College and Research Libraries Selecting a Circulation -Control System: a Mathematical Approach BY FREDERICK RUECKING, JR. AT RicE UNIVERSITY, as at many colleges and universities throughout the country, increasing use of library resources by both faculty and students has necessitated changes in circulation control. The task of selecting a suitable control system is complicated by the lack of a specific method of comparison. The Fry report brings together a considerable mass of data pertaining to control systems, but those data are restricted in value to a sin- gle . point in time and as a general norm for college and university libraries.1 A method of adapting the data to local con- ditions and projecting the results beyond a single point in time is lacking. Faced with this task at Rice Univer- sity, the library administration made an attempt to derive a technique which would ( 1) provide a means of projecting circu- lation and staffing requirements beyond a single point in time; (2) permit the use of Fry's organization and data; ( 3) ad- just Fry's data to local conditions; .and ( 4) produce a more accurate compa.nson of existing systems. The result of th1s ef- fort is a series of equations which are used in the Fondren library analysis of twelve charging systems. This comparative analysis has led to a recommendation to the Rice University administration for the installation of an automatic, punched-card charging system similar to that of the Montclair public li- brary. 2 It is felt that other college and 1 George Fry and Associates, Inc., Study of Cir- culation Control Systems (Chicago: ALA, 1961). 2 International Business Machines Corporation, Cir- culation Records Control by Punched Cards (N.Y., 1946) ; and Ralph H. Parker, Librar(JJ Applications of Punched Cards (Chicago : ALA, 1952) . SEPTEMBER 1964 Mr. Ruecking is Head of the Circulation Department, Fondren Library, Rice Univer- sity. university librarians, facing the problem of selecting a new circulation control system, will find the Rice viewpoin~ of interest and the mathematical technique helpful. HYPOTHESES OF THE STUDY The hypotheses upon which the Rice University study is based may be set forth in five statements. 1. If the conditions (rising enrollment, expansion of the collection, increase . of independent study programs, etc.) whic? affect circulation continue in the same di- rection with the same strength, the annual circulation is predictable by projecting known data. 2. If there is to be accurate compari- son the systems under consideration must be ~ompared on the basis of the same level of effectiveness. 3. A relationship exists between unit operating time (Fry's element time) and system operating time. . 4. Cost estimates for system operatiOn must include the cost of staffing. 5. The final evaluation of any charging system must include its cumulative costs, its benefits, its capabilities for growth, and, especially, its suitability for local conditions. PROJECTING CIRCULATION · If the annual circulation from · previous years at Rice University is plotted as a 385 graph (Fig. 1 a) , a curve resembling an exponential curve is produced. If the same data are plotted on logarithmic paper (Fig. 1b), a straight line may be drawn through the plotted points, suggesting that the Fondren library circulation is increas- ing exponentially. This line may be ex- pressed as a mathematical equation. If X n is the annual circulation, in thou- sands, after n years; X o is the annual cir- culation, in thousands, of the beginning year of the known data; and R IC is the average, annual rate of increase, the equa- tion is as follows : X n = X o (1 + R IC yn (1 ) If X n is extrapolated from the position of the line at a given point within the limits of the known data (such as at A in Fig. 1 b) , the value of R IC can be com- puted as follows: Log (1 + R x) = Log X n- Log . X o (2) n The annual circulation can be projected into the future (points A to B in Fig. 1 b) from equation 1, since R IC and X b are now known. As the report Automation and the Library of Congress implies, an ex- ponential increase could not continue in- definitely.3 At some point in time the ac- 3 U.S . Libra ry of Cong ress . A u tomation and the Library of Congress ( Washington: Government Print- in g Office , 1963 ) . 120 100 ~ 80 j~ _A'r l-A ~"' so ..,~ ~ ' . ...... ~""'" 40 ?~ ~1 c n 20 ·- ·· -- celerated gain will slacken and an ex- ponential regression would occur which would in later years resemble a linear re- gression. THE DOCTRINE OF EQUAL EFFECTIVENESS As charging systems are studied, it is soon evident that a means of providing a common ground of comparison is re- quired . Can one say that system A is the more suitable, being less expensive to operate than system B, although it does not produce the same results? A conclu- sion based upon such comparison is not mathematically valid. The common ground or equal level of effectiveness chosen by the Fondren library consists of six criteria. These are as follows: 1. Elimination of borrower participation in charging transactions. 2. Total random access to the circulation file by a) borrower b) date of issue c) call number d) overdue coding (tab, transaction number, etc.) e) type of record (loans, missing rec- ords, binding records, etc.) 3. Required use of library identification. 4. Rapid updating of the circulation file. .L IL_~ I FIG. la.-Annual circulation in thousands, Fondren library. 386 COLLEGE AND RESEARCH LIBRARIES 400 300 200 II v / B./ / 7 v 100 90 ,/ ~0 ~ ~/~. _/ """- 'I"' 0~~ Va . 7'' / 50 40 30 20 ' I 10 J • ' . ' t l T ~ r • I . "1 ' 1 I" T 1 J J. FIG. lb.-Annual circulation in thousands, Fondren library. 5. Rapid overdue processing. 6. Maintenance of an accurate and or- derly circulation file. Certain systems cannot be manipulated to meet these criteria. In the Fondren li- brary study such systems are eliminated from consideration. Other systems do not meet these criteria, but can be organized so that all six are included. Systems which can be so manipulated are compared in the Fondren library study. UNIT TIME AND OPERATING TIME The compilation of data in the Fry re- SEPTEMBER 1964 port is very useful if one recognizes its limitations. 4 One of these limitations is that the data are not applicable universal- ly. A second limitation is that the data for system A and system B may not be di- rectly comparable, because of the local conditions under which each is operated. A third limitation is the erroneous inter- pretation of the cause of filing and slip- ping time. Despite these limitations, the data may be used to project operating time and costs. The first step is to adjust Fry's data to 4 Fry, Op. cit., pp.49-53. Exhibit IV, A and B. · ' 387 the local situation. Consequently, it is necessary to measure the amount of time required under local conditions to per- form the operations listed. The results ob- tained may be used with Fry's correspond- ing data for the same system to produce a ratio which can be applied to the other systems given by Fry. If E 1 represents Fry's element time for the operation of a specific charging sys- tem, E l represents the element time meas- ured under local conditions; T e represents the element time given by Fry for the same operation of another charging sys- tem; and Tl is the element time for that operation and system under local condi- tions, the conversion equation is as fol- lows: Tl = T e E l E, (3) The data obtained are element times expressed in minutes per transaction. Care must be exercised in utilizing quantities given by Fry, since the proportions to Fry's standard of one thousand loan trans- actions will not apply in all cases. Certaill operations may be excluded from this re- duction ratio as being controlled by fac- tors outside the charging system. The lo- cal situation must be carefully reviewed before Fry's data are applied. The total times obtained from these computations provide a means of com- paring systems, but not at a point in time nor realistically. If one multiplies total element time by the annual circulation, in thousands, as Fry suggests, the product is not operating time. 5 A factor is missing which is controlled by other conditions (the time the desk is open for service, loan policies, etc.). Consequently, an equa- tion which expresses the computation of operating time may be stated. If Y is the operating time in hours; k is the conver- sion factor; X is the annual circulation, in thousands; and Z is the element time in hours per thousand circulation, the equation is as follows: II Jbu{, worksheetS~ ... Y = kXZ (4) The value of k can be approximated from the above equation by substituting ( 1 ) the total staffing, in hours, for sys- tem operation for the previous year for Y; ( 2) the annual circulation, in thou- sands, for the previous year for X; and (3) the measured element time for Z. Use of equation 4 provides a means of examining charging systems on a current basis. It cannot be used to project future operating time requirements. Certain operations are influenced by changes in circulation volume-for ex- ample, filing. It might require two hundred minutes to file one thousand cards into a twenty thousand card file, but if that file is increased to thirty thousand cards, it will require more than two hundred min- utes to file the same one hundred cards- filing time not being a function of a num- ber of cards to be filed, but of the size of the file. The change of element time, produced by a change in circulation volume, is of the same order as the change in circula- tion, but not necessarily of the same value. If other records are included . in the circulation file, it is possible that a 10 per cent increase in circulation might produce only a 6 per cent increase in file size. Consequently, it is necessary to study the comp9sition of the circulation file . · Since element time is subjected to the same kind of increase as circulation, the expansion ·of element time can be ex- pressed mathematically, by referring to equation ·1. Let · Z n be the amount of element time at the end of n years, Z o the element time measured by Fry (adjusted to local con- ditions) and R z the rate with which ele- ment time changes. Then, the equation is as follows : The value of R z can pe approximated by calculating the size of the file, measur- 388 COLLEGE AND RESEARCH LIBRARIES ing the amount of time required to file . a known number of cards, and performing some computations. If F 8 represents the size of the card file at present, F n represents the size of the file inn years, and T1 is the measured filing time required for one thousand cards at the present time, the equation is as follows: (~ - T,) (6) T, As suggested above, a change in cir- culation does not always produce changes in element time for all operations. Conse- quently, equation 5 must be altered to in- clude this variation. If C represents the amount of element time not affected by a ·change in circula- tion volume, then equation 5 must be re- stated as follows: Zn = (Z - C) ( 1 + R zJn - C ( 7) Now it is possible to project staffing re- quirements for any charging system, ad- justed to local conditions, into the future. Substituting equations 1 and 7 in equation . 4, the equation for projection is as fol- lows: Y n = kX o (1 + R xJn [(Zo - C) (1 + R zJn - C) (8) EsTIMATING STAFF CosTs To provide a more accurate means of comparing charging system suitability as well as forecasting budget requirements, the results of equation 8 may be used to predict costs. If the present ratio of full- time and part-time staffing is expected to continue, application of that ratio to Y n produces preliminary cost estimating equations. Let S1 represent the present annual staffing of full-time personnel, in hours, Sp the number of part-time hours used, p n the projected total of full-time needs in n years, and Sn the projected total of part-time hours needed in n years. Two equations may be stated, as follows: SEPTEMBER 1964 Pn = Yn (s, ; Sp) (9) Sn = Yn - Pn (10) Cost estimates can be obtained from these results. If W 8 is the average salary of the full-time staff, and Wp is the aver- age hourly wage, the projected annual cost En is calculated from the following equation: En = W 8 ( 2~;0 ) + WpSn (11) When this expense is added to the charging system cost schedule, as Fry provides, a more accurate comparison of total expense can be made. FINAL EVALUATION A charging system should not be se- lected merely because it is "cheaper" than others. If the selected system does not meet present and future library needs, the choice is poor. Determining the pre- cise needs is the first and most important step of charging system selection. Alter- native systems, regardless of cost, should be examined from the standpoint of suita- bility . The importance of cumulative costs cannot be overlooked. Increases in charg- ing system costs, stemming from circula- tion increases, are minor compared to in- creased costs for additional staff. There is a point in time at which manual meth- ods will become more expensive than mechanized methods, even on an annual cost basis. Similarly, a second point in time exists at which mechanized tech- niques will become more expensive than electronic methods. These points in time are not necessarily the same for all li- braries-the local situation is the con- trolling factor. A subsidiary factor, frequently over- looked in the evaluation of charging sys- tems, are the byproducts-added benefits. The amount of staff time released for other duties is an important benefit and one to which a value cannot always be 389 assigned. By adroit utilization of his staff, the librarian can provide better service to the library's public if the most appro- priate charging system is selected. In some instance the system may re- quire special equipment. Frequently, this equipment can be utilized for noncircula- tion procedures, providing added service to internal library operation. CoNCLUSION The suitability, cumulative cost, and derived benefits of any charging system constitute the determining factors of charg- ing system selection. Any one of these three may have special significance which may represent a controlling or limiting factor. . The Fondren library study reveals that the cumulative costs of a six-year period, including the initial cost of converting the collection to automatic processing, the continuing cost of ffiM rentals, and other expenses, including staff costs, would be the same as, or less than, any manual system-because the departmental staff at Rice University is primarily full-time. The total cumulative cost of the proposed system, by 1980, is estimated to be ap- proximately 50 per cent of the cumula- tive cost of any non-IBM system. Converting the collection at this time and installing the IBM 3 7 5 teleprocessing system will bring about an on-line com- puter application more quickly and make ultimate participation in a national elec- tronic system more feasible. It is our aim and hope to provide detailed studies on our techniques, decision, costs, and ex- periences in converting the collection and operating the proposed system. •• Book Illustration Papers Published 390 Essays on Book Illustration, the lectures presented at the third Rare Book Conference at Coral Gables in 1962, has been published by Verlag Gebr. Mann. 1 Berlin West 62, Hauptstrasse 26, West Germany. The papers were edited by Mrs. Frances J. Brewer, chief of the gifts and rare books division of Detroit public library. Mrs. Brewer was chair- man of ACRL's Rare Books Section at the time of the conference in which the papers were read. The volume is dedicated to Hellmut Lehmann-Haupt in honor of his sixtieth birthday, and includes, in addition to the papers, an annotated Checklist of Hellmut Lehmann- Haupt's Contributions to the Literature of Book Illustration. It is available from the publisher at $10 per copy. • • COLLEGE AND RESEARCH LIBRARIES