College and Research Libraries RICHARD W. TRUESWELL User Circulation Satisfaction vs. Size of Holdings at Three Academic Libraries In an effort to determine certain facts concerning the relation of cir- culation satisfaction to collection size, the author sampled the cclast circulation date" of stack books and of circulated books in three con- siderably different kinds of academic libraries. The experience of these three libraries proved to be surprisingly similar. The author speculates concerning potential uses to which such data might be profitably ap- plied. THE LIBRARY HAs many characteristics similar to the problem and decision cri- teria associated with the typical indus- trial inventory problem. The industrial inventory problem is really one of sup- plying the necessary quantity of the proper goods at the required time and at a minimum cost. Similarly, in the case of the library, it is necessary to provide the correct book when the user needs it, and ideally to have a second book available if desired by other users, all at minimum cost. In library work, some efforts have been directed at determining which books to keep on the shelf, which books to place in temporary or little used stor- age, and which books to weed. The problem is further complicated by the need to provide additional copies of certain volumes to satisfy their high re- quest rates. One approach1 to this problem em- 1 Philip M. Morse, " Prob abilistic Models for Li- brary Oper a tions," Association o f R esearch Libraries Minutes, 63d Meeting (January 1964), 9-19 . Dr. Trueswell ls H ead of the Depart- ment of Industrial Engineering in the Uni- versity of Massachusetts. A portion of the work herein d escrib ed was supported by National Science Foundation Grant GN- 0435. 204 I ploys frequency studies, where counts are made of the number of circulation transactions for certain sampled books. Attempts were then made to relate these frequency counts to book usage and user needs. One of the difficulties en- countered in this approach is that the book card seldom gives a complete his- tory of the transactions for a given book. A frequently used book will, of necessity, require a new book card more frequently than other books, and as each new book card is prepared, the old book card is usually destroyed. Thus relative- ly short transcription histories are usual- ly .available for frequently used books. Another approach2 to finding a pa- rameter for analyzing book usage has involved examining the last or previous circulation date for the book. Books may be categorized by this parameter insofar as there are dates available at which time they previously circulated or, in the case of new books, the time 2 Richa rd W . Trueswell , " D et em1ining the Optima l Number of V olumes for a Library's Core Collection," L ibri, XVI ( 1966 ), 49-60 ; Rich a rd W . Tru eswell , "A Quantitative M eas ure of User Circula tion R equirements and Its Possible Effect on Stack Thinnin g and Multiple Copy D e termin a tion ," American D ocumentation, XVI (January 1965), 20-25; Richard W. Trueswell , " T wo Characteristics of Circulation-and Their Effect on the Possible Imple m e nta tion of a Pun ch ed Card Circula- tion Control System," CRL, XXV (July 1964), 285- 91. User Circulation Satisfaction vs. Size of Holdings I 205 they entered the library. Circulation re- quirements may then be measured ac- cording to this parameter. 3 Figure 1 is a cumulative distribution. function representing a sampling of cir- culation and of stack holdings taken at the Deering Library of Northwestern University. 4 It should be noted that the plot of the circulation sample describes the circulation according to the last cir- culation date parameter. As noted, the plot reveals the percentage having the last circulation date not within the time period indicated; i.e., the percentage of current circulation not previously circu- lated within time "T." For example, only about 7 per cent of the circulation sam- ple had not previously circulated dur- ing the past five years. The stack sam- ple curve represents comparable data taken from a sampling of books in the stacks. Using both curves in Figure 1, it is possible to make such remarks as the following: at the five-year mark on the plot, approximately 7 per cent of the circulation sample had last circulation dates not within five years, or in effect were taken from a subset or portion of the stack population that comprised ap- proximately 40 per cent of the stack holdings; expressed differently, 93 per cent of the circulation came from 60 per cent of the holdings. As a second ex- ample, at the two-year mark the state- ment could be made that 20 per cent of the stack holdings satisfied .approximate- ly 70 per cent of the current circulation sample. From the information provided in Figure 1 it is possible to make state- ments about that portion of current cir- culation that is satisfied by a given per cent of stack holdings. Figure 2 repre- 3 Trueswell, Libri, op. cit.; Trueswell, American Documentation, op. cit.; Richard W. Trueswell, "User behavioral patterns and requirements and their effect on the possible applications of data processing and com- puter techniques in a University Library. " (Doctoral dissertation. Eva nston, Illinois: Northwestern U niver- sity, 1964). 4 Tru eswell, Libri, op. cit. sents a combining of the two curves found on Figure I. Thus we have .de- termined points on the curve in Figure 2 referring to their corresponding values on the stack sample curve and the cir- culation sample curve in Figure 1 for a given time period. For example, in Fig- ure 2 we see that approximately 50 per cent of the holdings satisfy 90 per cent of the circulation requirements. The data in Figures 1 and 2 represent a very small portion or subset of the holdings at the Deering Library at Northwestern University. The stack sample is approximately 1.7 per cent of the holdings in the 820's. Additional work has been in progress at the Goodell Library of the University of Massachusetts and also at the library of Mount Holyoke College. 5 The study at the Goodell Library covered one and one half months and approximately five thousand circulation transactions. These circulation data are plotted on Figure 3 along with stack holdings data and pro- vide some comparison with the very limited data from Northwestern Univer- sity. Note for simplicity the plots now are last circulation date "within" the time period rather than "not within." · Here, for example, 50 per cent of the holdings satisfy approximately 90 per cent of the circulation requirements. Figure 4 shows a curve similar to Figure 2 but .applying to the University of Mas- sachusetts. The U /Mass stack sample was approximately ~~ of 1 per cent of the library's holdings. The sampling procedure leaves some question as to the randomness of the sample because selection from a fixed number of shelves and a fixed indentation on each shelf was used. Figures 5 and 6 contain .a plot of the last circulation dat~ for the Mount Holy- oke College library circulation as re- corded over a four-month period. Ap- proximately nine thousand transactions 5 Ibid. ...., li4 ::2 ,.__, b z ,.__, ::r:: b §; b 0 z 0,) C/) 1:0 li4 0,) b """' < ~ ~ Q ~ z 0 • ,.__, <".1 b ~ < -~ .....:l ~ u ~ 0:::: -~ ~ ,.__, u ~ b ;,.. C/) ~ < c::u .....:1 c;;, c::u 0 ~ z -b ,.__, > c::u < t:),.Q ::r:: c::u ~ ~ c l) ............ 8 C'l 100 80 60 40 20 0 5 FIGURE 1 CIRCULATION AND STACK SAMPLES Deering Library Northwestern University 820's Sta c k Sample Cir c ulat ion Sa mple 10 15 20 25 30 35 4·0 TIME (In Years) " t" 45 50 t- 0 C'( .......... (of) Q() ~ ..... "'ij 0 ::t= '+-. Q 0 ~ ~ N I-( (;) ~ U) c.; I-( ~ ~ ~ ~ U) 0 ..... z -+-=> Q 0 ~ ~ I-( ~ ~ ~ ~ en ~ ~ u c ] p::; I-( u ~ ~ Q .~ 0 C,) ~ ~ ~ D 100 80 60 40 20 0 20 40 FIGURE 2 % CIRCULATION SATISFIED VS . % HOLDINGS FROl\1 WHICH CIRCULATION TAKEN D eering Library Northwestern University 820's 60 80 100 % OF HOLDINGS SATISFYING CIRCULATION ~ w ::::: ~ z @ t > ...... ~ Q '0 u ~ ~ ~ ~ C) \j ~ · ~ ...... < "' :I: ~ -~ w \j ~ ~ p.. ~ ::2 ..... ....;:j < [J) ....:: ~ \..) ~ 0 \j ~ "' ~ ~ --b ~ b..O ~ 0 l) .......... 00 0 0.1 100 80 60 40 20 0 30 GLC CIRCULATION OVERALL 60 90 120 150 0 FIGURE 3 CIRCULATION AND STACK SAMPLES OVERALL Goodell Library University of .Massachus.etts 180 210 CUMULATIVE TIME "t" (MO THS ) 240 270 User C-irculation Satisfaction vs. Size of Holdings I 209 100 80 60 40 20 0 20 40 60 FIG URE 4 %CIRCULATIO N SATISF IED VS . % HOLDI TGS FROM WHICH CIRC UL ATION TAK EN Stack & C irc ulati on Data Good e ll Library U nive rsity of lassachus e tts 80 100 <; OF HOL DIJ\ CS SATI SFYI I'\C CIR C LATIOJ\ were recorded in this sample. Also plot- ted on Figure 5 for comparison is the . last circulation date information for the circulation sample from the Goodell Li- brary and the information from the Deering Library at Northwestern Uni- versity (over a relatively short period of about one or two weeks). It is interesting to note the similarity of these plots, as they represent the ex- periences of three different libraries with widely various collections insofar as to- tal holdings are concerned. The shape of the curves indicates that there are a small number of books at each library which circulate very frequently, and suggests that these books could com- prise a core collection. The stack sample at the Mount Holy- oke library was also taken during the summer months when circulation was at a minimum. These data (approximately 1 per cent of the holdings) were then plotted as shown in Figure 6. The stack sample data were then plotted against the circulation sample data to obtain the plot shown in Figure 7, entitled "Percentage circulation satisfied vs. per- centage holdings from which circula- tion taken." This curve is similar to Figures 2 · and 4 .and illustrates the per- centage of the holdings satisfying a giv- en percentage of circulation. For ex- ample, we note from Figure 7 that ap- proximately 85 per cent of the circula- tion is satisfied by 40 per cent of the holdings. It should be noted that these data are quite different from the data collected for the 820's at Northwestern University. The 820's data were taken from a relatively small sample and were limited to a narrow subject category. It is interesting to observe from Fig- ure 7 and Figure 4 that the plots for the University of Massachusetts library and Mount Holyoke College library are somewhat comparable. Because of this kind of information, it is now possible to define core collections at any desired percentage of circulation 100 ., 80 ...... FIGURE 5 ~ ~ % CIRCULATION WITHIN TIME "t" >-; [--< z ~Mount Holyoke ~ ~ 60 Goodell ( U. :Mass. ) (;C) ~ ~ D ee ring (Northwestern) ........ ::> ~ ~ z ~ 0 ...... [--< ('.) ~ 40 ~ ......:l . .,... ~ ~ ~ u ,.s:) p:; . .,... G ~ ~ ~ Q 20 ~ ~ ~ ~ ~ r:x::: -b ~ 't),£) 10 15 ~ 0 5 ~ ~ c C,) '-... TIME (In Years) "t" 0 ...-i C\1 100 0 30 MHC CIRCULATION OVERALL MHC STACK OVERALL 60 90 120 FIGURE 6 CIRCULATION AND STACK SAMPLES OVERALL i\!fount Holyoke College 150 180 210 CUMULATIVE TIME " t " (MONTHS) e 240 270 Q ~ -~ (/) -~ --< 0) C/) co O':l z ~ 0 ~ -~ E-; ~ -< .....:l ":) 0 ~ u -~ p::; ~ -l,.. u ~ ::5 ~ ~ 0 \,) ~ l,.. ~ ~ ":) ~ 0:::: -b ~ Qi) ~ ......... c v .......... C\l ......-! C\1 100 80 60 40 20 0 20 40 FIGURE 7 % CIRCULATION SATISFIED VS. % I-IOLDINGS FROl\1 WHICH CIRCULATION TAKEN Stack & Circulation Data ~1ount Holyoke College 60 a·o 100 % OF HOLDINGS SATISFYING CIRCULATION User Circulation Satisfaction vs. Size of Holdings I 213 satisfaction. For example, in Figure 7 we could define a core collection com- prised of approximately 60 per cent of the current holdings that would satisfy over 94 per cent of the current circula- tion requirements. Such a core collec- tion could be identified by its last cir- culation date as taken from Figures 3 and 4. The .author is presently exploring the possibility of predicting the stack hold- ings distribution (as shown in Figures 3 and 6 ) utilizing only circulation data. This would require a computer simula- tion technique whereby the cumulative distribution function would be consid- er ed as not changing over time. Circula- tion rates which do vary over time would be used in this simulation. If it were possible to predict the stack holdings distribution for a given library using only circulation data from that li- . brary, it might then be possible to make statements about the size and circula- tion satisfaction rates of a core collec- tion. A . possible inference might be the conclusion for a given class or category of library collection, that the size of the core is a function only of the circulation per month or, in effect, only the circula- tion rate. Thus the size of the core col- lection for a given library user popula- tion would be a function only of the circulation rate expected from that pop- ulation. The actual percentage of total holdings serving as a core collection ( de- fined at a given satisfaction level) might also be used as an index number to measure the ccuse" of the library hold- ings. More work must be done in evaluat- ing the us e of the last circulation date cumulative distribution as a parameter for defining and predicting library cir- culation patterns. Specifically, this sta- tistic might be used for identifying those books requiring multiple copies ; for predicting conversion work loads for changes in classification systems or cir- culation systems, in studies of high use and low use books, for stack thinning, and as a guide in the selection of titles for new libraries. ••