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 by 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. i 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 il 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) 33 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 56 12 Response Time Standards: Comparison of Selected Parameters for the Optimal and Present Location Patterns of EMS Facilities (Annual Demand) 58 59 iv 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 By 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. 2 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 4 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 5 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 6 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. 8 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. 9 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." 10 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 11 «» 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 12 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 13 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 14 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] 16 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 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 I Total waiting time Service time Round-trip time Source: Stevenson (1974) 18 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. 19 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. 20 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. 21 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 22 I 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|, 0 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) 24 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 36 3.4 906 266.5 Private or nonprofit hospital 8 1.9 434 228.4 Local tax supported hospital 13 4.1 3,838 936.1 Volunteer fire department 25 1.3 133 102.3 Municipal, district or other fire department 37 1.8 811 455.5 Police department 7 3.4 3,714 1,092.4 Voluntary organizations or other local government services 14 4.1 7,975 1,945.1 Total 331 2.98 2,245 547 Source: 1968 Ambulance Survey. [California Department of Transportation, 1970] 26 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 2/ 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. 27 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 23 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). 29 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. 30 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. 31 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]. 32 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 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 15 473 29.7 BlgRg-Grldley Memorial Hospital (Grldley H.S.A.) 1,376 93.6 100 1,376 93.6 25 65 5 Butte County Conwunlty Hospital (Orovllle H S A ) Hedlcal Center Hospital 1,463 8,914 345.9 ino 24 1,463 2,139 120.0 0 60 26 0 0 24 Glenn County 60 2,063 40 1.375 (8.7 Glenn General Hospital (UUlowa H.S.A.) 3,438 221.8 40 1,375 88.7 20 30 20 Shasta County 83 21,707 15 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 15 20 40 35 10 30 Mayers Memorial Hospital (Fall River Mills H.S.A.) 1,971 281.6 26 512 73.1 60 20 10 Tehana County 85 4,547 14 752 25.5 Corning Memorial Hospital (Corning H.S.A.) 1,466 178.8 75 1,100 134.1 5 49 2 St. Elizabeth Coimunlty Hospital (Red Bluff H.S.A.) 3,884 182.3 52 2,000 93.9 5 31 2 Trinity County Trinity General Hospital (UeavervlUe H.S.A.) 1,220 162.7 50 610 81.3 Source: Superior California Comprehensive Health Planning Aasoclatlon. [1974] a/ Hospital Service Area b/ Dashes indicate data not reported 34 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 a/ 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 CO Source: California Department of Health, 1975. aj Hospital service areas, b/ Chico H.S.A. c/ Redding H.S.A. 36 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 number percent 1 number percent number percent number number Butte County 3,473 35.2 25 881 8.9 11 100 28 247 12 106 7.9 Glenn County 596 31.9 24 141 7.5 -jJ 68 96 52 74 3.6 Shasta County 2,807 35.4 42 1,169 14.8 7 78 63 740 29 343 10.42 Tehama County 584 20.1 30 176 6.1 14 24 55 97 26 45 4.5 Trinity County 237 26.0 68 160 17.6 3 4 34 54 19 30 14.3 California 839,135 42.6 46.7 391,977 19.9 11 43, U7 33 129,352 8 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. 38 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 I 39 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 40 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- a/ Degree of freedom R All Counties with constant constant suppressed Rural Counties (with less than 125,000 population) with constant constant suppressed -2,361.4 (-1.26) b/ -44.24 (-.25) 49.24 (27.19) 48.46 (28.4) 30.1 (9.47) 29.5 (14.8) 53 54 31 32 .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. 41 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 42 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 43 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). 45 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. 46 TABLE 9 — Study Area Demand Points and 23 Potential Facility Sites 1. Bangor 37. McArthur 2. Berry Creek 38. Millville 3. Biees* 39. Montgomery Creek 4. Butte Meadows* 40. Oak Run 5. Chico* 41. Old Station* 6. Durham* 42. Palo Cedro 7. Feather Falls 43. Platine* 8. Forbestown 44. Project City 9. 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. 47 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. 48 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 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 c/ 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 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 49 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 50 4 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 51 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 52 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 53 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 54 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 = XT 2 3 also has a distribution but it is unknown and, therefore, no statis- '^l tical tests of significance can be made. 55 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 1 14 1 2 12 1 3 61 5 4 11 1 5 1185 105 6 91 8 7 6 1 8 8 1 9 8 1 10 230 20 11 15 1 12 621 58 13 155 13 14 430 38 15 87 7 16 18 1 17 39 3 18 9 1 19 30 2 20 17 1 21 32 3 22 36 3 23 58 5 24 198 T 7 25 177 26 M 2 27 m 1 28 417 37 29 49 4 30 77 9 31 li 2 32 n 7 33 338 2t 3 34 41 35 44 3 36 17 9 37 23 2 38 17 1 39 26 2 40 38 3 41 19 3 42 10 X 43 3 1 X 44 207 45 801 71 / X 46 15 1 X 47 20 T X 48 26 a 49 4 1 X 50 83 7 51 141 1 7 52 191 1 7 53 21 1 X 54 97 a o 55 12 i. 56 3 a o 57 17 « 58 9 X 59 46 60 427 JO 61 9 1 X 62 33 3 ■J 63 9 1 64 20 2 65 14 1 66 6 1 67 44 4 68 16 1 69 12 2 70 30 4 71 8 1 72 43 5 Source: See Appendix B and C. 57 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 2/ 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. 58 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 served no. mil. $ no. pet. -Optimal System- 13 31 2.24 22 86.2 27 22 1.62 11 97.7 40 15 1.13 1 99.8 53 9 0.71 0 100.0 67 8 0.64 0 100.0 -Present System- 13 15 1.13 42 75.1 27 14 1.06 21 95.5 40 12 0.92 9 98.4 53 9 0.71 1 100.0 67 8 0.64 0 100.0 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 7,163 7,163 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 56 60 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. 61 Figure 6 Facilities and Demand Points associated with those facilities using the 13 minute response time standard (present system servicing annual demand) 62 TABLE 14— Optlul Lootlon of DIS Facilities: Keaulta for Selected Responae Tlaea (laaed on Annual Deaand Eatlaatea) tlal altes Oe 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 79 Butte Meadows 4 4 11 « 11 6.9 19 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 62 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 16 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 51 Yankee Hill 18 18 9 Princeton 19 19,22 66 Elk Creek 21 21 32 21 32 Baallton City 23 11,23 73 5.6.9,11,15,19, 2,344 20,21,22,23,24, 25,52,53,54,57, Orland 24 24 194 20.21 22 33 7L 895 59.61.62 25,52,53,54,57, Willows 25 Bieber 26 20,25 26 194 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 27 19 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 96 55,60 26 27 30 34 37 A1 205 26.27,30.34,37,41 205 Platlna 43 43 3 43 3 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 48 26 46,47.48,49.55,60 Dunsmiir 50 Coming 52 31,50 52 99 191 31,50 99 31,36,50 11,23.24,52,54, 116 614 31.36,50 116 31,50 99 Los Hollnoa 54 53,54,59,61,62 206 57,61,62 Mineral 56 Paskenta 57 56,58 57 12 17 56,58 57 12 17 56,58 12 56,58 12 4.36,58 23 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 71 29 6 60 e 63,64 43,66 67,68 29 9 60 43,66,67,68 69 43,66,67,68 69 Weavervllle 72 65,69,70,72 99 65,69,70,72 99 -65,69,70,71,72 107 63,64,65,69,70 136 63,64.65.69,70, 136 71,72 71,72 Total annual (2,244,319 region- $1,615,298 81,128,816 $709,262 $639,678 al cost Total calla 7,163 7,163 7,163 7,163 7,163 Deaand polota 1,2,7,8,9,15,17,28,30 .32, 7,8,36,39,40,46,47 .49, 55 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. 63 Figure 7 Relation Between Response Time, Total Regional Cost, and Percentage of Population Served Within Various Response Times (optimal system) S u o Ol o $2.4 2.0 1.6 1.2 .4 — ' — / Percent 1 1 M i K / V Cost X \ N \ • 1 I 1 I 1 1 100 95 90 85 13 27 40 53 Response Time in Minutes 67 > e o o 80 » u » a 64 Figure 8 Facilities and Demand Points associated with those facilities using the 40 minute response time standard (optimal system) 65 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 66 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 72 $649,652 ON Total month peak patients 666 666 666 666 666 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 6 10 10,51 32 12 1,2,7.8.12,13 75 14 14,17 41 18 18 1 19 19,22 5 21 21 3 23 11,23 6 24 24 17 25 20,25 17 26 26 2 27 27 1 29 29,38,39,40.42,46,49 13 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 21 19,20,22,24.25 26,27 29,38,39,40.42. 46,49 30,34,37 41 43 28,33,35.36.44, 45,47.48 31.50 56,58 57 32,52.53,54.55. 59.60,61 63,64 66 67.68 71 65.69,70.72 1 130 37 76 42 39 3 14 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 20 18 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 20 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 00 $2,253,148 $1,624,252 $1,138,102 $718,620 $649,412 Total calls during August 666 666 666 69 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 70 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 call Average Net Average Net no. dollars A5 Redding - 2,012 46 54 1.36 -0.23 b/ a/ 14 Paradise - 1,841 49 48 1.45 0.05 b/ b/ 12 Oroville - 1,266 66 49 1.94 0.51 b/ b/ a/ 52 Coming - 614 125 59 3.66 1.94 b/ b/ 60 Red Bluff - 581 129 51 3.79 2.31 b/ b/ 25 Willows 292 250 54 7.34 5.77 .82 0.06 a/ 50 Dunsmulr — 116 614 64 17.88 16.02 1.79 0.75 a/ 26 Bieber - 109 654 64 19.15 17.28 1.94 0.89 a/ 72 Weaverville — 107 655 60 19.09 17.38 1.91 1.01 41 Old Station 96 741 78 21.67 19.39 2.19 0.72 67 Hayfork - 60 1,177 102 34.54 31.56 3.35 1.18 64 Burnt Ranch 29 2,424 98 69.00 66.21 6.54 4.55 4 Butte Meadows 19 3,695 90 107.02 104.40 10.08 8.27 56 Mineral 12 5,845 84 153.81 151.60 14.43 12.95 66 Forest Glen 9 7,789 121 204.97 201.79 19.16 16.72 Study Area 7,163 158 53 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 CO 38 48 . 70 0.27 ItH 60 Red Bluff 878 89 51 2 .62 1 13 itii 12 Oroville 834 94 49 2 77 1 .34 1t4c Itit 14 Paradise 478 157 4o 4 61 3 19 Aft Itit 25 Willows 454 x«> J / 4 85 3 17 l^lt 10 Gridley 432 49 5 06 3 63 itit 29 Bella Vista 159 4S8 78 13 17 10 93 1.55 0.11 34 Fall River Mills 141 508 61 14 84 13 05 1.53 0.55 50 Dunsmulr n 717 60 20 98 19 23 2.07 1.14 72 Weaverville 99 718 57 20 64 19 00 2.06 1.22 67 Hayfork 60 1,177 101 34 54 31 56 3.35 1.18 26 Bleber 45 1,566 87 46 03 43 47 4.41 2.67 21 Elk Creek 32 2,198 81 64 64 62 26 6.12 4.57 64 Burnt Ranch 29 2,424 98 69 00 66 21 6.54 4.55 41 Old Station 19 3,694 100 107 82 104 90 10.13 8.03 57 Paskenta 17 4,128 82 115 99 113 67 10.89 9.36 56 Mineral 12 5,845 84 153.81 151 60 14.43 12.95 4 Butte Meadows U 6,374 103 185 48 182.48 17.34 15.16 71 Trinity Center 8 8,760 90 245 04 242 51 22.87 21.12 66 Forest Glen 6 11,677 127 305.94 302 61 28.52 25.92 43 Platina 3 • 23,343 108 619.74 616 87 57.66 55.53 Study Area 7.163 225 53 6. 62 5. 06 2.70 1.22 ** Facilities with greater than 400 calls per year where costs equal to those shown in the columns to the left 73 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 74 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 75 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. 76 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 77 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 78 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 79 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 \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. 86 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. 87 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. 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The Theory of General Economic Equilibrium. Princeton University Press, Princeton, New Jersey, 1963. Lefeber, L. Allocation of Space. North-Holland Publishing Co., Amsterdam, 1958. fO Logan, S. An Eaonomio Analysis of Scale Economies in Beef Slaughter Plants, Unpublished Ph.D. dissertation, Department of Agricultural Economics, University of California, Davis, 1962. Manne, A. "plant Location Under Economies-of-Scale: Decentralization and Computation," Management Science 11(1964) :213-235. Matthews, T. Health Services in Rural America, U.S. Department of Agriculture Information Bulletin No. 362, July 1973. Miller, B. and R. King. "Location Models in the Context of a Regional System," Southern Economic Joumaly Vol. 38, July 1971. Pacific Gas and Electric Co. Unpublished "Campground Attendance Data." San Francisco, 1972. Plaas, 11., D. Dodson, D. King, D. Pike, F. Shipley, and G. Beal. The Evaluation of Policy-Related Research in Emergency Medical Services y Vol. Ill, University of Tennessee, 1974. Revelle, C, D. Marks, and J. Liebman. "An Analysis of Private and Public Sector Location Models," Management Science y Vol. 16, No. 11, July 1970. Scott, A. "Location-Allocation Systems: A Review," Geographical Analysis ^ Vol. 2, No. 2, April 1970. Stevenson, K. Operational Aspects of Emergency Ambulance Services, Technical Report No. 61, Operations Research Center, Massachusetts Institute of Technology, Cambridge, May 1971. Ftollsteiner, J. "A TTorking Model for Plant Numbers and Location," Journal of Farm Economics^ Vol. 45, No. 3, August 1963. Superior California Comprehensive Planning Agency. Health Services and Facilities^ 1972, Regional Medical Program Survey, 1974. Takayama, T. and G. Judge. Spatial and Temporal Price Allocation Models, North-Holland Publishing Co., Amsterdam, 1971. U.S. Bureau of the Census. Census of Population: 1970 General Population Characteristics. Final Report PC(1)-E6, California, U.S. Government Printing Office, Washington, D.C., 1972. U.S. Department of the Interior. Public Use Report, Fish and Uildlife Service, unpublished data, calendar year (monthly) 1972. U.S. National Park Service. Public Use of the National Parks. Calendar year (monthly) 1972. 91 U.S. Forest Service. Recreation-Use Information. Forest Service, Admin- istrative Unit Summary: Ranger Districts, Regional Forester, California, calendar year 1972. VJagner, H. Principles of Operations Research with Applications to Managerial Decisions. Prentice-Hall, Englewood Cliffs, New Jersey, 1969. Faller, J., R. Curran, and F. Noyes. "Traffic Deaths: A Preliminary Study of Urban and Rural Fatalities in California," California Medicine^ Vol. 101, 1964. Faller, J., R. Garner, and R. Lawrence. "Utilization of Ambulance Services in a Rural Community," American Journal of Public Healthy Vol. 56, No. 3, March 1966. Weinschenck, G. , V.. Kenrichsoneyer , and F. Aldlncer. "The Theory of Spatial Equilibrium and Optimal Location In Agriculture: A Survey," Review of Marketing and Agricultural Economics ^ Vol. 37, No. 1, March 1969. Fillemaln, T. Th,e Status of Performa}^ce Measures for Emergency Medical Services. Technical Report No. 06-74, Operations Research Center, Massachusetts Institute of Technology, July 1974. 92 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. 93 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. 94 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. 95 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. 96 *"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.] 97 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. 98 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. 99 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 10 years Salvage Value $3,375 0 500 *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 10 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 04 $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 70 88 Interest on capital investment 280 350 (850) Licenses**** 70 300 *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 12 19-30, 38-40, 41-62 63-65 13 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 98 92, 94 93 95 66-91 96, 97, 99, 100 102, 103 16 101, 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) 19 Princeton 5 Glenn County Willows (HSA) 20 Artois 19 21 Elk Creek — 22 Glenn 18 24 Or land 1-4, 7, 9, 10 25 Willows 12-17, 20, 21 Total Shasta County m Redding (HSA) Anderson 74, 78-91 29 Bella Vista 72 32 Cottonwood 92-94 33 Enterprise 56-60 35 I go 96, 98 36 Lakehead 16, 17 Millville n J- -L. m Montgomery Creek 8, 9 m Oak Run 10 42 Palo Cedro 74 41 Platina 97 44 Project City 18-21, 28 45 Redding 26, 29-55, 61- 77 46 Shlngletown 12, 14 47 Summit City 27 48 Whiskeytown 95 49 Whitmore 13 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 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 3 0 o 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 11 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) 63 Big Bar 8 334 0 64 Burnt Ranch 9 685 0 65 Douglas City 6 489 0 66 Forest Glen 13 229 0 67 Hayfork 10, 12 1,493 1 68 Hyampon 11 552 0 m Junction City 7 425 0 m Lewiston 3. 5 1,040 0 n Trinity Center 4 286 0 m Weaverville 1, 2 1.489 2 Total 7,022 3 TOTAL - STUDY AREA 244,062 40 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 0 0 0 6.1 10.5 15.9 22.7 24.1 14.6 6.1 0 0 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. 1/3 Big Bar R.D. 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. 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. 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 .5 hours Route 5 .25 hours Route 20 .25 hours Route 32 .25 hours Forest Ranch, Butte Meadows .5 hours Route 36 .5 hours Route 44 .25 hours Route 65 .25 hours Route 70 .25 hours Yankee Hill .5 hours Route 89 .5 hours Route 99 .25 hours Route 113 .25 hours Route 299 .4 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. 7 * 22.7 a/ > Lassen Forest (V-D) 44.2 8 1.1 1.9 2.3 4.2 6.4 8.5 9.3 5.2 2.3 .7 .7 Rte 32 (T-D) 9.9 0 A .1 .2 .5 1.3 2.3 2.5 2.0 .7 .2 .1 Total 326.3 J4 . J Chlco (R-D) 28,939.0 2,411. 6 2.411.6 Bidwell Mansion S.P. (V-D) 31.5 2. 0 2.6 2.2 2.2 3.5 2.0 2.3 2.5 1.8 7.8 1.4 1.3 Rte 99 (T-D) 40.8 0 .1 .4 .7 2.1 5.5 9.7 10.3 8.3 2.8 .6 .3 Total 29,011. i Durham (R-D) 2,229.1 185. 8 185.8 Forest Ranch (R-D) 200.2 16. 7 16.7 Rte 32 (T-D) 10.9 0 A .1 .2 .6 1.5 2.6 2.8 2.2 .8 .2 .1 Total 211.1 19.5 Nord (R-D) 384.5 32. 0 32.0 Richardson Springs (R-D) 2,127.6 177 . 3 ITT "i *Hamllton City (R-D) 1,438.6 119. 9 1 T Q Q Rte 32 (T-D) 5.2 0 A A . X •a . J ■7 . / J. . 1 /. . J. A A 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 29.4 ■ Berry Creek (R-D) 304.6 25 4 25.4 Plumas Forest (V-D) 51. 2 9 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 13.8 Plumas Forest (V-D) 102.5 1 8 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 17 .2 Orovllle (R-D) 15,163.2 1,263 6 1 ,263 . 6 10 3 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 6 6 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 1 7 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 8 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 0 A .2 .3 .9 2.5 4.3 4.6 3.7 1.3 .3 .1 Total 15,887.9 1,356.1 Palermo (R-D) 3,794.4 316 .2 316.2 Richvale (R-D) 452.2 37 7 37.7 Yankee Hill (R-D) 229.0 19 .1 19.1 Plumas Forest (V-D) 51.2 9 1.2 2.2 2.6 4.9 7.6 10.1 10.8 6.0 2.6 1.4 .8 Rte 70 10.3 0 A .1 ,2 .5 1.4 2.5 2.6 2.0 .7 .2 .1 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 0 288.7 0 35.5 65.3 .6 73.9 0 396.1 0 360.6 1.4 0 2.3 A 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 .2 4.5 1.7 .9 .6 .2 A 4.6 1.6 .1 .3 1.4 1.4 9.4 3.2 .7 .3 N3 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 .1 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 9.7 3.3 .1 3.3 .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 90.6 Lakehead (R-D) 431.3 35.9 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 0 A . £. . 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 0 A . 1 • J Q . o X . H 1 c X.J 1 *y A 1 • X A A Total Montgomery Creek (R-D) 645.8 53.8 53.8 Rte 299 (T-D) 7.9 0 A .1 .1 .3 .5 1.5 1.6 1.3 .4 2.0 A Total Oj J . / Oak Run (R-D) 945.4 78.8 78.8 Platlna (R-D) 81.4 6.8 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 U A A * Z /. • ** 7 7 . 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 0 .1 .4 .7 2.2 5.6 9.9 10.6 8.5 2.9 .6 .3 Total J f yoy . / fi1 4 Q Redding (R-D) 19,570.3 1,630.8 1 ,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 .8 Rte 5 (T-D) 4/ .o U • 1 c • J A A D ■ 4 XX . J 19 1 XZ • X Q 7 y • / J.J 7 . J Total 19 , 645 . 4 X AA7 7 Shingletown (R-D) 423.4 35.3 35.3 McCumber (PG&E) (V-D) 3.3 0 0 0 .2 .3 .5 .7 .8 .5 .2 0 0 Rte 44 (T-D) 5.2 0 A . 1 .1 .3 .7 1.2 1.3 1.1 .4 .1 A Total 4 ji . y 17 4 Summit City (R-D) 504.0 42.0 42.0 Whiskey town (R-D) 653.0 54.4 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 yj A A 1 • J. •i o • o 1 4 1 7 1 n . 2 Total 1,420.5 217.0 Whltmore (R-D) 113.0 9.4 9.4 Palo Cedro (R-D) 260.6 21.7 21.7 Rte 44 (T-D) 13.9 0 A .1 ,2 .7 1.9 3.3 3.5 2.8 1.0 .2 .1 Total 274.5 25.2 Grand Total (P-D) 54,580.2 4 ,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 38 8 38 . 8 Rte 299 (T-D) 4.2 0 A A A A J. . Z . O 1 U \ . 1 D • 0 T • J . 1 A Total 469.3 39 o • o 637 . 2 53 1 53 .1 Rte 299 (T-D) 4.2 0 A A 1 9 • 0 1 ± n u 1 . X Q • O ■a ■1 .1 A Total 641.4 54 .2 Burney (R-D) 1,895.8 158 0 158 .0 McArthur-Burney Falls (S.P ) (V-D) 179.9 8 8 3 . 0 5 1 12 . 8 31 .0 46 6 45 .6 25 .1 6.3 1 .7 1 2 North Shnrp P n AT? ^^V— 7 ft u Q 0 5 Q . O 1 X 9 1 X ■ Q O 1 1 1 • X .5 U u Rte 299 (T-D) 23.6 0 _ 2 l^ 1 J. 0 . £. J s: J < O 6 .0 '* Q • 0 1.6 o Total 2,107.1 211 .5 Fall R-fvpr M-f 1 1 a TD-rt'^ i. , UU J . u o J 0 83 . 6 Crystal Lake Fish Hatchery (V-D) 13.7 4 5 .9 1. 4 _ 3 \ .2 9 2 .6 ]_ 7 1.0 • O J Cassel (P.G.&E) (V-D) 4.1 0 0 0 2 . • Q q .1 c ■ 0 .7 1 • J. 1 J. Rte 299 (T-D) 9.7 0 . \ 2 _ 5 1 X T • J 0 z • "J 2 .5 9 n • U . 7 • J. 1 L Total 1,030.5 fift oo o McArthur (R-D) 573.1 47 8 47 .8 Rte 299 (T-D) 9.0 0 A .1 2 .5 1 .2 2. 1 2 .3 1 .8 .6 .1 1 Total 582.1 50 ■ 0 Old Station (R-D) 468.7 39. 1 39 1 Lassen Forest (V-D) 168.7 3. 0 4 0 7 3 8. 6 16 .0 25 1 33. 2 35 .6 19 .9 8.6 4 .7 2. 5 Rte 89 (T-D) 9.5 0 A 1 2 .5 1 .2 2. 3 2 4 1 .9 .7 .1 1 Total 646.9 77 0 Grand Total (P-D) 5,477.3 522 2 Siskiyou Co. Mt. Shasta (H.S.A.) Dunsmuir (R-D) 2,029.7 169. 1 169 1 Rte 5 (T-D) 50.4 0 1 5 9 2 .6 6 8 11. 9 12 8 10 .3 3.5 .8 4 Total 2,080.1 181 9 Castella (R-D) 406.8 33 9 33 . 9 Castle Crags S.P. (V-D) Rte 5 (T-D) Total 61.6 43.5 511.9 0 2 3 1 1 .3 .4 2 1 8 4 2 .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. 8 42 .8 Los Molinos (R-D) 2,386.8 198. 9 198 .9 Rte 99 (T-D) 9.6 0 A 1 2 .5 1 .3 2. 3 2 .4 1 .9 .7 .1 1 Total 2,396.4 201 3 Mineral (R-D) 87.1 7. 3 7 3 Lassen Park (V-D) 494.7 9. 3 8 0 6 0 3. 9 19 .8 60 .2 122. 3 141 4 86 .9 22.9 5 .9 8. 0 Lassen Forest (V-D) 241.0 4. 3 5 8 10 4 12. 3 22 .9 35 9 47. 2 50 .9 28 .5 12.3 6 .8 3. 6 Rte 36 (T-D) 10.4 0 A 1 2 .5 1 4 2. 5 2 6 2 .1 .7 .2 1 Total 833.2 202 2 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) (V-D) 241.2 20.1 1.8 .1 17.5 .8 10.4 0 270.8 10,437.8 869.8 1.0 36.5 0 1,131.1 94 . 3 228.2 19.0 299. 5 25 .0 16,176.9 4,685.8 390.5 55.9 .9 31.9 0 4,773.3 435.6 36.3 69.1 1.2 20.3 .4 525.0 805.7 67.2 8.2 0 814.4 6,112.7 746.6 62.2 4.3 0 750.9 240.5 20.0 105.2 1.9 8.6 0 354. 3 493.2 41.1 105.2 1.9 11.8 0 610.2 1.8 A 1.6 .5 2.5 A 2.5 A 20.1 .2 .2 .2 .2 .3 .2 .2 .1 A A .8 2.8 1.3 .2 .2 .2 .5 8.2 .5 .4 .1 .2 .5 1.4 2.5 2.6 2.1 .7 .2 .1 23.1 869.8 .0 2.2 3.4 3.9 4.4 4.0 4.1 2.3 .8 .5 .4 .6 1.9 4.9 8. 6 9.2 7.4 2.5 .6 .3 883.1 Q4 1 19.0 25.0 1,490.8 390.5 .0 3.2 6.1 8.5 10.7 10.1 6.8 2.9 1.3 .7 .4 .6 1.8 4.8 8.4 9.0 3.5 2.5 .5 .3 409.6 36.3 .0 3.5 6.6 10.3 13.6 14.6 8.2 3.5 1.9 1.0 .6 1.0 2.0 2.0 3.0 4.6 4.3 1.0 .6 ,3 55.4 67.2 .1 .1 .5 1.2 2.1 2.2 1.8 .6 .1 .1 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 .3 5.4 .6 5.4 .8 .1 2.9 .4 2.9 .2 1.6 .1 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 29.3 Kte £.77 \1.—D) 10.4 0 A .1 .2 .6 1.4 2.5 2.6 2.1 .7 .2 .1 Total 362. 5 32.0 Forest Glen (R-D) 164.9 13.7 13.7 Six Rivers Forest (V-D) 21.2 .4 .5 .9 1.0 2.0 3.2 4.2 4.5 2.5 1.1 .6 .3 1.7 0 A A A .1 .2 .4 .4 .4 .1 A A Total 187.8 • 18.7 Hyampom (R-D) 397.4 33.1 33.1 Trinity Forest (V-D) 14.4 .3 .3 .6 .7 1.4 2.1 2.8 3.0 1.7 .7 .4 .2 Total 411.8 36.2 Junction City (R-D) 306.0 25.5 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 0 A .1 .1 .3 .8 1.5 1.6 1.2 .4 .1 A Total /IT / 417.4 49.3 Hayfork (R-D) 1,075.0 89.6 89.6 Trinity Forest (V-D) 43.1 .8 1.0 1.9 2.2 4.1 6.4 8.3 9.1 5.1 2.2 1.2 .6 Rte 3 (T-D) 14.8 0 A .1 .3 .8 2.0 3.5 3.7 3.0 1.0 .2 .1 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 .4 .6 .6 1.8 1.9 2.7 3.5 3.5 1.4 .4 .1 Total 934.8 101.6 Trinity Center (R-D) 205.9 17.2 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 0 A A .1 .2 .4 .7 .7 .6 .2 A A Total 313.7 40.0 Weavervllle (R-D) 1,072.1 89.3 89.3 Weavervllle Joss House SHP (V-D) 26.9 .4 .6 1.3 1.3 2.3 3.2 4.6 5.6 3.7 1.9 1.1 .8 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 0 A .2 .3 .9 2.4 4.3 4.6 3.7 1.2 .3 .1 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.