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A multiple-objective planning methodology for information service managers
A MULTIPLE-G3JECTIVE PLANNING METHODOLOGY FOR INFORMATION SERVICE MANAGERS J. GROSSand 3. TALAVAGE Purdue University, Lafayette, IN 47907,U.S.A.
Abstract-The problem of aIlocation of scarce resources in an organi~tion is frequently complicated by the presence of m~tipl~, often co~icting, managerial objectives and a high degree of ambiguity in the defi~tion of the orga~~tion’s purpose. This is p~ticuI~ly true within the operating environment of many public and privately operated i~ormation centers and special hbraries. in recent years, the managers of such centers have been pressed by both the funders and the users of their services to improve the efficiency of their operations. ~thou~ techniques are available for dete~ining and evaluating various measures of the performance of these centers, relatively little has been a~compiished with respect to the more fundamental decision making problem of allocating resources in order to optimize the achievement level of the various objectives of the decision maker. Tbe problem addressed in this research is the extension of existing techniques to more adequately deal with the resource allocation problem in an ambiguous environment. The technique known as goal programming is extended and a new methodology, termed goal-range pro~amming, is presented. The goal-range pro~ammi~ meth~ology is related to the information center planing environment trough examples derived from the inte~~tion of the authors with several centers.
In recent years, the increasing problem of scarcity of resources in both private and publicly
funded organizations has resulted in renewed interest in the development of practical techniques for improving the efficiency with which those resources are employed. Of particular interest in this research is the manner in which this problem of allocating scarce resources may be approached within the sometimes ambiguous planning environment of a library or information center. Managers of such organizations are being pressed to justify expenditures in terms which clearly demonstrate the value of their services. Many i~orma~on center managers are, for the first time, directly confronted with the economic fact of scarcity and they are being forced to devote more attention to the problem of empkrying the avaiiable resources in the most effective manner. As noted by GODDARDEII, two basic problems which must be addressed in response to this problem are: (a) what should be the objectives of the organization when it is forced to choose from among alternative activities and (b) how can resources be allocated to best achieve those objectives? Attention to the question of objectives and resource allocation has resulted in a number of decision analysis models designed to deal with various aspects of the operation of libraries and isolation centers. Decision analysis models provide a method, procedure, or technique designed to offer assistance to decision makers in the improvement of their choice behavior. The basic assumptions for the use of such models is that the decision maker anticipates the decision (e.g. decisions about future activities rather than ‘*onthe spot” decisions) and is able to be explicit (e.g. assign numerical values) about the pertinent aspects of the decision situation. In general terms, decision analysis techniques seek to express the relevant aspects of a real system in terms of a mathematical model. This model may then be manipulated to determine the effects of alternative actions available to the decision maker or may be used to provide the decision maker with a strategy or operating plan which is, in some sense, optimal. The model is p~icul~~y useful when similar m~ipuIations or changes in the configuration of the real system would be overly disruptive or costly. The results of actions taken on the model may be
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J. TALAVAGE
observed and compared and, depending on the accuracy of the model, inferences regarding the impact of decisions on the real system may be made. Some of these models are discussed later. However, nearly all such models consider the center as having a single objective. Real world allocation problems are complicated by the presence of a number of objectives, rather than a single one, and the fact that some of the objectives are in conflict. For example, a manager may wish to maximize profits, cut costs and provide a high level of service all at the same time. In most cases, such objectives cannot be achieved simultaneously. The combined problems of scarce resources, confIicting objectives and ambiguity in defining objectives have motivated the development of new pIanning techniques. OBJECTIVE The intent of this paper, then is to develop a methodology that will be useful in resolving the conflicts among the manager’s objectives which arise during the planning process and will obtain an acceptable solution by modeling his preferences concerning those objectives in a realistic fashion. The motivation for this development is the lack of such methodologies to be found in the literature of the information sciences and the shortcomings of applying other existing techniques to this area. The methodology developed in this work, termed goal-range pro~amming (GRP) is compared to other planning techniques, notable goal pro~ammi~ (GP). The advantages of this generalized technique are demonstrated through examples and illustrations. The experience and observations of the authors gained from applying this technique to a specific information center are also described. GENERAL LITERATURE There is a growing pressure from both within and outside the information services profession to adopt the techniques of the management sciences. As GRR[~]states, this pressure has been generated by the success of such techniques in other fields and by their adoption by sponsoring agencies. Further, increasing competition for funding and the increasingly complex and critical nature of decisions concerning new technological options require the adoption of quantitative methods for making decisions. Increasingly, information center managers are being pressed to cut costs, improve efficiency, and justify their existence in terms which are easily understood by higher levels of management. WIL.$ON[~] has noted that 1972 was a turning point for the approach to quantitative analysis in this area. At that time, a need for measuring the effects and contributions of i~ormation products and services had been recognized and analysis techniques became concerned with costs and benefits. As noted by EVANSet al. [4], techniques developed to that time did not seek to measure the “goodness” of services nor to describe the relationship between a given service and the achievement of the goals of management. In fact, in most of the hundreds of studies reviewed by them, objectives were not mentioned and the purpose of the measures being developed was not at all clear. DEPROSPO et al. [5], succeeded in developing measures of several attributes of library user demand, measuring factors such as book circulation, hours, and equipment utilization. They agree, however, that such measures indicated only the use of resources and that the manager must still be responsible for determining the extent to which the objectives of the organization are met. Dealing directly with the evaluation of services in the information center environment, ~USSELMAN and TALAVAGE [6] propose a measurement technique based on three attributes of the service itself: quality from a user’s viewpoint, value to the organization, and effectiveness from a performance standpoint. They further divide each attribute into factors, suggesting such measures as accessibility, applicability, technical quality, timeliness, recall ratio, and precision ratio. They conclude that application of this evaluation methodology will allow the information center manager to recognize when his system is not responding to the needs of those who use it and he will be aware of the direction in which to improve. BAKERand NANCE[~]suggested a library/user/funder model of the behavior of the participants in a university library system. Funders of the library are defined to be those who provide the necessary resources for library operation. The funders of a library typically impose upon the library resource constraints, such as an overall budget, and operational constraints,
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which are usually in the form of guidelines describing acceptable operating characteristics. In addition, the users inthrence the behavior of the library by interacing with the funders and the library itself. In developing two fundamental measures of library effectiveness, RZASA and BAKER[~] build on the assumption that the behavior and utility of a university library is constrained and influenced by actions of its funders and users. They suggest three overall objectives of the library system: (1) Maximize user need satisfaction, (2) minimize time loss to the user, and (3) increase the total number of users. In contrast to these genera1 approaches, LEW et al. 191 have constructed a detailed simulation model of the information center and its interaction with its environment. The model, termed the Information Center Management System (ICMS) model, is a management tool designed to measure the performance of a “simulated” information center which may be used to represent the manager’s own operating environments. This center may have a single objective or a combination of objectives and may be altered by the model-user to evaluate the performance of the counterpart real world system as it currently exists or to evaluate the results of possible changes in system configuration. RESOURCEALLOCATIONLITERATURE COLE[ IO] notes two distinct ways in which effectiveness measures have been used to aid the decision making process. The first of these, employed by ROUSE[~ I], seeks to maximize some measure of effectiveness subject to a set of cost constraints. The second approach, used in the Hamburg study [12], is concerned with developing cost/benefit ratios for each service, then concentrating resources on those services offering the greatest return, With regard to this second technique, Cole states that costs are frequently difficult to determine for each specific activity, adding to the already imposing problem of benefit assessment. She also discusses a goal programming approach in which labor requirements are emphasized. The justification for this emphasis is that labor is the largest cost involved in the operation of the center. The RGP model developed below is able to consider the tradeoff between quality and time objectives, and (as in the examples) to determ~e Iabor requ~ements, but it need not be limited to this. MCGEEHANfl3~ presents a detailed description of the application of goal pro~ammi~ in the planning environment of the Defense ~cumentation Center (DDC). His model approaches the problem of preparing a budget over the DDCs planning period to best achieve their operational goals. The scope of his study is limited to testing the appiication potential of the goal programming methodology for resource allocation and project evaluation. No attempt is made to model the full complexity of the DDCs operation, but a workable, aggregate model is obtained which does succeed in demonstrating the usefulness of this technique. The primary improvements over the DDCs traditional decision making process are listed by McGeehan as: (1) It helps define the decision environment in unambiguous terms. (2) It provides systematic consideration of alternative decision strategies, often involving different levels of m~agement. (3) It ensures that all key eIements are considered each time a decision strategy is evaluated. (4) It creates a documented record of the decision process, and (5) It provides quantitative solutions to management problems. Further, the methodology helps decision makers establish priorities for proposed operating programs and define objectives to justify information products, services and projects. MODEL FORMULATION For the decision analysis models to be discussed in this work, the first step in model formulation is the isolation of the decision variables. Decision variables (sometimes called “control variables”} are those factors over which the decision maker has control and which serve to determine the outcome of the decision. Frequency used decision variables are Anacin resources (dollars) allocated to investment alternatives (physical space, equipment) and man-
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J. GROSSand J. TALAVAGE
power (hours) allocated to specific activities. The second step in the modeling process is to determine the decision maker’s objectives. This constitutes a set of criteria by which the relative merits of alternative decisions may be compared. Typical objectives are: (1) maximizing profit, (2) minimizing cost, (3) maximizing user satisfaction, (4) minimizing response times, and (5) maximizing personnel utilization. Once the objectives have been determined, a set of relationships relating the decision variables with the degree of goal achievement must be determined. Through these relationships, the effect of alternative decisions (a decision is one set of values for the decision variables) on the (modeled) outcomes may be compared and a “best” solution obtained. Determining which solution is “best” is not likely to be a simple task, however, except in very simple cases. When two or more objectives are involved, some assumptions concerning the decision maker’s preferences for the objectives must be incorporated into the model since the objectives may be in confhct. This may be done in a variety of ways. One of these ways is the use of goal programming methodology. GOAL
PROGRAMMING
The concept of an objective in goal programming is explicit and rather intuitive. From IGNIZIO[~~], an objective function is a function fi(X) of the decision variables. Every objective function is associated with an objective equation in one of the forms fi(X) g bi
where bi is a numerical value. Generally, an objective equation expresses an upper bound on available resources or a lower bound on organizational activity. Thus, there is usually a difference between the value of fi(X) and bi. This difference is made explicit by re-expressing the objective equation as
where ni and pi represent the negative and positive deviations of fi(X) from bi. Depending on the manager’s objective and the nature of the objective equation, it is desired to select X so as to: (a) equal or exceed the value of biyor (b) equal or be less than the value of bi, or (c) exactly equal the value of bi. These three representations for objectives correspond to: (a) minimize %, (b) minimize pi, (c) minimize (ni + pi) respectively. Thus, in goal programming, a manager’s objectives are ultimately stated in terms of negative and/or positive deviations in the objective equations. The existence of multiple (conflicting) objectives requires that a priority or relative degree of importance be assigned to the achievement of each one. Stated simply, the decision maker must specify which objectives are more important and which, though desired, are less critical. There are two distinct approaches to this ranking problem which we will denote as the ordinal ranking and cardinal ranking methods. Implementation of goal programming by either method is straightforward when we have: (i) a linear objective function; (ii) a ranking or weighting of the relative importance of the organization’s objectives; and (iii) a numerical value associated with each objective function in an objective equation, where henceforth this value is referred to as a goal. Regarding (i), it is not necessary that the problem be formulated in linear terms. IGNUO[ 141 shows two of many possible solution procedures to the nonlinear goal programming problem. It is the case however that such problems may require more restricted structure in order to be solved by those methods. The specification of goal value mentioned in (iii) implies that the user of a goal program has
A multiple-objective planning methodology for information service managers
I59
explicitly stated those objectives pertinent to the problem. Furthermore, such objectives must be representable in numerical terms. As shown by example later in the paper, this class of objectives does exist and is of great significance to the manager. It cannot be denied though that other objectives exist which are difficult to state in explicit terms, or for which very little or no data for numerical specification is available. The presence of these latter objectives is not compatible with existing goal programming methodology. The specification of the goal is likely to be the most diacult, and frequently most arbitrary, step in developing a goal programming model. The procedure proposed in this paper circumvents some of this difficulty by allowing for a specification of a range of goal values. In order to describe this more general procedure, consider first the ranking methods for goal programming. Ordinal ranking method The ordinal ranking method requires that preemptive priorities be established for the
achievement of the various objectives. The highest priority set of objectives is indicated by P,, the second by PZ, etc. The main concept involved in preemptive priorities is that the achievement of those objectives that have priority level Pi is immeasurably more desired than the achievement of objectives that have level Pi, j > i. That is, the objectives with priority Z’i are preferred, regardless of any multiplier associated with the objectives of priority Pi. There is no tradeoff defined between the two priority levels. McGeehan’s model for the Defense Documentation Center is of this type. A variety of notations may be found in the literature for expressing the general form of this model. That used here is taken from IGNIZI0[14], as it is felt that it most clearly represents the intended meaning of the model. The general form of the goal programming model (with preemptive priorities) is: Find X=(x,,x2 ,..., x,) to minimize d ={b,(Y-,
Y+), bz(Y-, Y’), . . ., bK(Y-, Y’)}
such that: fi(M+Y;-YT=gi
and
i=l,2,...,m
X 7 y- 9 y+zo -
where the dimension of d represents the number (K) of preemptive priority levels among the objectives. bk(Y-, Y’) is a linear function of the deviation vectors Y- and Y’. hl is tr) ‘,c: minimized in a manner discussed below at priority level Pk, in the order (PI, Pz, . . ., PK). In other words, the function bI is associated with the objective that has highest priority, b2 with the second highest priority objective, etc. K I m i.e. the number of priority levels does not exceed the number of objectives. Y- is a m:vector (y;, . . ., y,J of negative deviation from goals. Y+ is a m-vector (y;, . . ., yi) of positive deviations from goals, and fi(X) is the objective function. Let G be the m-vector of measurable.goals, G = (gr, g2, . . . g,,,). G is constant and given. The minimization process for goal programming may be simply stated as follows: (1) Determine the solution(s) to the objective having top priority, (2) Move to the objective(s) having next highest priority and determine the “best” solution(s), where this “best” solution cannot degrade the solution(s) already achieved for higher priority objectives, (3) Repeat step (2) until all priority levels have been investigated. Cardinal ranking method
In the cardinal ranking method of goal programming, the objectives are “weighted” according to their importance. As a result of this weighting of priority levels, a sufficiently large increase in the achievement of a lower level objective can ofset a small gain at a higher priority. The objective function is then simply a sum of functions of the deviation variables (y; and y:, i = 1,2,. . ., m) weighted by their respective priorities. This may be written as:
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160
Minimize a = w,(b,(Y-, Y’))+w&(Y-,
Y+))+...+
w&b&Y-,
Y’))
such that: i=1,2,...,m
f{(X)+yf-y:=gi x, Y-, Y’rO
(In our case, the functions of fi(Z) will be limited to linear functions of _%,though more general forms are possible (see IGNIZIO[141).) As a practical matter, this cardinal ranking approach is frequently employed simply because it is readily adapted to standard Linear Pro~amming package (e.g. GIBES[ 151).Further, cardinal priorities may be used to approximate ordinal priorities by making the ration wi/wi+,sufficiently large so that more important objectives will be achieved before lower level ones are considered. Gibbs states that this approach, by making tradeoffs between objectives explicit, provides a more “finely tuned” result and employs it in his analysis of alternative configurations for a corporate systems analyst training program. In the vernacular of multiattribute utility theory, models employing the cardinal-ranking approach are termed “compensatory” models, implying that su~cient gains at some priority level may compensate for deficiencies elsewhere. DYER[~~] states that “the conditions that would justify the use of a non-compensatory model are very strict, and are unlikely to be met in a significant number of real-world multiple objective applications”. Based on these considerations, the model presented here will be compensatory. As it stands above, there is one practical shortcoming with GP models. That is, the specification of a single target value or goal by the manager may be perceived by him as difficult and unrealistic. In fact, the decision maker probably has some acceptable range of values for each goal. As long as the level of goal at~inment is within this range, the decision maker is satisfied. The extension of GP to allow the manager-user to specify and efficiently use a range of satisfactory goal values is the subject of the next sections. GOAL-RANGE
PROGRAMMING
The
motivation for a modification to conventional GP has been given above. This modification is referred to here as Goal-Range Programming, or GRP. The GRP model as used in this paper is a highly simplified version of a much more comprehensive model and solution procedure described by DAVIS and TALAVAGE[ 171. That comprehensive model and solution procedure was used to investigate information flow in a three level organization where one or more managers acted as mediators between their subordinates who proposed work activities and a superior who established overall (i.e. organizational) goals. Our simplification consists of limiting the number of managers to one, and further assuming that the subordinate work activities are already specified. Further, the nature of the superior’s interaction with the manager is restricted to the presence of the objective equation shown in the following model formulation. GENERAL The
FORh4 OF GRP MODEL.
general form of the GRP model is:
Minimize C,G+ W+Y++ W-Ysubject to AX+Y--Y+=G
and PGsGo x,y-,Y’rO
where Go is an mo-vector of “overall goals”. As noted below, “overall goals” may be interpreted as the upper and lower limits for the goals within which ~ff~i~~ffcf~~y performance is
A mukiple-objective planning methodology for information service managers
161
obtained, G is an m-vector of goals satisfying PC 5 Go, P is an mo X m matrix of coefficients relating the goal vector, G, to the overall goals, Go. C, is an m-vector of costs assigned to the goals, G. W’ is a vector of weights for the positive deviations and W- is a vector of weights for the negative deviations. The set of equations represented by PG cr GO,specifies what is termed the acceptable goal space. This region may result from the relationship of the manager’s goals to those of the overall organization, uncertainty on the manager’s part, or changes in the tradeoffs among goals at certain points. That is, GO may represent the overall goals of the orga~~tion such as specified annual growth rate or a specified profit margin. The relations~p PC 5 Go then relates “controllable” target variables such as manpower levels or project expenditures to the overall goals. Or, as in the example to follow, the manager may be uncertain or ambiguous as to specific goal values. Rather, he may be more willing to specify a desirable range of such values. The PG 5 Go relationships allow the expression of just such a set of desired ranges. The equation AX + Y- - Y+ = G represents part of the set of objective equations, as for conventional GP. (Our procedure reduces to conventional GP when C1 is zero and the feasible space of PC I GO is a unit set.) The weights W’ and W- are interpreted as “penalty costs” for deviations from goals just as for compensatory goal programming. The vector Cr is used to express preferences and tradeoffs concerning the goals within the limits prescribed by PG I Go. The values of C, are, in general, considerably smaller than W’ and W-. Thus, the solution ~o~thrn (based on Dar&zig-Wolfe decomposition procedures) attempts mainly to minimize the weighted deviations from the target values for the goats, with some consideration being given to optimizing by reducing CrG. GOAL-RANGE
PROGRAMMING-EXAMPLE
We will model a resource allocation problem with regard to the allocation of labor hours (manpower) among various activities in an information center on a semi-annual basis. This is not unrealistic as labor is frequently the most expensive resource of an information center. The manager of this example information center is concerned with objectives related to “circulation”, “response time”, and “relevance” performance measures. He also has objectives concerning “total personnel” and mi~mum stafFing levefs on certain activities. The objective functions are linear, and deviations from the goals are assigned weights by the manager. Although the example problem examined here does not represent any specific center, the relationships and data were based on the interactions of the authors with two existing information centers. For this example, we will define the following decision variables: xl = man-hours (in thousands) allocated to “acquisition research” and related activities which are intended to enhance the quality (in terms of usefulness to users) of newly acquired items, x2 = manhours (in thousands) allocated to answering “reference questions” and closely related activities, x3 = manhours (in thousands) allocated to “cataloging” activities, x4 = man-hours (in thousands) allocated to “retrieval” activities, xs = man-hours (in thousands) allocated to secretarial and “support” activities, xg = man-hours (in thousands) required by managerial and administrative personnel. The goals of the manager have been determined to be as follows: (1) Achieve a circulation measure, defined as “average number of circulations per newly acquired item in the first month”, at a value between 3.2 and 4.2. (2) Obtain a relevance measure (an index obtained via a questionnaire of the center’s users) at a value between 55 and 75%. (3) Provide an average response time (for serving reference questions) between 5.5 and 6.5 hr. (4) Do not exceed a salary budget range of $72,500 to $77,500 over the planning period (six months). (5) Up to 200 hr of secretarial and support activities is acceptable. (6) Up to 200 hr of managerial time is acceptable. (7) The number of staff should be between 11 and 13. (8) Due to other considerations, at least 1000hr of “cataloging” activity must be inchrded.
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(9) At least 1000hr of “management and administrative” duties must be included. ~termining the relationship between the decision variables, X, and the achievement of the goals, G, in mathematical terms may require a good deal of thought and analysis. For certain objectives, such as “response time”, concepts from specific areas of operations research, such as queueing theory, may provide the relationships. In other cases, linear regression techniques may provide the relationships. Inevitably, however, certain relationships will be necessarily specified by the manager’s judgment. In our example, goals 5, 6, 8 and 9 are of this nature. This is not undesirable, however, as frequently the manager engaged in the modeling effort can draw upon past experience and knowIedge of special constraints to arrive at reasonably accurate relationships. For the purposes of the present example, we will assume that all of that work has been accomplished, and that the results obtained are as follows: (1) It has been found that the circulation of new items is directly dependent on the amount of time devoted to “acquisition research”. The relationship which we will assume to hold for this example is: cl = -18.3+ 10.4~1 where cl represents the “average number of circulations per newly acquired item in the first month”. (2) Similarly, the subject of this example has observed a distinct relationship between the time spent in answering reference questions and the fraction of the references which prove to be relevant to the user’s needs. By fitting a linear regression model to data collected by the manager he has expressed the relevance of materials obtained as: r2 = 0.05 + 0.194x2. (3) The average turn~ound time to inqu~ies will be assumed to depend on the manpower to cataloging and retrieval activities. t3 = 12.375- 0.25~3- 2x.,. (4) The manager has a budget which constrains the manpower available to him, resulting in the relationship:
where the coefficients represent hourly pay rates. (5) The manager of this center has by experience obtained an appreciation for the amount of secretarial and support work required for other personnel to perform their duties and has arrived at a goal: x5 = 0.1x, +0.1x*+0.3x6. (6) Further, the managerial and administrative requirement is: & = 0.2(x, + x2 + x3
+ x4).
(7) Total staff is desired to be:
To allow for the possibility that not all of these goals wil1 be achieved, positive and negative deviations are introduced to arrive at the following:
10.4x,- 18.3+~;-~;=~,
A multiple-objective planning methodology for information service managers
0.194x,+o.o5+y;-y;=g* 0.25x,+2x,-12.375+y;-y;=g3 6.6~r + 6.6~2+6.0~3+6.0~4+5.0x*+7.8~6tY; - Y; =g4 -O.lx,-O.lx*+x~-0.3x~+y;-yf=g~ -O.Zxr - 0.2~~-0.2x3 - 0.2x4-I-x6 + y; - y$ = g6 x,+x*+xj+x4+xg+xg+y;-y;=g,
163
(2) (3) (4)
(5) (6) (7)
x3+Yi-YB+=g*
(8)
xs+YG-Y!z=f$
(9)
The goal-range pro~amming formulation requires the spec~cation of the W+ and Wvectors. Recall that the objective function includes W’Y’+ W-Y-, hence the w: and w; represent the relative importance to the decision maker of avoiding a deviation of y: or y;. For example, it is reasonable to assume that positive deviations from a budget goal would be penalized by a high value of w:, particularly if funds are scarce. In many cases, however, a negative deviation for this goal would be acceptable, as this would make funds available for other expenses. For this example, let W’ = (O,O,O,50,5,100,100,0,0) and w-=(1,10,2,0,10,100,100,1000,1000). The relationships to be represented by PG s GOwill define the ranges of the target vaiues or goals that the manager perceives as being satisfactory: 21.5sgr ~22.5 0.5 5 g2 5 0.7 5.875 I g3 5 6.875 72.5 I g., 5 77.5 OIgs10.2 OSggIO.2 llSg7Il3 g,= 1 gg= 1. (Note that the first three inequalities above have values which result from combining the values of goals and constants in the corresponding equations.) Further, the manager has decided that a unit increase (or decrease in g3, response time) in any of the first four goals is equally preferable, that is the value of a unit change is the same for each goal. This is unlikely to occur in practice, but it will suffice for this exampk. Thus, we have:
The vector Cr will push the goals toward more desired levels, but not at undue expense to other goals which are not yet achieved.
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164
The GRP formulation of this example is completely specified as: Minimize C,G + W+Y++ W-Y-
subject to AX+Y--Y+=G PG%Go
and
where:
10.4 0 0 6.6 -0.1 -0.2 _ 1
A=
0 0.194 0 6.6 -0.1 - 0.2 1
0
0
0
0
0
0
0 0
0 0
0.25 6.0 0 0.2 1
2.0 6.0 0 - 0.2 1
5.0
7.8
1 0 1
.0.3
1 1 _
W’ = (O,O,0,50,5, 100, lOO,O,0) w- = (1, 10,2,0,10,100,100,1000,1000)
P=
1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -0
0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
and G/, = (22.5, -21.5,0.7, -0.5,6.875, -5.875,77.5, -72.5,0.2,0,0.2,0,13,
-11,
1,
1)
The interpretation of the GRP solution of Table 1 may be summarized as follows: (1) Circulation was achieved at a level of 3.2, within the manager’s “reasonable range”. (2) The relevance goal was underachieved. The current result is 53%. (3) Response time is 6.5 hr, still within the manager’s “reasonable range”. (4) The budget was decreased to 72.5 and still underspent by 1.71, resulting in a net expenditure of 70.79. (5) The secretarial and support activity is not in excess. (6) The ratio of management to staff hours is met. (7) The number of stti is 11. (8) The cataloging activity is maintained at 1000. (9) The minimum of managerial time is exceeded.
A multiple-objective planning methodology for information service managers RESULTS
165
AND ANALYSIS
The optimal solution to the above example was obtained using the Davis-Talavage algorithm described in [17] and is summarized in Table 1. Table 1. Optimal solution to goal-range programming formulation (dollars and man-hours in thousands)
xl = 2.067
x4 = 2.81 xg = 0.956 xgj = 1.67
x2 = 2.48 x3 =
1.0
cr = 3.2(y; = y; = 0) rz = os3(y: = 0, y; = 0.017) fX= 6.5(y; = y: = 0) bc,= 72S(yQ = 0, y; = 1.71)
x5 = 0.956(y; = y; =0):(0.1x, +0.1x2 +0.3x6= 0.956) xg = 1.67(y; = y; = O);(x, +x2 +x3+ x7 =
x4 =
8.357)
ll(y; = y? = 0)
gs=f.qysf=ya=O) g, = l.O(ys+= 0.67, yp = 0)
This same problem was solved using conventional goal programming methods with the following goals or targets; G’= (21.8, 0.7, 6.375, 75, 0,0, 12, 1, 1). The results are shown in Table 2. The inte~retation of the conventions goal pro~amming may be summ~ized as follows: (I) The circulation goal of 3.5 was achieved. (2) The relevance goal of 0.75 was underachieved by 0.328 at 0.422. (3) A response time of 6.0 hr was achieved. (4) The budget of 75.0 was met exactly.
Table 2. Optimal solution to goal programming (dollars and man-hours in thousands)
xr = 2.09 X2= 1.91 XI,= 1.0
x4 = 3.06 x5=2.31 x6 = 1.61
cr = 3.5(yT = y; = 0) r2 = 0.422(y; = 0, y; = 0.328) f3 =
6.O(y: = y; = 0)
bq = 75.O(y: = y; = 0)
xg = 2.3l(y: = 1.42, y; = 0) xg = 1.61(y6+= y; = 0) x7
=
12(y: = y; = 0)
gs = I.o(ys+= ys = 0) gg= l*qy~=o*~5,y~=o)
J. GROSS and I.
166
TALAVAGE
The secretarial and support activity is overstaffed by 1420hr. (6) The ratio of managerial hours to staff is met exactly. (7) The desired number of personnel (12) is met exactly. (8) The constraint on cataloging is met exactly. (9) The constraint on managerial hours is met, and exceeded by 665. In comparing the two solutions, some points become evident. First, any goals that were achieved in the GP formulation appeared within the “reasonable range” of the GRP model. Second, as in the case of the second goal, some levels of goal achievement were improved in the GRP model even though the ultimate goal could not be attained. Third, the improved flexib~ity of the GRP model allowed one goal (gs) to be met which previously was not. The authors are aware that the solution reached by the GRP formulation could have been obtained by a “conventional” GP model with multiple iterations or with appropriate goals and weights defined. The point to be made here is that the GRP model more accurately portrays the decision maker’s perceptions of the situation facing him and the “satisficing” manner in which actual problems are solved. (5)
GOAL-RANGE PROGRAMMfNG-APPLICATION
The GRP model was applied to aid the budgeting decisions for a large information center of a multinational oil company. The budget for this center exhibited three major functional categories; namely, services, operations, and projects. Manpower and budget resources were to be allocated among these categories. There was extensive interaction with the center personnel to establish the range of target values for each goal as well as to establish relationships between resources to be allocated and target value ranges. The manpower and budget data provided by the company (as well as a prioritized list of projects for the coming year) is being treated as propriet~y formation. However, the situation can be summarized as follows: -Man-hours of each of three categories of personnel are to be allocated -Personnel are to be allocated among the service and operation functions (as well as among twenty-eight (28) projects, each project being for either service (5) or operation (23) function) -A target value range is specified for each personnel category-function combination, as well as for budget for each function -Forty-one (41) relationships exist among manpower, budgets, and projects -Nine (9) projects have distinguishably higher priority than others A very si~~~nt difference between the formuIation of this problem and of the example problem above arises from the “go-no go” nature of the proposed projects. However, it was a fairly simple process to transform this formulation of the GRP problem so that it could be solved by using a mixed integer program, MIPZI. The form of a typical solution is shown in Table 3. The problem was solved for various levels of target budget. The information center management was interested, for example, in one of the analysis results which showed the “lowest” level of target budget at which some projects would have to be cancelled. Table 3. GRP model solution for target-budget= $3~,~ Projects-Three (3) projects not funded includingthe most expensive project and two (2) low priorityprojects Daily
Daily Plus Project
Service -Professional man-hogs --Clerical man-hours -Vocational man-hours
3854 6500 1300
3975 6566 1300
Operations iProfessional man-hours -Clerical man-hours -Vocational man-hours
1879 17088 1700
2430 17850 1700
Budget= $300,000
A multiple-objective planning methodology for information service managers
167
CONCLUSIONS
This paper has presented a methodology which improves upon goal programming as it has been applied to the resource allocation problem in the information center decision environment. This approach is felt to more accurately portray the decision maker’s assessment of the situation in the sense that he is encouraged to express a range of satisfactory goal values and is provided with a methodology that employs those ranges in an efficient manner. Acknowledgement-This work was supported by part of a grant from the National Science Foundation, Division of Information Science and Technology, Grant No. DSI75-14772.
REFERENCES
[1] HAYNES CARSON, GODDARD,A Study in the Theory and Measurement of Benefits and Costs in the Public Library, Ph.D. Dissertation,Indiana University, 1970. [2] R. H. ORR,Measuring the goodness of library services: a general framework for considering quantitative measures. J. Docum. 1973,29, (3), 315-330. [3] JOHN H. WILSON, JR., Costs, budgeting and economics of information processing. Annual Review of Information
Science and Technology, Vol. 7, pp. 39-67. Washington, D.C., American Society for Information Science (1972). [4] EDWARDEVANS et al., Review of the criteria used to measure library effectiveness. Bull. Med. Library Assoc. 1972, 60, (1), 102-110. [5] ERNEST DEPROSPO et al., Performance measures for public libraries. Public Library Association, American Library Association, Chicago, Illinois, 1973, 71 pp. [6] R. MUSSELMAN and J. TALAVAGE, A managerial tool for evaluating information services. Working Paper, Purdue University, August, 1978. [7] NORMANR. BAKERand RICHARDE. NANCE,Organizational analyses and simulation studies of university libraries: a methodological overview. Iform. Stor. Retr. 1969,5, l-016. [8] PHILIPV. RZASA and NORMAN R. BAKER,Measures of effectiveness for a university library. Paper for the 39th Ann. ORSA Meeting, Dallas, Texas. [9] DAVID L. LEVY, JOSEPHJ. TALAVAGEand FERD L. LEIMKUHLER,A planningmodel for the financing of information centers. Rep. No. 1, NSF Grant DSI75-14772, Purdue, W. Lafayette, Indiana. [lo] DIANE D. COLE,Mathematical models in library management: planning, analysis and cost assessment. Ph.D. Dissertation, University of Texas at Austin, Austin, Texas, 1976. [11] WILLIAM B. ROUSE, Optimal resource allocation in library systems. J. Am. Sot. Inform. Sci. 1975, 26(3), 157-164. [12] MORRISHAMBURG, R. C. CLELLAND,M. BOMMER,L. RAMIST and R. WHITEFIELD,Lib. Plan. Decision Making Systems, 274 pp. MIT Press, Cambridge, Mass. (1974). [ 131 THOMASMCGEEHAN,Decision analysis technique for program *valuation (goal programming). Defense Documentation Center, Alexandria, Virginia, ADO38800, April 1977. [14] J. P. IGNIZIO,Goal Programming and Extensions, Vol. 1. Heath, Lexington, Mass. (1976). [ 151 THOMASE. GIBBS,Goal programming. J. Systems Management May 1973,38-41. [16] JAMES S. DYER, On the Relationship between goal programming and multiattribute utility theory. Discussion Paper No. 69, Oct. 1977. [17] WAYNE DAVIS and J. TALAVAGE, Three level models for hierarchical coordination. Omega 1977, 5(6), I-12.
Abstract-The problem of aIlocation of scarce resources in an organi~tion is frequently complicated by the presence of m~tipl~, often co~icting, managerial objectives and a high degree of ambiguity in the defi~tion of the orga~~tion’s purpose. This is p~ticuI~ly true within the operating environment of many public and privately operated i~ormation centers and special hbraries. in recent years, the managers of such centers have been pressed by both the funders and the users of their services to improve the efficiency of their operations. ~thou~ techniques are available for dete~ining and evaluating various measures of the performance of these centers, relatively little has been a~compiished with respect to the more fundamental decision making problem of allocating resources in order to optimize the achievement level of the various objectives of the decision maker. Tbe problem addressed in this research is the extension of existing techniques to more adequately deal with the resource allocation problem in an ambiguous environment. The technique known as goal programming is extended and a new methodology, termed goal-range pro~amming, is presented. The goal-range pro~ammi~ meth~ology is related to the information center planing environment trough examples derived from the inte~~tion of the authors with several centers.
In recent years, the increasing problem of scarcity of resources in both private and publicly
funded organizations has resulted in renewed interest in the development of practical techniques for improving the efficiency with which those resources are employed. Of particular interest in this research is the manner in which this problem of allocating scarce resources may be approached within the sometimes ambiguous planning environment of a library or information center. Managers of such organizations are being pressed to justify expenditures in terms which clearly demonstrate the value of their services. Many i~orma~on center managers are, for the first time, directly confronted with the economic fact of scarcity and they are being forced to devote more attention to the problem of empkrying the avaiiable resources in the most effective manner. As noted by GODDARDEII, two basic problems which must be addressed in response to this problem are: (a) what should be the objectives of the organization when it is forced to choose from among alternative activities and (b) how can resources be allocated to best achieve those objectives? Attention to the question of objectives and resource allocation has resulted in a number of decision analysis models designed to deal with various aspects of the operation of libraries and isolation centers. Decision analysis models provide a method, procedure, or technique designed to offer assistance to decision makers in the improvement of their choice behavior. The basic assumptions for the use of such models is that the decision maker anticipates the decision (e.g. decisions about future activities rather than ‘*onthe spot” decisions) and is able to be explicit (e.g. assign numerical values) about the pertinent aspects of the decision situation. In general terms, decision analysis techniques seek to express the relevant aspects of a real system in terms of a mathematical model. This model may then be manipulated to determine the effects of alternative actions available to the decision maker or may be used to provide the decision maker with a strategy or operating plan which is, in some sense, optimal. The model is p~icul~~y useful when similar m~ipuIations or changes in the configuration of the real system would be overly disruptive or costly. The results of actions taken on the model may be
156
J. GRCSS and
J. TALAVAGE
observed and compared and, depending on the accuracy of the model, inferences regarding the impact of decisions on the real system may be made. Some of these models are discussed later. However, nearly all such models consider the center as having a single objective. Real world allocation problems are complicated by the presence of a number of objectives, rather than a single one, and the fact that some of the objectives are in conflict. For example, a manager may wish to maximize profits, cut costs and provide a high level of service all at the same time. In most cases, such objectives cannot be achieved simultaneously. The combined problems of scarce resources, confIicting objectives and ambiguity in defining objectives have motivated the development of new pIanning techniques. OBJECTIVE The intent of this paper, then is to develop a methodology that will be useful in resolving the conflicts among the manager’s objectives which arise during the planning process and will obtain an acceptable solution by modeling his preferences concerning those objectives in a realistic fashion. The motivation for this development is the lack of such methodologies to be found in the literature of the information sciences and the shortcomings of applying other existing techniques to this area. The methodology developed in this work, termed goal-range pro~amming (GRP) is compared to other planning techniques, notable goal pro~ammi~ (GP). The advantages of this generalized technique are demonstrated through examples and illustrations. The experience and observations of the authors gained from applying this technique to a specific information center are also described. GENERAL LITERATURE There is a growing pressure from both within and outside the information services profession to adopt the techniques of the management sciences. As GRR[~]states, this pressure has been generated by the success of such techniques in other fields and by their adoption by sponsoring agencies. Further, increasing competition for funding and the increasingly complex and critical nature of decisions concerning new technological options require the adoption of quantitative methods for making decisions. Increasingly, information center managers are being pressed to cut costs, improve efficiency, and justify their existence in terms which are easily understood by higher levels of management. WIL.$ON[~] has noted that 1972 was a turning point for the approach to quantitative analysis in this area. At that time, a need for measuring the effects and contributions of i~ormation products and services had been recognized and analysis techniques became concerned with costs and benefits. As noted by EVANSet al. [4], techniques developed to that time did not seek to measure the “goodness” of services nor to describe the relationship between a given service and the achievement of the goals of management. In fact, in most of the hundreds of studies reviewed by them, objectives were not mentioned and the purpose of the measures being developed was not at all clear. DEPROSPO et al. [5], succeeded in developing measures of several attributes of library user demand, measuring factors such as book circulation, hours, and equipment utilization. They agree, however, that such measures indicated only the use of resources and that the manager must still be responsible for determining the extent to which the objectives of the organization are met. Dealing directly with the evaluation of services in the information center environment, ~USSELMAN and TALAVAGE [6] propose a measurement technique based on three attributes of the service itself: quality from a user’s viewpoint, value to the organization, and effectiveness from a performance standpoint. They further divide each attribute into factors, suggesting such measures as accessibility, applicability, technical quality, timeliness, recall ratio, and precision ratio. They conclude that application of this evaluation methodology will allow the information center manager to recognize when his system is not responding to the needs of those who use it and he will be aware of the direction in which to improve. BAKERand NANCE[~]suggested a library/user/funder model of the behavior of the participants in a university library system. Funders of the library are defined to be those who provide the necessary resources for library operation. The funders of a library typically impose upon the library resource constraints, such as an overall budget, and operational constraints,
A multiple-objectiveplanningmethodologyfor informationservice managers
157
which are usually in the form of guidelines describing acceptable operating characteristics. In addition, the users inthrence the behavior of the library by interacing with the funders and the library itself. In developing two fundamental measures of library effectiveness, RZASA and BAKER[~] build on the assumption that the behavior and utility of a university library is constrained and influenced by actions of its funders and users. They suggest three overall objectives of the library system: (1) Maximize user need satisfaction, (2) minimize time loss to the user, and (3) increase the total number of users. In contrast to these genera1 approaches, LEW et al. 191 have constructed a detailed simulation model of the information center and its interaction with its environment. The model, termed the Information Center Management System (ICMS) model, is a management tool designed to measure the performance of a “simulated” information center which may be used to represent the manager’s own operating environments. This center may have a single objective or a combination of objectives and may be altered by the model-user to evaluate the performance of the counterpart real world system as it currently exists or to evaluate the results of possible changes in system configuration. RESOURCEALLOCATIONLITERATURE COLE[ IO] notes two distinct ways in which effectiveness measures have been used to aid the decision making process. The first of these, employed by ROUSE[~ I], seeks to maximize some measure of effectiveness subject to a set of cost constraints. The second approach, used in the Hamburg study [12], is concerned with developing cost/benefit ratios for each service, then concentrating resources on those services offering the greatest return, With regard to this second technique, Cole states that costs are frequently difficult to determine for each specific activity, adding to the already imposing problem of benefit assessment. She also discusses a goal programming approach in which labor requirements are emphasized. The justification for this emphasis is that labor is the largest cost involved in the operation of the center. The RGP model developed below is able to consider the tradeoff between quality and time objectives, and (as in the examples) to determ~e Iabor requ~ements, but it need not be limited to this. MCGEEHANfl3~ presents a detailed description of the application of goal pro~ammi~ in the planning environment of the Defense ~cumentation Center (DDC). His model approaches the problem of preparing a budget over the DDCs planning period to best achieve their operational goals. The scope of his study is limited to testing the appiication potential of the goal programming methodology for resource allocation and project evaluation. No attempt is made to model the full complexity of the DDCs operation, but a workable, aggregate model is obtained which does succeed in demonstrating the usefulness of this technique. The primary improvements over the DDCs traditional decision making process are listed by McGeehan as: (1) It helps define the decision environment in unambiguous terms. (2) It provides systematic consideration of alternative decision strategies, often involving different levels of m~agement. (3) It ensures that all key eIements are considered each time a decision strategy is evaluated. (4) It creates a documented record of the decision process, and (5) It provides quantitative solutions to management problems. Further, the methodology helps decision makers establish priorities for proposed operating programs and define objectives to justify information products, services and projects. MODEL FORMULATION For the decision analysis models to be discussed in this work, the first step in model formulation is the isolation of the decision variables. Decision variables (sometimes called “control variables”} are those factors over which the decision maker has control and which serve to determine the outcome of the decision. Frequency used decision variables are Anacin resources (dollars) allocated to investment alternatives (physical space, equipment) and man-
158
J. GROSSand J. TALAVAGE
power (hours) allocated to specific activities. The second step in the modeling process is to determine the decision maker’s objectives. This constitutes a set of criteria by which the relative merits of alternative decisions may be compared. Typical objectives are: (1) maximizing profit, (2) minimizing cost, (3) maximizing user satisfaction, (4) minimizing response times, and (5) maximizing personnel utilization. Once the objectives have been determined, a set of relationships relating the decision variables with the degree of goal achievement must be determined. Through these relationships, the effect of alternative decisions (a decision is one set of values for the decision variables) on the (modeled) outcomes may be compared and a “best” solution obtained. Determining which solution is “best” is not likely to be a simple task, however, except in very simple cases. When two or more objectives are involved, some assumptions concerning the decision maker’s preferences for the objectives must be incorporated into the model since the objectives may be in confhct. This may be done in a variety of ways. One of these ways is the use of goal programming methodology. GOAL
PROGRAMMING
The concept of an objective in goal programming is explicit and rather intuitive. From IGNIZIO[~~], an objective function is a function fi(X) of the decision variables. Every objective function is associated with an objective equation in one of the forms fi(X) g bi
where bi is a numerical value. Generally, an objective equation expresses an upper bound on available resources or a lower bound on organizational activity. Thus, there is usually a difference between the value of fi(X) and bi. This difference is made explicit by re-expressing the objective equation as
where ni and pi represent the negative and positive deviations of fi(X) from bi. Depending on the manager’s objective and the nature of the objective equation, it is desired to select X so as to: (a) equal or exceed the value of biyor (b) equal or be less than the value of bi, or (c) exactly equal the value of bi. These three representations for objectives correspond to: (a) minimize %, (b) minimize pi, (c) minimize (ni + pi) respectively. Thus, in goal programming, a manager’s objectives are ultimately stated in terms of negative and/or positive deviations in the objective equations. The existence of multiple (conflicting) objectives requires that a priority or relative degree of importance be assigned to the achievement of each one. Stated simply, the decision maker must specify which objectives are more important and which, though desired, are less critical. There are two distinct approaches to this ranking problem which we will denote as the ordinal ranking and cardinal ranking methods. Implementation of goal programming by either method is straightforward when we have: (i) a linear objective function; (ii) a ranking or weighting of the relative importance of the organization’s objectives; and (iii) a numerical value associated with each objective function in an objective equation, where henceforth this value is referred to as a goal. Regarding (i), it is not necessary that the problem be formulated in linear terms. IGNUO[ 141 shows two of many possible solution procedures to the nonlinear goal programming problem. It is the case however that such problems may require more restricted structure in order to be solved by those methods. The specification of goal value mentioned in (iii) implies that the user of a goal program has
A multiple-objective planning methodology for information service managers
I59
explicitly stated those objectives pertinent to the problem. Furthermore, such objectives must be representable in numerical terms. As shown by example later in the paper, this class of objectives does exist and is of great significance to the manager. It cannot be denied though that other objectives exist which are difficult to state in explicit terms, or for which very little or no data for numerical specification is available. The presence of these latter objectives is not compatible with existing goal programming methodology. The specification of the goal is likely to be the most diacult, and frequently most arbitrary, step in developing a goal programming model. The procedure proposed in this paper circumvents some of this difficulty by allowing for a specification of a range of goal values. In order to describe this more general procedure, consider first the ranking methods for goal programming. Ordinal ranking method The ordinal ranking method requires that preemptive priorities be established for the
achievement of the various objectives. The highest priority set of objectives is indicated by P,, the second by PZ, etc. The main concept involved in preemptive priorities is that the achievement of those objectives that have priority level Pi is immeasurably more desired than the achievement of objectives that have level Pi, j > i. That is, the objectives with priority Z’i are preferred, regardless of any multiplier associated with the objectives of priority Pi. There is no tradeoff defined between the two priority levels. McGeehan’s model for the Defense Documentation Center is of this type. A variety of notations may be found in the literature for expressing the general form of this model. That used here is taken from IGNIZI0[14], as it is felt that it most clearly represents the intended meaning of the model. The general form of the goal programming model (with preemptive priorities) is: Find X=(x,,x2 ,..., x,) to minimize d ={b,(Y-,
Y+), bz(Y-, Y’), . . ., bK(Y-, Y’)}
such that: fi(M+Y;-YT=gi
and
i=l,2,...,m
X 7 y- 9 y+zo -
where the dimension of d represents the number (K) of preemptive priority levels among the objectives. bk(Y-, Y’) is a linear function of the deviation vectors Y- and Y’. hl is tr) ‘,c: minimized in a manner discussed below at priority level Pk, in the order (PI, Pz, . . ., PK). In other words, the function bI is associated with the objective that has highest priority, b2 with the second highest priority objective, etc. K I m i.e. the number of priority levels does not exceed the number of objectives. Y- is a m:vector (y;, . . ., y,J of negative deviation from goals. Y+ is a m-vector (y;, . . ., yi) of positive deviations from goals, and fi(X) is the objective function. Let G be the m-vector of measurable.goals, G = (gr, g2, . . . g,,,). G is constant and given. The minimization process for goal programming may be simply stated as follows: (1) Determine the solution(s) to the objective having top priority, (2) Move to the objective(s) having next highest priority and determine the “best” solution(s), where this “best” solution cannot degrade the solution(s) already achieved for higher priority objectives, (3) Repeat step (2) until all priority levels have been investigated. Cardinal ranking method
In the cardinal ranking method of goal programming, the objectives are “weighted” according to their importance. As a result of this weighting of priority levels, a sufficiently large increase in the achievement of a lower level objective can ofset a small gain at a higher priority. The objective function is then simply a sum of functions of the deviation variables (y; and y:, i = 1,2,. . ., m) weighted by their respective priorities. This may be written as:
J. GROSSand J. TALAVAGE
160
Minimize a = w,(b,(Y-, Y’))+w&(Y-,
Y+))+...+
w&b&Y-,
Y’))
such that: i=1,2,...,m
f{(X)+yf-y:=gi x, Y-, Y’rO
(In our case, the functions of fi(Z) will be limited to linear functions of _%,though more general forms are possible (see IGNIZIO[141).) As a practical matter, this cardinal ranking approach is frequently employed simply because it is readily adapted to standard Linear Pro~amming package (e.g. GIBES[ 151).Further, cardinal priorities may be used to approximate ordinal priorities by making the ration wi/wi+,sufficiently large so that more important objectives will be achieved before lower level ones are considered. Gibbs states that this approach, by making tradeoffs between objectives explicit, provides a more “finely tuned” result and employs it in his analysis of alternative configurations for a corporate systems analyst training program. In the vernacular of multiattribute utility theory, models employing the cardinal-ranking approach are termed “compensatory” models, implying that su~cient gains at some priority level may compensate for deficiencies elsewhere. DYER[~~] states that “the conditions that would justify the use of a non-compensatory model are very strict, and are unlikely to be met in a significant number of real-world multiple objective applications”. Based on these considerations, the model presented here will be compensatory. As it stands above, there is one practical shortcoming with GP models. That is, the specification of a single target value or goal by the manager may be perceived by him as difficult and unrealistic. In fact, the decision maker probably has some acceptable range of values for each goal. As long as the level of goal at~inment is within this range, the decision maker is satisfied. The extension of GP to allow the manager-user to specify and efficiently use a range of satisfactory goal values is the subject of the next sections. GOAL-RANGE
PROGRAMMING
The
motivation for a modification to conventional GP has been given above. This modification is referred to here as Goal-Range Programming, or GRP. The GRP model as used in this paper is a highly simplified version of a much more comprehensive model and solution procedure described by DAVIS and TALAVAGE[ 171. That comprehensive model and solution procedure was used to investigate information flow in a three level organization where one or more managers acted as mediators between their subordinates who proposed work activities and a superior who established overall (i.e. organizational) goals. Our simplification consists of limiting the number of managers to one, and further assuming that the subordinate work activities are already specified. Further, the nature of the superior’s interaction with the manager is restricted to the presence of the objective equation shown in the following model formulation. GENERAL The
FORh4 OF GRP MODEL.
general form of the GRP model is:
Minimize C,G+ W+Y++ W-Ysubject to AX+Y--Y+=G
and PGsGo x,y-,Y’rO
where Go is an mo-vector of “overall goals”. As noted below, “overall goals” may be interpreted as the upper and lower limits for the goals within which ~ff~i~~ffcf~~y performance is
A mukiple-objective planning methodology for information service managers
161
obtained, G is an m-vector of goals satisfying PC 5 Go, P is an mo X m matrix of coefficients relating the goal vector, G, to the overall goals, Go. C, is an m-vector of costs assigned to the goals, G. W’ is a vector of weights for the positive deviations and W- is a vector of weights for the negative deviations. The set of equations represented by PG cr GO,specifies what is termed the acceptable goal space. This region may result from the relationship of the manager’s goals to those of the overall organization, uncertainty on the manager’s part, or changes in the tradeoffs among goals at certain points. That is, GO may represent the overall goals of the orga~~tion such as specified annual growth rate or a specified profit margin. The relations~p PC 5 Go then relates “controllable” target variables such as manpower levels or project expenditures to the overall goals. Or, as in the example to follow, the manager may be uncertain or ambiguous as to specific goal values. Rather, he may be more willing to specify a desirable range of such values. The PG 5 Go relationships allow the expression of just such a set of desired ranges. The equation AX + Y- - Y+ = G represents part of the set of objective equations, as for conventional GP. (Our procedure reduces to conventional GP when C1 is zero and the feasible space of PC I GO is a unit set.) The weights W’ and W- are interpreted as “penalty costs” for deviations from goals just as for compensatory goal programming. The vector Cr is used to express preferences and tradeoffs concerning the goals within the limits prescribed by PG I Go. The values of C, are, in general, considerably smaller than W’ and W-. Thus, the solution ~o~thrn (based on Dar&zig-Wolfe decomposition procedures) attempts mainly to minimize the weighted deviations from the target values for the goats, with some consideration being given to optimizing by reducing CrG. GOAL-RANGE
PROGRAMMING-EXAMPLE
We will model a resource allocation problem with regard to the allocation of labor hours (manpower) among various activities in an information center on a semi-annual basis. This is not unrealistic as labor is frequently the most expensive resource of an information center. The manager of this example information center is concerned with objectives related to “circulation”, “response time”, and “relevance” performance measures. He also has objectives concerning “total personnel” and mi~mum stafFing levefs on certain activities. The objective functions are linear, and deviations from the goals are assigned weights by the manager. Although the example problem examined here does not represent any specific center, the relationships and data were based on the interactions of the authors with two existing information centers. For this example, we will define the following decision variables: xl = man-hours (in thousands) allocated to “acquisition research” and related activities which are intended to enhance the quality (in terms of usefulness to users) of newly acquired items, x2 = manhours (in thousands) allocated to answering “reference questions” and closely related activities, x3 = manhours (in thousands) allocated to “cataloging” activities, x4 = man-hours (in thousands) allocated to “retrieval” activities, xs = man-hours (in thousands) allocated to secretarial and “support” activities, xg = man-hours (in thousands) required by managerial and administrative personnel. The goals of the manager have been determined to be as follows: (1) Achieve a circulation measure, defined as “average number of circulations per newly acquired item in the first month”, at a value between 3.2 and 4.2. (2) Obtain a relevance measure (an index obtained via a questionnaire of the center’s users) at a value between 55 and 75%. (3) Provide an average response time (for serving reference questions) between 5.5 and 6.5 hr. (4) Do not exceed a salary budget range of $72,500 to $77,500 over the planning period (six months). (5) Up to 200 hr of secretarial and support activities is acceptable. (6) Up to 200 hr of managerial time is acceptable. (7) The number of staff should be between 11 and 13. (8) Due to other considerations, at least 1000hr of “cataloging” activity must be inchrded.
J. GROSSand J. TALAVAGE
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(9) At least 1000hr of “management and administrative” duties must be included. ~termining the relationship between the decision variables, X, and the achievement of the goals, G, in mathematical terms may require a good deal of thought and analysis. For certain objectives, such as “response time”, concepts from specific areas of operations research, such as queueing theory, may provide the relationships. In other cases, linear regression techniques may provide the relationships. Inevitably, however, certain relationships will be necessarily specified by the manager’s judgment. In our example, goals 5, 6, 8 and 9 are of this nature. This is not undesirable, however, as frequently the manager engaged in the modeling effort can draw upon past experience and knowIedge of special constraints to arrive at reasonably accurate relationships. For the purposes of the present example, we will assume that all of that work has been accomplished, and that the results obtained are as follows: (1) It has been found that the circulation of new items is directly dependent on the amount of time devoted to “acquisition research”. The relationship which we will assume to hold for this example is: cl = -18.3+ 10.4~1 where cl represents the “average number of circulations per newly acquired item in the first month”. (2) Similarly, the subject of this example has observed a distinct relationship between the time spent in answering reference questions and the fraction of the references which prove to be relevant to the user’s needs. By fitting a linear regression model to data collected by the manager he has expressed the relevance of materials obtained as: r2 = 0.05 + 0.194x2. (3) The average turn~ound time to inqu~ies will be assumed to depend on the manpower to cataloging and retrieval activities. t3 = 12.375- 0.25~3- 2x.,. (4) The manager has a budget which constrains the manpower available to him, resulting in the relationship:
where the coefficients represent hourly pay rates. (5) The manager of this center has by experience obtained an appreciation for the amount of secretarial and support work required for other personnel to perform their duties and has arrived at a goal: x5 = 0.1x, +0.1x*+0.3x6. (6) Further, the managerial and administrative requirement is: & = 0.2(x, + x2 + x3
+ x4).
(7) Total staff is desired to be:
To allow for the possibility that not all of these goals wil1 be achieved, positive and negative deviations are introduced to arrive at the following:
10.4x,- 18.3+~;-~;=~,
A multiple-objective planning methodology for information service managers
0.194x,+o.o5+y;-y;=g* 0.25x,+2x,-12.375+y;-y;=g3 6.6~r + 6.6~2+6.0~3+6.0~4+5.0x*+7.8~6tY; - Y; =g4 -O.lx,-O.lx*+x~-0.3x~+y;-yf=g~ -O.Zxr - 0.2~~-0.2x3 - 0.2x4-I-x6 + y; - y$ = g6 x,+x*+xj+x4+xg+xg+y;-y;=g,
163
(2) (3) (4)
(5) (6) (7)
x3+Yi-YB+=g*
(8)
xs+YG-Y!z=f$
(9)
The goal-range pro~amming formulation requires the spec~cation of the W+ and Wvectors. Recall that the objective function includes W’Y’+ W-Y-, hence the w: and w; represent the relative importance to the decision maker of avoiding a deviation of y: or y;. For example, it is reasonable to assume that positive deviations from a budget goal would be penalized by a high value of w:, particularly if funds are scarce. In many cases, however, a negative deviation for this goal would be acceptable, as this would make funds available for other expenses. For this example, let W’ = (O,O,O,50,5,100,100,0,0) and w-=(1,10,2,0,10,100,100,1000,1000). The relationships to be represented by PG s GOwill define the ranges of the target vaiues or goals that the manager perceives as being satisfactory: 21.5sgr ~22.5 0.5 5 g2 5 0.7 5.875 I g3 5 6.875 72.5 I g., 5 77.5 OIgs10.2 OSggIO.2 llSg7Il3 g,= 1 gg= 1. (Note that the first three inequalities above have values which result from combining the values of goals and constants in the corresponding equations.) Further, the manager has decided that a unit increase (or decrease in g3, response time) in any of the first four goals is equally preferable, that is the value of a unit change is the same for each goal. This is unlikely to occur in practice, but it will suffice for this exampk. Thus, we have:
The vector Cr will push the goals toward more desired levels, but not at undue expense to other goals which are not yet achieved.
J. GROSSand J. TALAVAGE
164
The GRP formulation of this example is completely specified as: Minimize C,G + W+Y++ W-Y-
subject to AX+Y--Y+=G PG%Go
and
where:
10.4 0 0 6.6 -0.1 -0.2 _ 1
A=
0 0.194 0 6.6 -0.1 - 0.2 1
0
0
0
0
0
0
0 0
0 0
0.25 6.0 0 0.2 1
2.0 6.0 0 - 0.2 1
5.0
7.8
1 0 1
.0.3
1 1 _
W’ = (O,O,0,50,5, 100, lOO,O,0) w- = (1, 10,2,0,10,100,100,1000,1000)
P=
1 -1 0 0 0 0 0 0 0 0 0 0 0 0 0 -0
0 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 1 -1 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 1 -1 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 1 -1 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 1 -1 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 1 -1 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
and G/, = (22.5, -21.5,0.7, -0.5,6.875, -5.875,77.5, -72.5,0.2,0,0.2,0,13,
-11,
1,
1)
The interpretation of the GRP solution of Table 1 may be summarized as follows: (1) Circulation was achieved at a level of 3.2, within the manager’s “reasonable range”. (2) The relevance goal was underachieved. The current result is 53%. (3) Response time is 6.5 hr, still within the manager’s “reasonable range”. (4) The budget was decreased to 72.5 and still underspent by 1.71, resulting in a net expenditure of 70.79. (5) The secretarial and support activity is not in excess. (6) The ratio of management to staff hours is met. (7) The number of stti is 11. (8) The cataloging activity is maintained at 1000. (9) The minimum of managerial time is exceeded.
A multiple-objective planning methodology for information service managers RESULTS
165
AND ANALYSIS
The optimal solution to the above example was obtained using the Davis-Talavage algorithm described in [17] and is summarized in Table 1. Table 1. Optimal solution to goal-range programming formulation (dollars and man-hours in thousands)
xl = 2.067
x4 = 2.81 xg = 0.956 xgj = 1.67
x2 = 2.48 x3 =
1.0
cr = 3.2(y; = y; = 0) rz = os3(y: = 0, y; = 0.017) fX= 6.5(y; = y: = 0) bc,= 72S(yQ = 0, y; = 1.71)
x5 = 0.956(y; = y; =0):(0.1x, +0.1x2 +0.3x6= 0.956) xg = 1.67(y; = y; = O);(x, +x2 +x3+ x7 =
x4 =
8.357)
ll(y; = y? = 0)
gs=f.qysf=ya=O) g, = l.O(ys+= 0.67, yp = 0)
This same problem was solved using conventional goal programming methods with the following goals or targets; G’= (21.8, 0.7, 6.375, 75, 0,0, 12, 1, 1). The results are shown in Table 2. The inte~retation of the conventions goal pro~amming may be summ~ized as follows: (I) The circulation goal of 3.5 was achieved. (2) The relevance goal of 0.75 was underachieved by 0.328 at 0.422. (3) A response time of 6.0 hr was achieved. (4) The budget of 75.0 was met exactly.
Table 2. Optimal solution to goal programming (dollars and man-hours in thousands)
xr = 2.09 X2= 1.91 XI,= 1.0
x4 = 3.06 x5=2.31 x6 = 1.61
cr = 3.5(yT = y; = 0) r2 = 0.422(y; = 0, y; = 0.328) f3 =
6.O(y: = y; = 0)
bq = 75.O(y: = y; = 0)
xg = 2.3l(y: = 1.42, y; = 0) xg = 1.61(y6+= y; = 0) x7
=
12(y: = y; = 0)
gs = I.o(ys+= ys = 0) gg= l*qy~=o*~5,y~=o)
J. GROSS and I.
166
TALAVAGE
The secretarial and support activity is overstaffed by 1420hr. (6) The ratio of managerial hours to staff is met exactly. (7) The desired number of personnel (12) is met exactly. (8) The constraint on cataloging is met exactly. (9) The constraint on managerial hours is met, and exceeded by 665. In comparing the two solutions, some points become evident. First, any goals that were achieved in the GP formulation appeared within the “reasonable range” of the GRP model. Second, as in the case of the second goal, some levels of goal achievement were improved in the GRP model even though the ultimate goal could not be attained. Third, the improved flexib~ity of the GRP model allowed one goal (gs) to be met which previously was not. The authors are aware that the solution reached by the GRP formulation could have been obtained by a “conventional” GP model with multiple iterations or with appropriate goals and weights defined. The point to be made here is that the GRP model more accurately portrays the decision maker’s perceptions of the situation facing him and the “satisficing” manner in which actual problems are solved. (5)
GOAL-RANGE PROGRAMMfNG-APPLICATION
The GRP model was applied to aid the budgeting decisions for a large information center of a multinational oil company. The budget for this center exhibited three major functional categories; namely, services, operations, and projects. Manpower and budget resources were to be allocated among these categories. There was extensive interaction with the center personnel to establish the range of target values for each goal as well as to establish relationships between resources to be allocated and target value ranges. The manpower and budget data provided by the company (as well as a prioritized list of projects for the coming year) is being treated as propriet~y formation. However, the situation can be summarized as follows: -Man-hours of each of three categories of personnel are to be allocated -Personnel are to be allocated among the service and operation functions (as well as among twenty-eight (28) projects, each project being for either service (5) or operation (23) function) -A target value range is specified for each personnel category-function combination, as well as for budget for each function -Forty-one (41) relationships exist among manpower, budgets, and projects -Nine (9) projects have distinguishably higher priority than others A very si~~~nt difference between the formuIation of this problem and of the example problem above arises from the “go-no go” nature of the proposed projects. However, it was a fairly simple process to transform this formulation of the GRP problem so that it could be solved by using a mixed integer program, MIPZI. The form of a typical solution is shown in Table 3. The problem was solved for various levels of target budget. The information center management was interested, for example, in one of the analysis results which showed the “lowest” level of target budget at which some projects would have to be cancelled. Table 3. GRP model solution for target-budget= $3~,~ Projects-Three (3) projects not funded includingthe most expensive project and two (2) low priorityprojects Daily
Daily Plus Project
Service -Professional man-hogs --Clerical man-hours -Vocational man-hours
3854 6500 1300
3975 6566 1300
Operations iProfessional man-hours -Clerical man-hours -Vocational man-hours
1879 17088 1700
2430 17850 1700
Budget= $300,000
A multiple-objective planning methodology for information service managers
167
CONCLUSIONS
This paper has presented a methodology which improves upon goal programming as it has been applied to the resource allocation problem in the information center decision environment. This approach is felt to more accurately portray the decision maker’s assessment of the situation in the sense that he is encouraged to express a range of satisfactory goal values and is provided with a methodology that employs those ranges in an efficient manner. Acknowledgement-This work was supported by part of a grant from the National Science Foundation, Division of Information Science and Technology, Grant No. DSI75-14772.
REFERENCES
[1] HAYNES CARSON, GODDARD,A Study in the Theory and Measurement of Benefits and Costs in the Public Library, Ph.D. Dissertation,Indiana University, 1970. [2] R. H. ORR,Measuring the goodness of library services: a general framework for considering quantitative measures. J. Docum. 1973,29, (3), 315-330. [3] JOHN H. WILSON, JR., Costs, budgeting and economics of information processing. Annual Review of Information
Science and Technology, Vol. 7, pp. 39-67. Washington, D.C., American Society for Information Science (1972). [4] EDWARDEVANS et al., Review of the criteria used to measure library effectiveness. Bull. Med. Library Assoc. 1972, 60, (1), 102-110. [5] ERNEST DEPROSPO et al., Performance measures for public libraries. Public Library Association, American Library Association, Chicago, Illinois, 1973, 71 pp. [6] R. MUSSELMAN and J. TALAVAGE, A managerial tool for evaluating information services. Working Paper, Purdue University, August, 1978. [7] NORMANR. BAKERand RICHARDE. NANCE,Organizational analyses and simulation studies of university libraries: a methodological overview. Iform. Stor. Retr. 1969,5, l-016. [8] PHILIPV. RZASA and NORMAN R. BAKER,Measures of effectiveness for a university library. Paper for the 39th Ann. ORSA Meeting, Dallas, Texas. [9] DAVID L. LEVY, JOSEPHJ. TALAVAGEand FERD L. LEIMKUHLER,A planningmodel for the financing of information centers. Rep. No. 1, NSF Grant DSI75-14772, Purdue, W. Lafayette, Indiana. [lo] DIANE D. COLE,Mathematical models in library management: planning, analysis and cost assessment. Ph.D. Dissertation, University of Texas at Austin, Austin, Texas, 1976. [11] WILLIAM B. ROUSE, Optimal resource allocation in library systems. J. Am. Sot. Inform. Sci. 1975, 26(3), 157-164. [12] MORRISHAMBURG, R. C. CLELLAND,M. BOMMER,L. RAMIST and R. WHITEFIELD,Lib. Plan. Decision Making Systems, 274 pp. MIT Press, Cambridge, Mass. (1974). [ 131 THOMASMCGEEHAN,Decision analysis technique for program *valuation (goal programming). Defense Documentation Center, Alexandria, Virginia, ADO38800, April 1977. [14] J. P. IGNIZIO,Goal Programming and Extensions, Vol. 1. Heath, Lexington, Mass. (1976). [ 151 THOMASE. GIBBS,Goal programming. J. Systems Management May 1973,38-41. [16] JAMES S. DYER, On the Relationship between goal programming and multiattribute utility theory. Discussion Paper No. 69, Oct. 1977. [17] WAYNE DAVIS and J. TALAVAGE, Three level models for hierarchical coordination. Omega 1977, 5(6), I-12.