a few differences, however, in the location of facilities for the service

and response time standards. Given locations of hospitals, the service
time model locates EMS facilities so as to minimize backtracking. Figure
6 indicates the location (number in parentheses) of the following study
area hospitals: Chlco (5), Paradise (lA), Oroville (12), Gridley (10),
Fillows (25), Redding (45), Fall River Mills (34), Red Bluff (60),
Corning (52), and Weaverville (72).

VI. FINANCIAL ANALYSIS OF EMS FACILITIES AND FUNDING ALTERNATIVES

This section is concerned with the economic viability of the EMS
facilities vjhich entered the optimal solutions. The 40-minute and 27-
minute response time spatial patterns are examined in detail to show the
costs and revenues for each EMS facility which entered the optimal solutions.
Although other response times could have been analyzed, the 40-minute and
27-minute response times seemed most appropriate for a semlrural area.
The 27-minute standard most nearly approximates the 30-minute standard

Table 15 — Present Location of EMS Facilities as Possible Sites: Results for
Selected Response Times (Based on Peak Month Demand)

13 minutes

Demand points served by each

Demand point
indices

No.

of pa-
tients

27 minutes

potential facility site for selected response times

Demand point
Indices

No.

of pa-
tients

40 minutes

Demand point
Indices

No.

of pa-
tients

53 minutes

Demand point

J jj of pa-

indices .

tlents

67 minutes

Demand point
Indices

No.

of pa-
tients

Total
cost

4,5,6,9,11,15 123

3,10,19,22,51 42

1,2,7,8,12,13,16 76

14,17,18 42

21 3

20,23,24,25 39

26 2

27 1
30,34,37,41 17
28,29,33,35,36,38, 198
39,40,42,44,45,46,
47,48,49

31,50 9

52,54,57,61,62 31

32,53,55,56,58,59,60 60

43,66,67,68 7

63,64,65,69,70,71,72 16

$1,134,852

4,5,6,9,11,15 123

3,10,19,22,51 42

1,2,7,8,12,13,16 76

14,17,18 42

21 3

20,23,24,25 39

26,27 3

30,34,37,41 17

28,29,33,35,36,38, 198
39.40,42,44,45,46,
47,48,49

31.50 9

52,54,57,61,62 31

32,53,55,56,58,59, 60
60

43,66,67,68 7

63,64,65,69,70,71 16

$1,064,864

4,5,6,9,11,15, 131

22,23

1,2,3,7.8,10,12, 115
13,16,19,51

14,17,18 42

21,25 19

26,27 3

30,34.37.41 17

28.29,33,35,36, 198

38,39,40,42.44.

45.46.47,48.49

31,50 9

20.24.52.54.57, 49
61,62

32.53.55.56.58, 60
59,60

43,66,67,68 7
63.64.65.69,70, 16
71,72

4,5,6,9,11,14,15,
17,62

167

$925,952

1,2,3,7,8,10,12,13, 116
16,18,19,51

20,21,22,23,24,25, 64
52,57

26,27,30,34,37,41 20
28,29,33,35,36,38, 198
39,40,42,44,45,46,
47,48.49

31.50 9

32.53,54,55,56, 69
58,59,60,61

43,66,67,68 7
63,64,65,69,70, 16
71,72

$716,712

1,2,3,4,5,6,7,8,9, 283

10,11,12,13,14,15,

16,17,18,19,51,62

20,21.22,23,24,25, 64
52,57

26,27,30,34,37,41 20
28,29,33,35,36,38, 198
39,40,42,44,45,46,
47,48,49

31.50 9

32,53,54,55,56,58, 69
59.60.61

43.66,67,68 7
63,64,65,69,70,71, 16

$649,652

Total
month

peak
patients

666

NOTE: See Table 13 for indices of demand points which do not meet the time constraint.

TABLE 16 — Optimal Location of EMS Facilities: Results for Selected
Response Times (Based on Peak Month Demand)

Poten-
tial
site
indices

13 minutes

Demand points served by each potential facility site for selected response times

Demand point
indices

No.

of pa-
tients

27 minutes

Demand point
Indices

No.

of pa-
tients

40 minutes

Demand point
indices

No.

of pa
tients

53 minutes

Demand point
indices

No.

of pa-
tients

67 minutes

Demand point
Indices

No.

of pa-
tients

3,16

5.6,9,15

6
1

121

10,51

1,2,7.8.12,13

14,17

19,22

11,23

20,25

29,38,39,40.42,46,49

30,34,37 14

41 3

43 1

28,33,35,36.44,45,47 176

48 9

31.50 9

52 17

53,54,59,61,62 17

56.58 9

57 2

32,55,60 46

63.64 3

66 1

67,68 5

71 1

65,69,70.72 12

5.6.9.11.15.23.
62

3.10.51

1.2,7,8,12,13,16

14,17,18

19,20,22,24.25
26,27

29,38,39,40.42.
46,49

30,34,37

28,33,35.36.44,
45,47.48

31.50

56,58
57

32,52.53,54.55.

59.60,61

63,64

67.68
71

65.69,70.72

130

37
76

39
3

14
3
1

185

9
2
76

3
1
5
1
12

4,9

1,2.3.7,8,10,12,

13.16.51

5,6,14,15,17.18

19.20.21.22,25
26,27.34.37

28,29,33,35,38,
39,40,42,44.45,
46.47.48.49

30,41
43

31,36,50

11.23.24,52,54.

57.61.62

56,58

32.53,55,59,60
63,64
66,67.68
65.69.70,71,72

113
162

25
8

189

12
1

18
54

9
51
3
6
13

4,5,6,9,11,14,15, 167
17,62

1,2,3,7,8,10,12, 116
13,16,18,19,51

20,21,22,23,24,25, 78
52,53,54,57,59.61

28,29,32,33,35,38.
39,40,42,44,45,46,
47,48,49.55,60
26,27,30,34,37.41

31,36,50

56,58

43,66,67,68

63,64,65,69,70,71,
72

235

7
16

1,2.3.4,5,6,7.8, 288
9.10,11,12,13,14.
15,16,17.18.19,22,
23,51

26,27,30,34.37.41

28,39,33,35,36,38, 198

39,40,42,44,45,46,

47,48.49

31,50 9
20,21,24,25,52,54, 68
57,61,62

32.53,55,56.58. 60
59,60

43.66,67,68 7

63,64.65,69.70. 16
71,72

$2,253,148

$1,624,252

$1,138,102

$718,620

$649,412

Total calls during August

666

promulgated by health planning agencies. The initial discussion pertains
to the present revenue structure for EMS purveyors in Northern California.
Belated to this topic is the rate of noncollectible charges experienced
by ambulance operators. In addition, the procedure for calculating EMS
facility costs and revenues is made explicit.

Revenue Structure

Conversations with health planning officials (Northern California
Emergency Medical Care Council and Superior California Comprehensive
Health Association) indicated that private ambulance operators in the study
area commonly charge a basic rate per call, a mileage rate, and a charge
for use of incidentals (e.g., linens, bandages, oxygen, splints, resusci-
tator, etc.) (According to the 1968 Arnhulanoe Survey [California Depart-
ment of Transportation, 1970], some ambulance purveyors also charge extra
for night calls and emergency calls [p. 137].) The basic charge per call
is $A5 plus $2 per mile transport charge. The charge for supplies is
highly variable, depending on the circumstances of the medical emergency.
For purposes of this study, the charge for supplies was assumed to be $10
per call based on conversations with area ambulance providers. The
transport charge was assumed to be $2 per mile where the total transport
mileage consisted of the distance from the demand point to the nearest
hospital. The set of demand points served by each hospital is given in
Appendix B. No distinction is made between patient transfers (i.e.,
hospital to hospital or hospital to other points) and emergency calls.

The 1968 Ambulance Survey (California Department of Transportation,
1970) as well as the study area's health planning personnel reported that

the collection rate, particularly from individuals without health in-
surance or those not qualifying for Medicare or Medi-Cal, is much less
than 100 percent. According to the survey, 14 percent of rural ambulance
services collected less tlian half of their charges, 35 percent collected
between 50 and 74 percent, 43 percent collected between 75 and P>9 percent
and 4 percent collected 90 to 100 percent of their charges (p. 132),
Insurance companies and the Medicare and Medi-Cal agencies often times
pay only a certain percent of a bill submitted by an ambulance purveyor.
Based on the above, it is assumed that the total charge is collected from
80 percent of the calls. No provision is made for dry runs, although
adjustments in the cost estimates could be made to allow for such occur-
rences.

Table 17 indicates several financial measures which can be used to
evaluate the economic viability of the EMS facilities optimally located
to serve the region's annual demand within a 40-minute response time.
Table 18 reports the same numbers for the 27-minute response time. The
wide variation in costs and revenues among the various facilities is
obviously due to the large difference in total number of calls serviced
by each EMS facility. The facilities which served the largest number of
calls for either response time standard had the lowest cost per call.
Oroville, Paradise, Chico, Redding, Willows, Gridley, Corning, and
Red Bluff were in this category. The remaining facilities had very high
costs per call due to the extremely low number of calls serviced per
year. The highest revenue per call is generated in the more remote areas
such as Elk Creek, Hayfork, Burnt Ranch, Forest Glen, Mineral, Old

TABLE 17 — Financial Analysis of the 15 Facilities Entering Optimal Program
with 40-Minute Response Time (Annual Demand Model)

Volunteer facility for

Fully-staffed

facility (24 hours per day)

< 400 calls

per year

r aClJ-Xty

Total

Cost/

Revenue/

Cost per

resident

Cost per

resident

site

calls

call

Average

Net

Average

Net

no.

dollars

A5 Redding -

2,012

1.36

-0.23

14 Paradise -

1,841

1.45

0.05

12 Oroville -

1,266

1.94

0.51

52 Coming -

614

125

3.66

1.94

60 Red Bluff -

581

129

3.79

2.31

25 Willows

292

250

7.34

5.77

.82

0.06

50 Dunsmulr —

116

614

17.88

16.02

1.79

0.75

26 Bieber -

109

654

19.15

17.28

1.94

0.89

72 Weaverville —

107

655

19.09

17.38

1.91

1.01

41 Old Station

741

21.67

19.39

2.19

0.72

67 Hayfork -

1,177

102

34.54

31.56

3.35

1.18

64 Burnt Ranch

2,424

69.00

66.21

6.54

4.55

4 Butte Meadows

3,695

107.02

104.40

10.08

8.27

56 Mineral

5,845

153.81

151.60

14.43

12.95

66 Forest Glen

7,789

121

204.97

201.79

19.16

16.72

Study Area

7,163

158

4.63

3.06

2.01

0.54

&j Indicates cities which currently either have commercial or volunteer ambulance services.

W Facilities with greater than 400 calls per year where costs equal those shown in columns to the left.

TABLE 18 — Financial Analysis of the 22 Facilities Entering the Optimal Solution
with a 27 Minute Response Time Standard {Based on the Annual Demand
Model)

Volunteer facility for

Fully-staffed facility (24 hours per day) < 400 calls per year

Facility Total Cost/ Revenue/ Cost per resident Cost per resident

site calls call call Average Net Average Net

no ■ dollars

45 Redding

1,870

D J

1.41

-0.14

itii

5 Chlco

1,477

. 70

0.27

ItH

60 Red Bluff

878

.62

itii

12 Oroville

834

.34

1t4c

Itit

14 Paradise

478

157

Aft

Itit

25 Willows

454

x«>

J /

l^lt

10 Gridley

432

itit

29 Bella Vista

159

4S8

1.55

0.11

34 Fall River Mills 141

508

1.53

0.55

50 Dunsmulr

717

2.07

1.14

72 Weaverville

718

2.06

1.22

67 Hayfork

1,177

101

3.35

1.18

26 Bleber

1,566

4.41

2.67

21 Elk Creek

2,198

6.12

4.57

64 Burnt Ranch

2,424

6.54

4.55

41 Old Station

3,694

100

107

104

10.13

8.03

57 Paskenta

4,128

115

113

10.89

9.36

56 Mineral

5,845

153.81

151

14.43

12.95

4 Butte Meadows

6,374

103

185

182.48

17.34

15.16

71 Trinity Center

8,760

245

242

22.87

21.12

66 Forest Glen

11,677

127

305.94

302

28.52

25.92

43 Platina

3 •

23,343

108

619.74

616

57.66

55.53

Study Area

7.163

225

2.70

1.22

** Facilities with

greater than 400

calls per

year where

costs equal to those

shown in

the columns to

the left

Station, Platina, Trinity Center, Paskenta, and Butte Meadows. These
facilities generate larger revenues per call because of their distance
from a hospital; and, thus, the $2 per mile charge becomes significant.

Rather than attempting to cover all costs through patient payments,
two alternative funding mechanisms are presented in the fourth and fifth
columns of Tables 17 and 18. Should the local residents decide to support
a ?.A-hour per day EMS facility within a 40-minute or 27-minute response,
then these columns of Table 17 and 18, respectively, are relevant. As would
be expected, the facilities which serve the fewest number of people must
shoulder a much higher cost per resident. The residents served within
^0 minutes by Butte Meadows, Mineral, Forest Glen, and Burnt Ranch faci-
lities have particularly high burdens. Rutte Mcadov/s, Old Station, Platina,
Mineral, Paskenta, Forest Glen, and Trinity Center have very high per
unit costs under the 27 minute constraint. Obviously, such a high annual
per resident cost may prohibit the establishment of an EMS facility at
those points. If the total study area, however, decided to provide an
EMS system on a regional basis, the annual cost per regional resident
would be $A.63 in the first situation and $6.62 in the second. If the
present revenue structure were utilized (i.e., user fee collected), the
regional per resident cost would fall to $3.06 for the AO-minute standard
and $5.06 for the 27-minute standard.

Funding Alternatives for Low Volume EMS Facilities
Given the exceedingly high costs of sustaining an MS facility which
serves a low number of annual calls, it seems appropriate to discuss
several alternatives available to these facilities. Facilities may

employ one or more of the folloi^ing techniques to ensure economic via-
bility. The discussion is divided into two parts. The first part is
concerned with funding alternatives which will allow the maintenance of a
high quality EMS system as proposed in this study. The exact standards
of this 24-hour per day, 365 days per year system are given in Appendix
A. The second part of the discussion centers on alternatives which
involve reduction in the quality of EMS in the low demand areas of the
region.

Subsidy Schemes

The funding alternatives needed to maintain a high quality EMS system
revolve around a variety of direct subsidy schemes or indirect subsidies
which are designed to reduce competitive pressures. These subsidy
schemes can originate at the local, regional, state, or federal level.
At the local (i.e., area served by one facility) level, the city, county,
or regulatory body in charge of EMS can institute an indirect subsidy by
creating spatial monopolies for the EMS purveyor whether it be a privately
or publicly owned concern. Such an ordinance or regulation essentially
reduces or eliminates competition for ambulance calls. Thus, franchising,
exclusive contracts, and zoning allow EMS facilities to exploit more fully
the decreasing average costs exhibited by the facilities.

Direct subsidies at the local level can also take a variety of forms.
Local tax revenues can be used to reimburse the EMS purveyor for non-
collectible charges, dry runs, or indigent patients not covered by Medi-
care or Medi-Cal. These funds might be obtained by forming an EMS tax

district. Estimates for the size of the per call subsidy can be taken
from Tables 17 and 18.—''

If a regional EMS regulatory body (e.g., the Northern California
Emergency Medical Care Council or the Northern California Health Systems
Agency), regional funding measures might be applicable. In this case,
the regional operation of EMS facilities might be arranged similarly to
that of a cooperative. Questions of public or private ownership and
operation of the facilities would immediately arise. Perhaps the profits
of the economically viable operators might be used to assist the eco-
nomically depressed purveyors. An alternative might be a regional
(multi-county) taxing district to raise the necessary revenue. Tables 17
and 18 provide estimates of the per call subsidies needed for a regional
subsidy arrangement.

Subsidy measures which use state or federal tax funds represent a
fundamental shift in philosophy from previous funding schemes which
obtained revenue from EMS users or from local or regional tax sources.
State and federal tax funds are collected from residents but also from
nonresidents of the study areas. In other words, the user or Immediate

11 The use of prepaid EMS is another possibility. There are two
problems here: (a) the costs would be prohibitive unless funding is on
a regional basis and low density areas would be subsidized by high density
areas and (b) since EMS is rarely denied anyone in need of emergency care,
a "free rider" problem develops. One reviewer noted that demand may be
affected by this type of financial mechanism. The simultaneous nature
of demand, location, and type of pajmient is acknowledged, but the investi-
gation of such a system was beyond the scope of this study. This question
is also commonly debated with regard to the issue of national health insur-
ance.

potential user of the EMS facility does not fully pay the cost of the
service. The argument most often given by proponents of the out-of-region
subsidy, centers on the use of EMS facilities by nonresidents. Due to
the presence of a major highway and extensive recreational opportunities
in the study area, nonresidents constitute a large proportion of potential

users. Since nonresidents are rarely denied access to local EMS re-
sources, a case can be made for the state or federal governments helping
to shoulder the burden of funding EMS facilities. Funding mechanisms are
described below.

At the state level, at least one funding alternative is operational —
the state sales tax. Currently one percent of this tax is returned to the
governments of the cities and counties from which it was collected. The
returned money was collected from residents of the area as xrell as non-
residents passing through or temporarily staying in the area. The money
collected from nonresidents can conceivably be viewed as payment to the
local government for services rendered to the nonresident (e.g., streets,
roads, parks, police, and fire protection). The use of a portion of this
money for the support of an EMS system to be utilized by nonresidents as
well as residents seems appropriate.

Grants, either at the state or federal level, also offer funding
opportunities. Federal and state agencies, as well as some private founda-
tions, concerned with EMS have, in the past, been willing and able to pro-
vide equipment directly or funds with which to purchase ambulances, com-
munication equipment, etc. Regional Medical Programs, Robert Wood Johnson
Foundation, Cranston Funds (P.L. 93-154), and the California Office of

Traffic Safety are examples of organizations which have contributed to EMS
resources. The grantee, however, needs to be aware of the circumstances
surrounding the grant. Unless the grant is an annual stipend for an ex-
tended length of tim.e, the receiver can only use the stipend to offset
costs for a short period of time. This may be ideal if demand for EMS is
expected to grovr to levels sufficient to make the Ef^S facility economically
viable. Direct donations of EMS equipment are essentially annual grants
over the depreciated life of the equipment. At the end of that period,
another piece of equipment, or some similar subsidy must again be found.

Should none of the above funding measures be adequate to sustain EMS
at the quality level proposed in the analysis, quality might be reduced.
This reduction could range from the elimination of an E>!S to a modification
of the EMS system analyzed above. Modification could mean that small
isolated population clusters will be served by ms facilities outside the
specified response or service time applicable to the majority of the popu-
lation. Another alternative modification scheme is the establishment of
a volunteer emergency medical service. A volunteer system may not be as
well-trained or responsive as the system analyzed in this study. If a
governing agency (i.e., city, county or health planning board) is not
willing or is unable to fund an EMS facility, or if a private purveyor is
unable to operate economically, then a reduction in quality or even cessa-
tion of EMS is unavoidable.

Volunteer Systems

The last two columns of Tables 17 and 18 present projected costs for
a volunteer EMS system. Only facilities serving less than 400 calls a

year were considered candidates for a volunteer system. The annual fixed
cost estimate of $6,500 is based on the following assumptions: (1) no
labor overhead (no full-time drivers or attendants, or paid clerical staff);
(2) rent, phone, and utilities at one-half the cost of the full-time system;
and (3) insurance and depreciation at the same level as the full-time system.
Revenues generated are based on a $20 per call charge plus $2 per mile to
the nearest hospital with the collectible portion still at 80 percent.

The general conclusion from Tables 17 and 18 is that volunteer systems
are more attractive from a cost-per-resident standpoint as well as from the
cost-per-patient view. Facilities with annual usage of less than 50 calls
per year, however, are still faced with relatively large per unit and total
costs. In such low usage areas the only alternatives may be to rely on
V.KS facilities outside of the 40-minute or 27-minute response time boundary
or not provide W.S in any form.

VII. SIMIARY AlID CONCLUSIONS

Uses of the Model
The location analysis in this report utilized spatial EMS demand
estimates representing population clusters in the study area. Using
estimated annual cost of EMS facilities and transport costs, the location
algorithm determined the optimal (least-cost) size, number, and location
of EMS facilities. The location analysis was performed under varying
circumstances. Solutions were found for estimated annual demand and for
resident plus nonresident demand in the peak usage month. The above solu-
tions were constrained by two measures of effective EMS delivery: response

time and service time. The optimal solutions from the above analyses
were compared to the solutions which allowed only existing EMS facilities
to enter. In addition to the size, number and location of facilities, the
results provided total annual regional cost of the EMS system as well as
the demand points served by each facility.

Very little difference in location analysis results \<ras found between
annual demand based on per capita data and peak month demand based on
resident plus nonresident data. The Implication for health planners is
that the influx of nonresidents does not change the optimal location
pattern of EMS facilities found for the resident population. This does
not mean, however, that the nonresident influx problem disappears, for
even though EMS facilities are optimally (least-cost) located to serve
nonresident demand, individual facilities may experience periodic in-
creased need for their services. The Increase in demand is no problem if
the facility is underutilized during the remainder of the year, but if the
facility was operating at capacity then Increased service and/or response
times for all users— resident and nonresident — ^would result.

Two measures of EMS system effectiveness V7ere also evaluated: response
time (time from the notification of an emergency situation to the arrival
of an ambulance at the scene) and service time (time from the notification
of an emergency situation to the arrival of an ambulance at a given destina-
tion — usually the nearest hospital). The EMS facility location patterns
varied somewhat between the two measures. As would be expected, the
service time criterion, in general, located EMS facilities by proximity
to a hospital, while the response time locational pattern was influenced

primarily by the size and location of demand points. From a health
planner's point of view, the choice between the two measures should rest
on their respective influence on mortality and morbidity. A response time
measure accentuates the importance of an ambulance reaching the scene of
an emergency quickly and initiating treatment. Service time implies that
rapid transport to a nearby hospital is of critical importance.

Locational patterns also varied according to whether a large number
of potential facility sites were allowed to enter the solution (the
optimal system) or whether only the existing facility sites were allowed
to enter. The comparison of the existing spatial arrangement with the
optimal location pattern indicated a possible pattern toward which the
present system could adjust over time. Because of the large number of
facilities called for in the optimal solution, the system would be much
more costly to maintain than is the present system. Under the present
system, however, large numbers of people cannot be served within the various
time standards — particularly the 13- and 27-minute standards. Hence,
decision makers are faced x-rith the trade off between cost and people
served, vrithin the various time standards.

From the results of this study health planners can examine these
trade offs under the various response and service time standards proposed
for a regional EHS system. The standards can be set to match those of an
urban area (response time of 15 minutes or less) or can be lowered to a
response time of over an hour. As would be expected, as time standards
are weakened, costs fall.

The discussion highlights a critical aspect of EMS delivery — the
type of the region under consideration. A highly concentrated population
within a region requires fewer facilities than does a region with a
highly dispersed population, given the same time standards and sanie total
population. Suppose the standard for the State of California required
that 90 percent of the residents have EMS available within 30 minutes.
Such a standard is already met, since nearly all major and minor urban
areas have EMS facilities; but in rural or semirural areas (as in this
study) a very low percentage of the residents are currently within 30
minutes of EMS. The problem is one of efficiency versus equity: should
the state's limited EMS resources be distributed in a least-cost manner
or on an equitable basis to the total population? Establishing comparable
EMS for the remaining 10 percent of the state's population may be more
costly than the benefits derived therefrom in dollar terms, but such a
goal might be desirable from an equity or fairness goal.

Funding alternatives range from revenues generated entirely by
f ee-for-servlce to complete public funding through taxes or some other
subsidy form. All funding alternatives can be viewed from a local,
regional, state or federal level. The local analysis identified several
sparsely settled rural areas which generated very few ambulance calls per
year. Such areas could support a sophisticated, fast response RMS
facility only at a very high cost per patient or through high cost per
resident via taxes. Subsidies (including direct equipment donations)
through a regional EMS system, or from state or federal sources are poten-
tial sources of revenue for such areas. Several of the more densely

populated areas within the study area had EHS facilities which were
economically viable through user fees. Such facilities were able to
exploit the economies of size aspect of EMS production.

Sparsely settled rural areas which cannot generate revenues or sub-
sidles to support an EMS facility of the caliber suggested In this study
do have other alternatives. In the past, these areas have sacrificed some
quality in FKS service to reduce costs. Establishing a volunteer EMS
rather than a full-tine facility is an obvious way to reduce costs (and
possibly lose quality). Other communities, for various reasons, have not
established any EMS, but rely on distant EMS facilities or private autos
and accept the consequences.

Extensions of the Analysis
Several extensions and refinements to the basic model are possible.
The demand for EMS, which is proportional to population size in this model,
may be investigated further as better utilization data become available.
For example, it was assumed in this model that a serious accident or
acute illness generates a need for an ambulance irrespective of the price
of the medical and transport service. It is also plausible to expect
some price elasticity for EMS depending upon the degree of serious-
ness or acuteness. The demand for routine transfers (l.e,, hospital to
hospital, hospital to home, etc.) is likely to be very elastic or at
least related to the Insurance coverage of the patient. Public awareness
or education about the desirability and/or the availability of EMS also
plays an Important role in the usage of these services. Again, little

data are available concerning public awareness of EMS availability.
Uith the introduction of a "911" emergency telephone number, public aware-
ness may be enhanced.

Another problem with assessing demand lies with the supply of EMS.
The data show that up to 80 percent of the arrivals at a hospital emer-
gency room with "true" emergencies arrive in a private auto. Is this
due to a lack of immediate EMS resources or to ignorance on the part of
consumers or both? Is the public aware of the benefits of using a
trained EMS staff in conjunction with rapid transport instead of merely
using a private auto in a true emergency situation? If no EMS resources
are nearby, of course, then private auto is the only form of transport
available.

The influx of nonresidents into the study area during certain times
of the year poses an additional demand problem. Some rather admittedly
crude aggregations of visitation and traffic data sources were attempted.
Should better estimates become available, they can be incorporated readily
into the analysis. The impact of nonresidents on the EMS system should
not be taken lightly. Due to the increases in leisure time and incomes
the attraction of the many recreation sites in Northern California, the
influx of nonresidents into the area will continue to grow.

Once the facilities have been located, the question of capacity or
number of ambulances becomes paramount. This study is not specifically
concerned with this aspect of EMS planning. The answer to such a question
depends partially on the demand level and time period one considers. In
this study, the shortest time period analyzed was one month — the demand

level for the peak usage month. Shorter periods of time (a week, a weekend,
or even one hour) may exhibit high EMS demands. In providing for the
possibility of disaster, the health planner or EMS facility manager must
consider what length of peak demand period to plan for when deciding on
the number of ambulances. Queueing theory is the applicable technique
for such an extension of the analysis. The location model used here
essentially assumed that an ambulance was available at all times at each
potential facility site. Most study area EMS facility sites utilized a
very old, fully depreciated vehicle as a backup ambulance. Costs for
such a backup are minimal, but its usefulness in an emergency situation
may be questionable.

A valuable addition to the analysis would be that of dynamics or time
phasing of facilities. A time path accounting for projected spatial
demand would allow planners to move from the present location pattern of
facilities to one more nearly optimal at some future date. The uncertainty
of the location of demand and its intensity offers another challenge to
health planners. The systems approach to EMS planning, used in this study,
assumed that various subsystems such as public education, communications,
transport, manpower development, and disaster planning to be at a constant
level. Perhaps a simulation analysis would provide a more comprehensive
approach. An examination of the relations between each of various
components of the EMS system and the reduction in mortality and morbidity
would be very useful.

Throughout the analysis presented earlier, the location of EMS facil-
ities was assumed not to influence the demand or usage of EMS, If such

an assumption is unwarranted, v/hat is the interaction of E1>TS supply and
demand? Finally, the present study does not deal with the stability of
optimal location patterns with respect to changes in costs or in demand
over time. Sensitivity analysis could provide some answers in this area.

Forms of emergency transport other than the ground ambulance were not
considered in the analysis. Helicopters, airplanes, and water vehicles
can be alternatives to the ground based system in some areas. These
transport forms could be included in the analysis. Earlier studies
indicated that the cost of air transport forms tended to be prohibitive
(see Plaas et at. [1975]), In addition, inclement weather reduces the
effectiveness of air transport during certain times of the year. Water
transport systems are limited to specialized geographical areas for
obvious reasons.

The study also ignored secondary EMS resources such as the availability
of personnel and equipment from the U.S. Forest Service, California
Highway Patrol, and other governmental agencies located in the study
area. It was felt that EMS was not the main function of these agencies
but rather an occasional service rendered. Such assistance, therefore,
should not be included in planning an EMS system.

Conclusions

A primary purpose of the study was to minimize costs of EMS delivery,
given various objectives and standards suggested by the State Department
of Health. The study does show that several of these standards can be
met more efficiently through a spatial reallocation of facilities.

Setting goals or standards at some arbitrarily high level, no matter how
noble the goal, requires substantial financing. Prescribing standards
which are acceptable or common in urban areas may be prohibitively costly
to rural residents because of the low number of consumers, their widespread
spatial dispersion, and the inability of EMS to exploit economies of
scale in serving such a small number. In addition, rural area residents
tend to have lower incomes and may exhibit different tastes, preferences,
and attitudes about EMS than their urban counterparts.

Currently one finds that instead of an urban type EMS system in rural
areas, these areas have adopted EMS systems reflecting a choice of lower
personal and public expenditures. Hence, volunteer systems or long response
times are common in rural areas, and rural residents accept a higher
level of risk with regard to injury and death. It may be that other ser-
vices common in urban areas are also less sophisticated in rural areas.
Fire and police services, sanitation, medical care, transportation
services, communication, energy distribution, education and other social
services such as welfare, and city and county planning agencies may
reflect an area's lack of fiscal resources. Sources of financing for
such services must be viewed in a broader-than-local context including
state and federal tax structures. Recommendations on funding of a
particular service, such as EMS, would be presumptuous without analysis
of all demands on a rural economy. Whatever the major category of service-
delivery under consideration, however, if the goal is efficiency, then the
analysis should be on a broad enough regional basis to allow consideration
of locational reorganization.

The emphasis of this study is on the cost side of providing a regional
EMS system. From a societal viewpoint, the benefits or medical payoffs
(reduction of death, disability, and suffering) must be provided to
define the optimal level of EMS. At present, such data are not available.
Indeed, the impact of time-to-treatment on mortality and morbidity is a
much debated topic in medical circles. This study, however, provides
much of the needed framework and information for more rational decision
making.

8/28/79

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APPENDIX A

Ambulance Cost Estimates
The cost estimates derived on the following pages are based on data
and techniques from tvo sources: (1) Dunlop and Associates, Inc. [1968],
EoononrLcs of Highiiay Emergency Ambulanae Service ^ and (2) the California
/jnbulance Association [personal interview, 1975], Ambulance firm costs
differ because of manning variations in: the number of policies for
drivers and attendants; the combination of managerial, clerical and
dispatching personnel; employee fringe benefits; facility size and rent;
the type of complementary enterprises (e.g., medical supply, taxi services,
etc.); advertising and legal costs; the number of ambulances, and the
type of service area (square miles, size of population, roads, terrain,
etc.). In addition, some firms are able to take advantage of substantial
discounts on vehicles, supplies, and equipment, available T-jith bulk
purchases.

Dunlop and Associates [1968] estimated that approximately 85 percent
of total costs are fixed; the remainder, variable (i.e., on a per call
basis). Labor costs, which account for about 60 percent of the total
cost of private providers, are the single most expensive item. According
to Dunlop, government ambulance services tend to pay higher salaries than
do private providers, while the volunteer services obviously have very
small expenditures for labor. The labor cost per hour used in this study
is based on the 1974 minimum wage.

ALTE?JiATIVF BITDGETS

I. Driver/Attendant (D/A) — Annual wages under various manning policies
Assumptions :

1) 2A-hour service/day, 365 days/year; Ik hours x 365 days x 2
persons = man-hours required.

2) 2-person crev on call at all tines.

3) Emergency Medical Technician — I (EMT-I) training level.

A) Calculations are for one-manned ambulance — additional manned
ambulances are multiples of these calculations.

5) Average number of calls per unit time is constant over a 24-hour
period. This assumption could be modified to allow,

for example, for increased demand during daytime hours.)

6) A private provider. Government or volunteer services will
have different costs than the private purveyor especially
for labor costs.

MANITIKG POLICY A

Assumptions: 40 hours /week/man
No overtime

1 week paid vacation/year (AO hours)

1 week paid sick leave and downtime (vehicle repair) and

technical training/year
$2,00/hour wage (present minimum wage)

Calculations:

AO hours X 50 = 2,000 hours /year

^o'nnn man-hours required = 8.76 men required/year

2,000 hours x $2. 00 /hour = $A,000/year (salary)

80 hours X $2. 00 /hour = 160/year (vacation/sick leave)

$ A,160/year/man

$A,160/year/inan x 8,76 men = $36,AA2/year total wages for system.

MAIINIITG POLICY V,^ (Typical Situation)

Assumptions: On duty 24 hours — off duty 24 hours. (Average of 84 hours
on duty /week.)
$2.00/hour waf^e for 40 hours /week/man

$4.00/hour wage (txjice ninimum wage) for work in excess of
40 hours

Personnel receive 5 hours uninterrupted sleep and 2 hours
meal time; demand for ambulance service is sufficient to
provide an average of 17 hours of work during 24-hour duty
shift.''-

1 x-rcek paid vacation

1 week sic): leave and dovrntime.

Calculations:

P'4 hours/v7eek x 50 weeks = 4,200 hours on duty/year/man
'^4 ^'^00 '^^""^''"^s required = 4.17 men required/year

17 hours work/shift x 3.5 shif ts/x^eek = 59.5 hours work/week

2,000 hours/year $2.00/hour = $4,000/year (base) (40 hours/week

X 50 weeks)

975 hours/year P $4.00/hour = 3,900/3'ear (overtime) (19.5 hours/week

X 50 weeks)

P,n hours/year 0 S2.00/hour = lf,n (vacation/sick leave)

$3,n(S0/year/man

S8,0fi0/year/man x 4.17 men = $33,r.lO/year total wage for system.

MAnTiiTG POLICY P,^ (Minimum Situation)

Assumptions: Same as for T".^ except demand for emergency service provides

an average of only 13 hours work/24-hour shift (i.e., 8 hours
of uninterrupted sleep and 3 hours meal tine).*

Calculations:

84 hours/vTeek x 50 weeks = 4,200 hours on duty/year/man
"^^^200 ™n-hours required = 4.17 men required/year

13-hour work shift x 3.5 shifts/vjeek = 45.5 hours worked/week

2,000 hours/year H $2.00/hour = $4,000/year (base) (40 hours/week

X 50 weeks)

275 hours/year $4.00/hour = 1,100/year (overtime) (5.5 hours/week

X 50 x^eeks)

80 hours/year $2.00/hour = 160/y ear (vacatlon/slck leave)

$5, 260/year/man

$5,260/year/man :: 4.17 men = $21,934.

*See end of Manning Policies for explanation of asterisk.

MiANKING POLICY C^^ (California Typical Situation)

Assumptions: Eleven 24-hour on duty shif ts/2-ivreek period. (Average of 132
hours on duty/week.)
$2.10/hour wage for 40 hours A-Teek/man

$3.15/hour wape for hours in excess of 40 hours (1-1/2 times
base rate)

Demand is sufficient to provide 16 hours of work/24-hour shift.*
1 V7eek paid vacation/year

1 week paid sick leave and dovrntime and traininp/year.

Calculations:

132 hours /week x 50 weeks = 6,600 hours on duty /year/man
man-hours required = 2.65 men required/year

6,600

17 hours work/shift x 5.5 shifts/week = 93.5 hours work/week

2,000 hours/year g $2.10/hour = $ 4,200/year (base) (40 hours/week

X 50 weeks)

2,675 hours/year C $3.15/hour = 8,426/year (overtime) (53.5 hours/week

X 50 weeks)

80 hours/year @ $2.10/hour = 168/y ear (vacation /sick leave)

$12,794/year/man

$12,794/year/man x 2.65 men = $33,904/year total wages for system.
MiANNING POLICY (California Minimum Situation)

Assumptions: Same as C^^ except demand for emergency service provides an

average of only 13 hours work/24-hour shift.*
Employees are guaranteed 13 hours of work regardless of the
number of calls received.

Calculations :

132 hours/week x 50 weeks = 6,600 hours on duty/year/man

— ^^ ' 2 man-hours required = 2.65 men required/year
D,bUU

13 hours work/shift x 5.5 shifts/week = 71.5 hours work/week

2,000 hours/year @ $2.10/hour = $4,200/year (base) (40 hours/week

X 50 vreeks)

1,575 hours/year (? $3.15/hour = 4,961/year (overtime) (31.5 hours/week

X 50 weeks)

80 hours/year @ $2.10/hour = 168/y ear (vacation/sick leave)

$9,329/year/man

$9,329/year/man x 2.65 men = $24,722 total wages for system.

*See end of Manning Policies for explanation of asterisk.

*"nien personnel are hired to work a shift of at least 24 hours, minimum
wape and hour legislation exempts the employer from paying for three hours
legitimate eating and eight hours sleeping period provided the employees
have five hours uninterrupted sleep. Therefore, an employee could be paid
for a minimum of 13 hours or a maximum, of 21 hours for a 24-hour shift"
[p. 27, Dunlop and Associates, Inc.]

II. Support Personnel Wages — Dispatch, Clerical, Management

Assumptions: Dispatch employees can be utilizer! for some clerical work
at the one-ambulance level
$2.00/hour wage for dispatchers for 40 hour/week
1 week paid vacation
1 week paid sick leave
No overtime

24-hour/day x 365 days /year = .",,760 hours/year dispatch
Requirements for support personnel follov/ this relation:

8,760 hours + 2,000 (x-1) = Total Hours Required* where

X is the number of manned ambulances.

Calculations :

40 hours X 50 weeks/year = 2,000 hours /year /man

2'qqq man-hours required = 4.38 men required
One-manned ambulance cost:

2,000 hours/man/year x $2.00/hour = $4,000/man (salary)

80 hours/man/year x $2.00/hour = 160/m an (vacation/sick leave)

$4,160/ man/ year

4,160/year x 4.38 = $18,220 cost of support personnel for entire system.
Two-manned ambulance cost:

8,760 hours + 2,000 hours = 10,760 hours required

10,760 _ c oQ 4 J

2 QQQ =5.38 men required

2,000 hours/man/year x $2.00/hour = $4,000/man (salary)

80 hours /man/year x $2.00/hour = 160/m an (vacation/sick leave)

$4 , 160/man/year

$4,160/man/year x 5.38 men = $22,380 cost of system.

*This relationship is a compromise between the Dunlop and Associates rela-
tionship (e.g., total support hours required = 6,750(x) where x is the number
of ambulances) and the relationship suggested by data from the California
Ambulance Association.

III. Employee Benefits
Assumptions :

Unemployment Insurance (California)
Workman's Compensation (California)
Social Security Contribution (United
Medical and Hospital Insurance*

Percent of Gross Salary

D/A Clerical

3.60 3.60

8.00 .58

States) 5.85 5.85

5.00 5.00

22.45 15.03

*Dunlop and Associates, Inc., estimate.

IV. Vehicle and Equipment Depreciation
Assumptions :

Standard van-type ambulance
Equipment on ambulance**
Equipment at each location***

Price
?13,500
2,000
5,000

Capital Costs*
Average
Life

5 years

10 years

Salvage
Value

$3,375

500

*Estimates from the California Ambulance Association.

**List of equipment conforms to the legal requirements of the California
Highway Patrol and U.S. Department of Transportation, National Highway
Safety Administration, Vol. 11.

***Includes office, communication and personnel equipment (Dunlop and
Associates, Inc., p. 72).

Calculation:

Ambulance: $13,500-$3.375 ^ 10,125

5 5

Ambulance equipment: 2,000

Equipment : 5,000-500
10

= $2,025/year/ambulance

200/year /ambulance

450/year /location

100

V. Facility Operations and Maintenance

Assumptions: (From Dunlop and Associates, Inc., pp. 80-81)

Square footage required = 1,400 square feet + 500 square feet (x-1)

where x is the number of ambulances

Rent: $2.00/square foot/year

Utilities: 25 percent of rent

Maintenance and supplies: 30 percent of rent

Phone*: $1,235 /manned ambulance

*Dunlop's figure of $988/manned ambulance was increased 25 percent to allow
for inflation.

VI. Insurance

Basic liability/vehicle

Excess limits liability/vehicle

(500,000 limit)
Malpractice liability /manned ambulance

Business insurance (general liability
fire insurance, equipment & building)

(17 percent of $1,200 according to Dunlop)

CAA*

$1,200

204

Dunlop**

145
465

$1,404 /vehicle $714/vehicle

*California Ambulance Association estimates.
**Dunlop and Associates, Inc.

101

VII. Other Fixed Costs

Per ambulance

Dunlop*

Adjusted**

Advertising & promotion

680

850

Legal and accounting

400

500

Dues & subscriptions

Interest on capital investment

280

350 (850)

Licenses****

300

*Dunlop and Associates, Inc., estimates, p. 82.
**Dunlop estimates adjusted for inflation by a factor of 1.25.
**AAverage annual value of capital investment multiplied by 7 percent.
*A**License costs were estimated through personal interview. California
ambulances must have commercial tags; the cost is dependent on the weight
and age of the vehicle.

VIII. Variable Ambulance Costs (cost/call)

Items included are ambulance repair, maintenance, and other miscella-
neous costs.

Dunlop suggests an average figure of $2.25/call. California Ambulance
Association estimates this cost at approximately $5.00/call.

This estimate is obviously dependent on the mileage/ call as well as
terrain, roads, and climatic conditions, and therefore, this figure is
highly variable. A more precise estimate is a cost/mile figure. But such
an estimate is also highly variable. The figure of $4.00/call was used
primarily to reflect inflation and the high mileage/call in rural areas.

IX. Other Variable Costs (cost/call)

Items include ambulance supplies, linens, uniforms, laundry, postage,
stationery, and collection costs.

Dunlop estimated these charges as $0.41/call for uniforms and linens
and $0.37/call for postage and stationery plus 40 percent of the variable
ambulance costs of section VIII. Adjusting the per call figures for in-
flation (1.25 factor), gives approximately a new figure of $1.00/call for
postage and linens. The 40 percent estimate is not changed. CAA indicates
that collection costs average nearly $2.00/call.

102

Example #1: Cost/year of one-manned ambulance at one location*

Fixed Cost: Dollars

Driver and attendant wages 30,122

(Average of the 5 manning policies)

Support personnel 18,220
Benefits

D/A (22.45% X 30,122) 6,762

Support personnel (15.03% x 18,220) 2,738

Depreciation (vehicles and equipment) 2,675

Facilities

Rent ($2.00/square foot x 1400 square feet) 2,800

Utilities (25% x $2,800) 700

Maintenance and supplies (30% x $2,800) 840

Telephone 1,235

Insurance (liability, malpractice and general) 1,404

Other fixed cost (advertising, legal, etc.) 2,588

Total Fixed Cost 70,084

Variable Cost (cost/call) :

Ambulance repair, miscellaneous

Ambulance supplies, linens, uniforms, etc.

(40% x $5.00)
Postage, stationery
Collection costs

Total

$ 6.00/call

2.00/call
1.00/call
2.00 /call
$ 10.40/call**

*Costs will vary from firm to firm due to:

a) Manning policy for D/A,

b) Combination of management, clerical, and dispatch personnel,

c) Employee benefits,

d) Facility rent and maintenance,

e) The ambulance service area— size (square miles), population, roads,
terrain, etc., which affect over-the-road costs,

f) Size or number of capital purchases (e.g., discounts),

g) many ambulance providers operate complementary businesses, e.g.,
medical supplies.

**Drew, T., S. Webb, D. Pearson, and J. Thompson, "Emergency Medical Services
and the Hospital: A Statewide Analysis," Hospital Administration, Summer
1974, estimated the variable cost of a hospital-based ambulance system as
$14.48/call.

(

103

Example #2: Cost/year of two-manned ambulances at one location

Fixed Cost: Dollars

Driver and attendant wages 60,244

Support personnel ($4,160/man x 5.38 men) 22,380
Benefits

D/A ($60,244 X 22.45%) 13,524

Support personnel ($22,380 x 15.03%) 3,364

Depreciation (vehicles and equipment) 4,900

Facilities :

Rent (1900 square feet x $2.00/square foot) 3,800

Utilities (25% x $3,800) 950

Maintenance and supplies (30% x $3,800) 1,140

Telephone 2,470

Insurance 2,808

Other fixed costs 5 ,176

Total Fixed Costs 120,756

Variable Costs (cost/call) :

Same as in Example #1.

104

APPEJ3DIX B

Resident Population Estimates by Demand Point

TABLE B-1 — Resident Population Estimates by Demand Point

Demand
point

designation

Demand points listed
by hospital service
area (HSA)

Census county enumeration
districts associated with
each demand point

Estimated
resident pop-
ulation in 1970

Number of
ambulances
in 1975

Butte County
Chico (HSA)

4 Butte Meadows

5 Chico

6 Durham

9 Forest Ranch

11 Nord
15 Richardson Springs

23 Hamilton City (Glenn Co.)

Total

19-30, 38-40, 41-62

63-65

33-36

31, 32, 37
5, 6, 11

378
40,193
3,096
278
534
2,955
1,998

49,432

0
7
0
0
0
0
0

Paradise (HSA)
14 Paradise

17 Sterling City

Total

Oroville (HSA)

1 Bangor

2 Berry Creek

7 Feather Falls

8 Forbestown

12 Oroville

13 Palerma
16 Richvale

18 Yankee Hill

Total

Grldley (HSA)

3 Biggs
10 Gridley

51 Live Oak (Sutter Co.)

Total

1-11, 17, 18
14

92, 94

66-91

96, 97, 99, 100

102, 103

101, 104, 105

106-113

1-7

14,598
1,340

15,938

490
423
230
286
21,060
5,270
628
318

28,705

2,084
7,808
4,811

14,703

5
0

0
0
0
0
3
0
0
0

0
2
0

continued on next page

TABLE B-1 continued

Demand Demand points listed Census county enumeration Estimated Number of

point by hospital service districts associated with resident pop- ambulances
designation area (HSA) each demand point ulatlon in 1970 in 1975

Colusa County

Colusa (HSA)

Princeton

Glenn County

Willows (HSA)

Artois

Elk Creek

—

Glenn

Or land

1-4, 7, 9, 10

Willows

12-17, 20, 21

Total

Shasta County

Redding (HSA)

Anderson

74, 78-91

Bella Vista

Cottonwood

92-94

Enterprise

56-60

I go

96, 98

Lakehead

16, 17

Millville

J- -L.

Montgomery Creek

8, 9

Oak Run

Palo Cedro

Platina

Project City

18-21, 28

Redding

26, 29-55, 61-

Shlngletown

12, 14

Summit City

Whiskeytown

Whitmore

1,037

592

1,088
1,231
6,602
6.010

15,523

14,164
1,669
2,574
11,486
1,510
599
606
897
1,313
362
113
7,031
21,181

528

0
1
0

Total

907

157

71,797

0
0
0
0
0
0
0
0
0
0
0
0
7

0
(>
0
0

continued on next page

TABLE B-1 continued

Demand
point

designation

Demand points listed
by hospital service
area (HSA)

Census county enumeration
districts associated with
each demand point

Estimated
resident pop-
ulation in 1970

Number of
cimbu lances
in 1975

Fall River Mills (HSA)

30 Burney

34 Fall River Mills

37 McArthur

41 Old Station

27 Adin (Lassen County)

26 Bieber (Lassen County)

Total

1, 2. 7
4. 5

3
6

13
14

2,633
1,393
796
651
646
885

7,004

0
1
0
0
1
1

Siskiyou County
Mt. Shasta (HSA)
50 Dunsmuir
31 Castella (Shasta Co.)

Total

9, 10
15

2,819
565

3,384

Tehama County
Red Bluff (HSA)

53 Gerber

54 Los Molinas

55 Manton

56 Mineral

58 Paynes Creek

59 Proberta

60 Red Bluff

61 Tehama

Total

21, 24
1. 2
3A

38
16

4-10, 13-15, 17, 19, 20,

22, 23

713
3,315
416
121
335
1,571
14,497

317
21,285

0
0
0
0
0
0
4

0
4

Corning HSA
52 Corning
57 Paskenta
62 Vina

Total

27-33
18

25, 26

6,508
605
1.119

8,232

1
0
0

continued on next page

TABLE B-1 continued

Demand Demand points listed Census county enumeration Estimated Number of

point by hospital service districts associated with resident pop- ambulances
designation area (HSA) each demand point ulation in 1970 in 1975

Trinity County

Weaverville (HSA)

Big Bar

334

Burnt Ranch

685

Douglas City

489

Forest Glen

229

Hayfork

10, 12

1,493

Hyampon

552

Junction City

425

Lewiston

3. 5

1,040

Trinity Center

286

Weaverville

1, 2

1.489

Total

7,022

TOTAL - STUDY AREA

244,062

Source: U.S. Bureau of the Census, 1972 and California Department of Transportation, Division of Highways, 1971.

109

APPE^JDIX C

Population-Day Estimates

In this appendix section estimates are made for the total number of
"population-days" (12 hours) spent in the study area by residents and
nonresidents. Three groups are involved: local residents, visitors to
the area's recreation sites, and transients passing through on the area's
highways. This section explains how estimates of visitor-days, transient-
days, and resident-days were made and how they were adjusted to a similar
basis alloxd.ng their aggregation for a total population-day estimate.
Both visitor-days and transient-days had to be adjusted dox^mward to allow
for residents visiting recreation sites and using the area's highways, to
avoid double counting when added to the resident-day totals. These
population-day estimates should prove broadly useful to planners of any
delivery service in the study area.

Derivation of Visitor-Day Estimates

Data from several sources were gathered and adjusted in order to be
combined into a visitor-day measure. Visits to the area's national forests,
state parks, national parks. Pacific Gas and Electric Sites, and state
wildlife areas and fish hatcheries are counted by the U.S. Forest Service,
The California State Parks and Recreation Department, U.S. National Park
Service, Pacific Gas and Electric Company, and The California Department
of Fish and Game.

110

U.S. Forest Service Data

The federal f^overnment owns over one-third of the land In the study
area; the najorlty of the f ederally-ovmed land Is administered by the U.S.
Forest Service. The study area Includes parts of the Lassen, Mendocino,
Shasta, Six Pivers, Trinity, and Plunas national Forests. The U.S. Forest
Service (1972) records recreation use by various geographical delinea-
tions: counties, forests, and ranger districts. Ranger districts are the
stnallest areas within a national Forest for which visitor-day data are
available. Visitor-days arc associated with a particular ranger district
in a rather arbitrary manner. No other data, however, are available to
locate on a more rational basis the people involved in outdoor recreation
activities. In some instances, visitor-days for a particular ranger
district are divided between two or three demand points due to the
proximity of the district to several demand points.

Although specific data are not available by month, U.S. Forest per-
sonnel are aware of the peak usage months during the year [personal inter-
view, 10741. In general, recreation use in the U.S. forests is minimal
during the winter months, with activity slowly increasing to Memorial
Day. Recreation use then normally declines slightly until a few days
before July Ath. Peak usage occurs between July Ath and Labor Day. Usage
then gradually declines until October 1st, when activity again becomes
minimal.

Service data estimates of monthly recreation use in the U.S. forests
TTere assumed to follow the same monthly percentage distribution as the
attendance at the VThiskeytown National Recreation Area (imA) because

Ill

detailed data are available on a Fionthly basis and the use pattern there
appeared representative of recreation use In Northern California. For
those recreation sites vhere the VTiiskeytovTi VRj^. attendance distribution
was not appropriate because of significant ancunts of skiinp and huntinp,
adjustnents in the percentages were nade. /Appendix Table C-1 shows the
monthly distribution pattern in the Vhiskeytovm KRA, the adjusted distri-
bution In several ranker districts where huntinp is popular, and the
Pacific Gas and Electric canppround rdonthly distribution. The allocation
of U.S. Forest visitor-days atnonp demand points by forest and by ranper
district is plven in Appendix Table C-2,

California State Parks and Recreation Data

In state parks the count is by visitor-days. Each visitor is assumed
to spend 12 hours at the recreation site; an overnight visitor, an addi-
tional 12 hours; so a visitor-day equals 12 hours. To put these data on a
monthly basis, the following conversion was made:

Total number of visitor-days per month =

(No. visitors per month) (visitor-days per visitor) +
(No. overnights per month) (visitor-days per overnight)

U.S. National Park Service

A similar computation was made to put visitor-days in the national
parks on a monthly basis:

Total number of visitor-days per month =

(No. visitors per month) (visitor-days per visitor) +
(No, overnights per month) (visitor-days per overnight)

TABLE C-1 — Adjusted Distribution for Almanor, Glenn County, and Corning
Ranger Districts and P.G.&E. Campgrounds

Total Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

percent

General

Monthly distribution 100.0 1.8 2.4 4.3 5,1 9.5 14.9 19.7 21.1 11.8 5.1 2.8 1.5
in Whiskeytown NRA
Adjusted distribution

Almanor R.D. a/

100.0

1.8

2.4

4.3

5.1

9.5

14.9

19.2

20 6

11.8

5.1

3.8

1.5

Glenn County b/

100.0

1.8

2.4

4.3

5.1

9.5

14.9

17.7

21.1

13.8

5.1

3.8

1.5

Corning R.D. b/

100.0

1.8

2.4

4.3

5.1

9.5

9.9

14.7

22.1

20.8

5.1

4.8

1.5

P.G.&E. Campgrounds

100.0

6.1

10.5

15.9

22.7

24.1

14.6

6.1

a/ Adjusted for large influx of hunters during November.
h_/ Adjusted for large influx of hunters during September.
General use distribution is similar to that of Whiskeytown NRA.

113

TABLE C-2 — Allocation of U.S. Forest Visitor-Days Among Demand Points
Forest and Ranger District.

Forest

Mendocino Forest

Glenn County (total)
Tehama County

1/2 Corning R.D.

Six Rivers Forest

Trinity County

Mad River R.D.

Trinity Forest

Shasta County

1/2 Yolla-Bolla R.D.
Tehama County

1/2 Yolla-Bolla R.D.
Trinity County

1/3 Big Bar R.D.

3/4 Hayfork R.D.

1/4 Hayfork R.D.

Coffee Creek R.D.

1/2 Weaverville R.D.

Shasta Forest

Shasta County

1/2 Lake Shasta R.D.
1/2 Lake Shasta R.D.

Lassen Forest

Shasta County
Hat Creek

Tehama County

Mineral R.D

Butte County

1/4 Almanor

R.D.

Plumas Forest

Butte County

1/2 Oroville R.D.
1/4 Oroville R.D.
1/4 Oroville R.D.

Demand Point

Elk Creek
Paskenta

Forest Glen

Platina

Paskenta

Big Bar
Burnt Ranch
Junction City
Hayfork
Hyampom
Trinity Center
Weaverville
Lewis ton

Lakehead
Project City

Old Station
Mineral
Butte Meadows

Feather Falls
Yankee Hill
Berry Creek

114

Pacific Gas and Electric Data

P.G. S E. reports use statistics in terms of occupancy-days. According
to P.O. f\ E. personnel, one occupancy-day is equivalent to 1.42 visitor-days
as defined hy the U.S. Forest Service. The monthly percentage attendance
at P.G. & E. campgrounds, which are open only from April through October,
were given earlier in Appendix Table C-1.

California Department of Fish and Game

The Fish and Game Department reports monthly attendance in terms of
use-days — one person performing one activity for 24 hours. Due to the
nature of the counting system, a person performing more than one activity
(e.g., camping and boating) during one day may account for more than one
use-day. Since the preceding data sources define visitor-days in terms
of a 12-hour period with little or no double counting possible, it was
decided to count each use-day as equivalent to one visitor-day.

Derivation of Transient-Day Estimates

The California Department of Transportation, Division of Highways,
samples the traffic flow at a sufficient number of intervals on all state
hiehways to indicate the general pattern of traffic flow on an average
dailv basis. By assuming an average speed between counting stations, the
average length of time a vehicle is in the vicinity of a counting station
can be determined. The time dimension and average dally traffic flow is
converted to an estimate of transient population for a specific site on a
monthly basis as follows:

115

Transient-days per month = (Averape No. vehicles per day)
(30 days per month) (2.4 transients per vehicle) (No.

hours in vicinity)
(one transient-day per 12 transient-hours).

The highways which were included in the count of transient vehicles are

shown in Appendix Table C-3 in which the estimated number of hours each

vehicle was in the vicinity of the counting station for each route is

indicated.

TABLE C-3 — Highways Used to Calculate Transient Population and
the Number of Hours Each Vehicle Was Near a Counting
Station on Each Route

Route 3

hours

Route 5

.25

hours

Route 20

.25

hours

Route 32

.25

hours

Forest Ranch, Butte Meadows

hours

Route 36

hours

Route 44

.25

hours

Route 65

.25

hours

Route 70

.25

hours

Yankee Hill

hours

Route 89

hours

Route 99

.25

hours

Route 113

.25

hours

Route 299

hours

Adjustments to Visitor-Days and Transient-Days Estimates

As mentioned earlier, adjustments had to be made in both the visitor-
day and the transient-day monthly totals to allow for residents who visit
recreation sites and who use the highways but who are already counted
among the resident population.

116

Use of the recreation sites by residents is estimated by origin-of-
visitor data. Two sources of data are available for Northern California.
One is the P.G. & E, visitor attendance reports which reveal the origin
of all registered campers in each of their campgrounds [Pacific Gas and
Electric, 1972], For 1972, the P.G. & E. campgrounds of North Shore,
Cassel, and Macumber reported that 23 percent, 16 percent, and AO percent,
respectively, of the total number of visitors originated from within the
study area. The second source is U.S. Forest Service data on visitors to
the Wilderness Areas. The Salmon-Trinity, Yolla-Bolla, and 1,000 Lakes
vrilderness areas reported that 14 percent, 7.3 percent, and 31.4 percent,
respectively, of the total attendance were from the study area [U.S.
Forest Service, 1972]. In addition, the U.S. Forest Service, during
1971-72, conducted skier point studies for the Mt. Lassen and Mt. Shasta
ski areas. These studies revealed that 70.6 percent and 79 percent of
the skiers at Mt. Shasta and Mt. Lassen, respectively, came from the area.

In spite of this information, it is virtually impossible to adjust
each recreation site population accurately for resident visitors. The
number of visitor-days at each recreation site, therefore, was arbitrarily
reduced by 25 percent.

The adjustments to the transient population for resident use of state
highways also required several stringent assumptions. Traffic flow on
most major highways exhibits an annual pattern of high summer use, with
the peak during August, and low use during the winter, with January the
low usage month. In order to isolate only the transient traffic flow, it

117

was assumed that the monthly local resident traffic could be approximated
by the January traffic flow estimate. Accordingly, the January traffic
fipure was subtracted from all the remaining monthly estimates. For high-
ways with high transient use during the entire year, the figures will be
somewhat low (Highways 99 and 20). For highways which exhibit high summer
usage, the figures are realistic. Highways 3, 5, 36, 44, 70, S9, and 299
exhibit high variance in usage throughout the year.

Further adjustments in transient-days were also necessary. Data on
traffic flow at a particular site are given both in terms of average annual
daily traffic (AADT) and average daily traffic for the peak month. To
extrapolate this information into monthly estimates of transient popula-
tion, some relationships from the California Department of Transportation
were used:

= A(1.0 + R • I^) i = particular month =1, 2, 12

= average daily traffic for month i
A = average daily traffic for 1970 (AADT)

R = annual variance factor = E summer months traffic - T winter months

(6) (AADT)

= the degree of shift in the R factor peculiar to each month, i.

Appendix Table C-4 gives the I factors for each month of the year.

The I factors are explained as follows [California Department of

Transportation, 1971, p. 7]:

The curve pattern formed by annual fluctuation between
summer and winter traffic volume is generally consistent from
one place to another to the extent that the volume for each
month of the year tends to retain its position in the pattern
relative to those of all other months, but varies in its de-
parture for AADT as the R factor varies. Each unit of change
in the R factor (expressed in hundredths) is accompanied by a

118

TABLE C-4 — I Factors for Each Month

Month

Factor

January

- 56

February

-.55

March

-.49

April

-.44

May

-.20

June

.35

July

1.08

August

1.20

September

.62

October

-.08

November

-.45

December

-.51

Source: California Department of Transportation,
Division of Highways, unpublished data
manual, December 1971.

119

corresponding shift in the position that each month bears
in relation to AADT. The denree of shift per unit of R
factor is a constant value peculiar to each month termed
the I (increment) factor.

As noted above, the information available at each counting station or
demand point consists of the AADT and the average daily traffic for the
peak usage month. By assuming the peak month of traffic flow is August
and that the minimum traffic flow or local commute traffic is approxi-
mated by the January traffic flow, the number of transient vehicles can
be estimated for each demand point on a monthly basis. The calculation
for a particular point for month i is as follows:

^AUG " A^^-*^ + ^^AUG^
P = ^AUG - ^
"^■■-AUG

Average number transient vehicles (month i) = - V

JAK

= Ad.O + RI^) - A(1.0 + RIj^^)
= AP.I^ - ARIj^^

(Substitute R from above) = ^^AUG _ v

i ~ JAfr

AUG

For example, the number of transient vehicles for a particular site for
the month of February is found as follows:

Average number transient vehicles ^^EE) ~ '^^ i" 2^'^^^ ^^AUG ~

.008 (V^^g - A)

120

Resident-Day Estimates

Although the resident population of the demand points is known fairly
accurately from the census, adjustments had to be made in the totals so
that they could be added to the visitor-day and transient-day adjusted
monthly estimates. All three populations must be put on a time basis.
It was not only the number of people who visited recreation sites that
was counted but also the time each person spent at the site. For tran-
sients, it \7as not the num.ber passing through, but time spent in the area.
Similarly the resident population count must be put on a time basis. The
folloviing conversion V7as m,ade:

i'o. resident-days per month =

(No. residents) (24 hours per day) ( 1 resident-day ) (30 days per mon

12 resident-hours

Population-Day Estimates

The monthly estimates of 12 hour population-days by demand points
in the study area are presented in Appendix Table C-5. Population-day
estim.ates represent the sum of visitor-days, transient-days, and resident-
days which have incorporated all the adjustments discussed above.

TABLE C-5~Estlinates of Population-days (P-D) , Visitor-days (V-D) , Transient-days (T-D) and Resident-
days (R-D) by Demand Point and by Month of the Year (1972) for the Hosnital Service Areas
in the Study area (in 1,000's)

Total

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Chico (H.S.A.)

Butte Meadows (R-D)

272.2

22.

* 22.7

Lassen Forest (V-D)

44.2

1.1

1.9

2.3

4.2

6.4

8.5

9.3

5.2

2.3

Rte 32 (T-D)

9.9

1.3

2.3

2.5

2.0

Total

326.3

J4 . J

Chlco (R-D)

28,939.0

2,411.

2.411.6

Bidwell Mansion S.P. (V-D)

31.5

2.6

2.2

3.5

2.0

2.3

2.5

1.8

7.8

1.4

1.3

Rte 99 (T-D)

40.8

2.1

5.5

9.7

10.3

8.3

2.8

Total

29,011. i

Durham (R-D)

2,229.1

185.

185.8

Forest Ranch (R-D)

200.2

16.

16.7

Rte 32 (T-D)

10.9

1.5

2.6

2.8

2.2

Total

211.1

19.5

Nord (R-D)

384.5

32.

32.0

Richardson Springs (R-D)

2,127.6

177 .

ITT "i

*Hamllton City (R-D)

1,438.6

119.

1 T Q Q

Rte 32 (T-D)

5.2

. X

•a
. J

■7
. /

J. . 1

. J.

Total

1,443.8

121 . 2

kjlslusI xQuax yr-^u/

35 ^ 733. 7

2,994.7

Orovllle (H.S.A.)

Bangor (R-D)

352.8

29.4

■

Berry Creek (R-D)

304.6

25.4

Plumas Forest (V-D)

51. 2

1.2

2.2

2.6

4.9

7 . 6

10.1

10 . 8

6.0

2.6

1.4

. 8

Total

355.8

Jo . Z

Feather Falls (R-D)

165.6

13.8

Plumas Forest (V-D)

102.5

2.5

4.4

5.2

9.7

15.3

20.2

21.6

12.1

5.2

2.9

1.6

Total

268.0

35.4

Forbestown (R-D)

206.0

17 .2

Orovllle (R-D)

15,163.2

1,263

1 ,263 . 6

15 .6

24.0

34 . 8

60.6

61.1

63 . 3

57 .2

39. 7

22 . 7

19. 3

7.9

Lake Orovllle Overlook (V-D)

157.3

7.8

11.5

15.8

24.4

16.9

18.0

18.2

15.1

10.7

7.0

5.3

Orovllle Wildlife & Recreation

Area (V-D)

33.3

2.1

2.8

3.0

4.2

3.4

3.3

2.4

3.1

3.0

2.6

1.7

Feather River Fish Hatchery (V-D)

99.5

1.5

8.3

10.4

12.0

8.2

5.9

10.0

11.6

13.4

11.3

5.0

Rte 70 (T-D)

18.3

2.5

4.3

4.6

3.7

1.3

Total

15,887.9

1,356.1

Palermo (R-D)

3,794.4

316

316.2

Richvale (R-D)

452.2

37.7

Yankee Hill (R-D)

229.0

19.1

Plumas Forest (V-D)

51.2

1.2

2.2

2.6

4.9

7.6

10.1

10.8

6.0

2.6

1.4

Rte 70

10.3

1.4

2.5

2.6

2.0

Total

290.5

32.5

rs3

GRAND TOTAL (P-D)

21,607.6

1,984.0

— Continued on next page.

Table C-5 (continued)

Total

Jan.

Paradise (H.S.A.)
Paradise (R-D)
Sterling City (R-D)
Grand Total

Gridley (H.S.A.)
Biggs (R-D)
Gridley (R-D)

Grey Lodge Wildlife Area (V-D)

Rte 99 (T-D)
Total

Live Oak (R-D)

Rte 99 (T-D)
Total

Grand Total (P-D)

Glenn Co .

Willows (H.S.A.)
Artois (R-D)
Elk Creek (R-D)

Mendocino Forest (V-D)
Total

Glenn (R-D)

Rte 45 (T-D)
Total

Orland (R-D)

Rte 5 (T-D)
Total

Willows (R-D)

Sacramento National Wildlife
Refuge (V-D)

Rte 5 (T-D)
Total

Grand Total (P-D)

Feb.

Mar.

Apr. May Jun.

Jul.

Aug.

Sep.

Oct.

Nov. Dec.

10,510.6
964.8
11,475.4

1,500.5
5,621.8
28.7
20.9
5,671.4

3,463.9
20.9
3,484.8
10,665.7

426.2
783.4
32.6
816.0

886.3
3.0
889.3

4.753.4
22.6
4.776.0

4,327.2

5.2
46.1
4,378.5
11.286.0

875.9
80.4

125.0
468.5

4.3

288.7

35.5
65.3
.6

73.9
0

396.1
0

360.6

1.4
0

2.3

1.9 1.5 .8 1.5 1.5
.2 .4 1.1 2.8 4.9

.4 1.1 2.8 4.9

1.4 1.7 3.1 4.9 5.8

.1 .2

.4 1.2 3.0 5.3

AAA
2.4 6.2 10.9

875.9
80.4
956.3

125.0
468.5
1.1
5.3
474.9

288.7
5.3
293.9
893.9

35,
65.
6,
72-

73.9
.8
74.7

396.1
5.7
401.8

360.6

A
11.7
372.3
956.4

1.6
4.2

4.2

2.0 5.4 4.7
1.4 .3 .2

1.4 .3

4.5 1.7 .9

.6 .2 A

4.6 1.6

.1 .3 1.4 1.4
9.4 3.2 .7 .3

Shasta Co .
Redding (H,

S.A.)

Anderson (R-D)

10,198.1

Rte 5 (T-D)

47.8

Total

10,245.9

Bella Vista (R-D)

1,201.7

Rte 299 (T-D)

2.1

Total

1,203.8

Cottonwood (R-D)

1,853.3

Rte 5 (T-D)

47.8

Total

1,901.1

849.8
0

100.1
0

154.4
0

2.5 6.4 11.3

.1 .2 .4

2.5 6.4 11.3

849.8
12.1
861.9

100.1
.7

100.8

154.4
12.1
166.5

9.7

3.3

-Continued on next page.

Table C-5 (continued)

Total

Jan.

Feb.

Mar.

Apr.

May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Shasta Co.

Redding (U.S.A.)

689.2

Enterprise (R-D)

8,269.9

689.2

Igo (R-D)

1,087.2

90.6

Lakehead (R-D)

431.3

35.9

Shasta N.R.A. (V-D)

865.2

15 . 0

OA Q

IT O

/. A 1

oz . z

xzo . y

1 7(1 A
X/ U .

in*? 1

AA 1

9A 9
z*# ■ z

1 n

i J • u

Rte 5 (T-D)

22.4

. £.

. J

1. U

A 7

J . u

*♦ . u

T ft

-a
• J

. X

Total

1,318.9

223,4

Mlllvllle (R-D)

H JO . J

JO . 4

Ifi 4

Rte 44 (T-D)

6.1

. 1

• J

. o

X . H

1 c
X.J

1 *y

• X

A
A

Total

Montgomery Creek (R-D)

645.8

53.8

Rte 299 (T-D)

7.9

1.5

1.6

1.3

2.0

Total

Oj J . /

Oak Run (R-D)

945.4

78.8

Platlna (R-D)

81.4

6.8

Trinity Forest (V-D)

69.1

1.2

1.7

3.0

3.5

6.6

10.3

13.6

14.6

8.2

3.5

1.9

1.0

Rte Jo (T-D)

0 o
/ . 7

* Z

• **

. 0

9
. Z

A
A

A
n

Total

153.4

ZZ • X

Project City (R-D)

5,062.3

421.8

421.9

Shasta N.R.A. (V-D)

865.2

15.6

20.8

37.2

44.1

82.2

128.9

170.4

182.5

102.1

44.1

24.2

13.0

Rte 5 (T-D)

41.7

2.2

5.6

9.9

10.6

8.5

2.9

Total

J f yoy . /

fi1 4 Q

Redding (R-D)

19,570.3

1,630.8

,630.8

Shasta State Historical

Park (V-D)

27.3

1.0

1.3

1.9

1.8

2.8

3.4

4.0

4.7

2.8

1.8

1.1

Rte 5 (T-D)

4/ .o

• 1

• J

A A
D ■ 4

XX . J

19 1
XZ • X

Q 7

y • /

J.J

. J

Total

19 , 645 . 4

AA7 7

Shingletown (R-D)

423.4

35.3

McCumber (PG&E) (V-D)

3.3

Rte 44 (T-D)

5.2

. 1

1.2

1.3

1.1

Total

4 ji . y

17 4

Summit City (R-D)

504.0

42.0

Whiskey town (R-D)

653.0

54.4

Whiskey town N.P. (V-D)

752.9

13.9

18.4

32.2

38.1

71.3

111.8

148.0

158.9

88.8

38.1

21.1

12.3

Kte zyy ^i—

Lh ,0

A
A

• J.

•i

o
• o

1 4

1 7

1 n

. 2

Total

1,420.5

217.0

Whltmore (R-D)

113.0

9.4

Palo Cedro (R-D)

260.6

21.7

Rte 44 (T-D)

13.9

1.9

3.3

3.5

2.8

1.0

Total

274.5

25.2

Grand Total (P-D)

54,580.2

,920.2

— Continued on next page.

Table C-5 (continued)

Total

Jan .

Feb.

Mar.

Apr.

May

Jun.

Jul.

Sep.

Oct •

Nov.

Dec.

Shasta Co.

Fall River Mills (H.S.A.)

*Adin (R-D)

465.1

. 8

Rte 299 (T-D)

4.2

A
A

. Z

. O

. 1

• 0

T
• J

. 1

Total

469.3

o
• o

637 . 2

Rte 299 (T-D)

4.2

• 0

1
±

n
u

. X

Q
• O

■a

■1

Total

641.4

Burney (R-D)

1,895.8

158

McArthur-Burney Falls (S.P

) (V-D)

179.9

. 0

. 8

6.3

North Shnrp P n AT? ^^V—

7 ft

Q
. O

X ■

Q
O

• X

Rte 299 (T-D)

23.6

_ 2

0
. £.

J <

Q
• 0

1.6

Total

2,107.1

211

Fall R-fvpr M-f 1 1 a TD-rt'^

i. , UU J . u

o J

. 6

Crystal Lake Fish Hatchery

(V-D)

13.7

_ 3

1.0

• O

Cassel (P.G.&E) (V-D)

4.1

• Q

c
■ 0

• J.

1
J.

Rte 299 (T-D)

9.7

. \

_ 5

T
• J

z •

n
• U

. 7

• J.

1
L

Total

1,030.5

fift

McArthur (R-D)

573.1

Rte 299 (T-D)

9.0

Total

582.1

■ 0

Old Station (R-D)

468.7

39.

Lassen Forest (V-D)

168.7

33.

8.6

Rte 89 (T-D)

9.5

Total

646.9

Grand Total (P-D)

5,477.3

522

Siskiyou Co.

Mt. Shasta (H.S.A.)

Dunsmuir (R-D)

2,029.7

169.

169

Rte 5 (T-D)

50.4

11.

3.5

Total

2,080.1

181

Castella (R-D)

406.8

. 9

Castle Crags S.P. (V-D)

Rte 5 (T-D)
Total

61.6
43.5
511.9

3
1

.3
.4

.7
.2

10
5

.3
.9

14
10

8
3

15
11
60

. 6
.0
.5

9
8

.0
.9

3.0

. 7
. 7

3
3

Tehajsa Co.

Kea Dlutr ^H.o.A.^

Gerber (R-D)

513.4

42.

Los Molinos (R-D)

2,386.8

198.

198

Rte 99 (T-D)

9.6

Total

2,396.4

201

Mineral (R-D)

87.1

Lassen Park (V-D)

494.7

122.

141

22.9

Lassen Forest (V-D)

241.0

12.

47.

12.3

Rte 36 (T-D)

10.4

Total

833.2

202

4^•

— Continued on next page .

Table e-5 (continued)

Total

Jan.

Feb.

Mar . Ap r . May

Jun.

Jul.

Aug.

Sep.

Oct.

Nov.

Dec.

Tehama Co .

Red Bluff (H.S.A.)
Paynes Creek (R-D)

Darrah Springs Fish Hatchery
(V-D)

Tehama Wildlife Mgt. Area (V-D)
Rte 36 (T-D)
Total

Red Bluff (R-D)

William Ide Abode SHP (V-D)

Rte 5 (T-D)
Total

Proberta (R-D)
Tehama (R-D)
Manton (R-D)

Grand Total (P-D)

Corning (H.S.A.)
Corning (R-D)

Woodson Bridge SRA (V-D)

Rte 5 (T-D)
Total

Paskenta (R-D)

Trinity Forest (V-D)
Mendocino Forest (V-D)

Total

Vina (R-D)

Rte 99 (T-D)
Total

Grand Total

(P-D)

Colusa Co.

Princeton (R-D)

Rte 45 (T-D)
Total

Trinity Co .

Weavervllle (H.S.A.)
Big Bar (R-D)
Trinity Forest
Rte 299 (T-D)
Total

Burnt Ranch (R-D)
Trinity Forest
Rte 299 (T-D)

Total

(V-D)

241.2

20.1

1.8

17.5

10.4

270.8

10,437.8

869.8

1.0

36.5

1,131.1

94 . 3

228.2

19.0

299. 5

25 .0

16,176.9

4,685.8

390.5

55.9

31.9

4,773.3

435.6

36.3

69.1

1.2

20.3

525.0

805.7

67.2

8.2

814.4

6,112.7

746.6

62.2

4.3

750.9

240.5

20.0

105.2

1.9

8.6

354. 3

493.2

41.1

105.2

1.9

11.8

610.2

1.8

1.6
.5

2.5
A

20.1

2.8

1.3

8.2

1.4

2.5

2.6

2.1

23.1

869.8

2.2

3.4

3.9

4.4

4.0

4.1

2.3

1.9

4.9

8. 6

9.2

7.4

2.5

883.1

Q4 1

19.0

25.0

1,490.8

390.5

3.2

6.1

8.5

10.7

10.1

6.8

2.9

1.3

1.8

4.8

8.4

9.0

3.5

2.5

409.6

36.3

3.5

6.6

10.3

13.6

14.6

8.2

3.5

1.9

1.0

2.0

3.0

4.6

4.3

1.0

55.4

67.2

1.2

2.1

2.2

1.8

4.5
A

4.5
.1

5.4
.1

5.4
.2

.6 1.0

10.0
.4

10.0
.6

15.7
1.1

15.7
1.6

20.7
2.0

20.7
2.8

69.3
534.4

62.2
1.1
63.3

20.0
22.2
2.1
44.3

41.1
22.2
3.0
66.3

12.4
1.7

12.4
2.4

5.4
.6

5.4
.8

2.9
.4

2.9
.2

1.6
.1

— Continued on next page.

Table C-5 (continued)

Total Jan. Feb. Mar. Apr. May Jun. Jul. Aug. Sep. Oct. Nov. Dec.

Trinity Co .

Weavervllle (H.S.A.)

Douglas City (R-D)

352.1

29.3

Kte £.77 \1.—D)

10.4

1.4

2.5

2.6

2.1

Total

362. 5

32.0

Forest Glen (R-D)

164.9

13.7

Six Rivers Forest (V-D)

21.2

1.0

2.0

3.2

4.2

4.5

2.5

1.1

1.7

Total

187.8

•

18.7

Hyampom (R-D)

397.4

33.1

Trinity Forest (V-D)

14.4

1.4

2.1

2.8

3.0

1.7

Total

411.8

36.2

Junction City (R-D)

306.0

25.5

Trinity Forest (V-D)

105.2

1.9

2.5

4.5

5.4

10.0

15.7

20.7

22.2

12.4

5.4

2.9

1.6

Rte 299 (T-D)

6.2

1.5

1.6

1.2

Total

/IT /

417.4

49.3

Hayfork (R-D)

1,075.0

89.6

Trinity Forest (V-D)

43.1

1.0

1.9

2.2

4.1

6.4

8.3

9.1

5.1

2.2

1.2

Rte 3 (T-D)

14.8

2.0

3.5

3.7

3.0

1.0

Total

1,132.9

102.4

Lewis ton (R-D)

748. 8

62 . 4

02 . 4

Trinity Forest (V-D)

168.8

3.0

4.1

7.3

8.6

16.0

25.2

33.3

35.6

19.9

8.6

4.7

2.5

Trinity River Fish Hatchery

(V-D)

17.2

1.8

1.9

2.7

3.5

1.4

Total

934.8

101.6

Trinity Center (R-D)

205.9

17.2

Trinity Forest (V-D)

104.9

1.9

2.5

4.5

5.4

10.0

15.6

20.7

22.1

12.4

5.4

2.9

1.6

Rte 3 (T-D)

2.9

Total

313.7

40.0

Weavervllle (R-D)

1,072.1

89.3

Weavervllle Joss House SHP (V-D)

26.9

1.3

2.3

3.2

4.6

5.6

3.7

1.9

1.1

Trinity Forest (V-D)

168.8

3.0

4.1

7.3

8.6

16.0

25.2

33.3

35.6

19.9

8.6

4.7

2.5

Rte 299 (T-D)

18.0

2.4

4.3

4.6

3.7

1.2

Total

1,2RS.8

135.1

Grand Total (P-D)

6,011.2

625.?

— Continued on next page.

* Demand points located in an adjoining county.

A - less than 50 visitor-days or transient-days.

R-D - Resident-days; V-D - Visitor-days; T-D = Transient-days; P-D = Population-days (V-D's + R-D's + T-D's).
NOTE: Total may not equal sum because of rounding.

Sources: U.S. Forest Data: U.S. Forest Service, unpublished Recreation-Use Information. Administrative Unit Summary: Ranger District Region-
al Forester California. CY 1972. California State Parks and Recreation Data: California, The Resources Agency, Department of Parks
and Recreation. Man agement Reports , unpublished monthly data. FY 1971-72. 1972-73. National Park Data: U.S. Department of the

\,..L .. pL. ...Jr.. P. '.hHc use of the National Parks . CY (monthly) 1972. National Wildlife Refuge ■>-": U S. Depart-
ment of the Interior. Fish and Wildlife Service. Public Use Report , unpublished data, CY (monthly) 1972. California State Wildlife
Areas and Fish Hatchery Data: California, The Resources Agency. Department of Fish and Game. Public Recreation Use °p State Owned
or Operated Areas , unpublished monthly data. FY 1971-72, 1972-73. Pacific Gas & Electric Co., unpublished CampRround Attendance
Data . San Francisco, 1972.

Transient Data: California. Business and Transportation Agency. Division of Highways. 1972 Traffic Volumes on California State High-
ways . 1972.

a/ Entries in January and August represent resident-days which are assumed constant for all months for each demand point.