Pergamon Socio-Ectm, Plann. Sci. Vol. 28. No. 3. pp. 197-206. 1994

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Integrating the Analytic Hierarchy Process (AHP) into the Multiobjective Budgeting

Models of Public Sector Organizations ROBERT R. GREENBERGt and THOMAS R. NUNAMAKER

Department of Accounting and Business Law, Washington State University. Pullman. WA 99164-4850. U.S.A.

Abstract--In this research, a multiobjective budgeting approach for governmental and nonprofit organizations is developed and applied to a government-sponsored public radiofl'V facility. The approach is designed to accommodate many features characteristic of the governmental/nonprofit sector such as multiple goals, multiple restricted funding sources, changing funding levels, and lack of data usually needed for model specification. Saaty's eigenvalue method (Analytic Hierarchy Process) is utilized to subjectively estimate selected components ofa multiobjective budgeting model that incorporates multiple restricted funding sources. An interactive interval criterion weights algorithm is then used to generate alternative feasible budgets and assist the decision-maker in selecting a preferred budget allocation.

INTRODUCTION

A difficult problem confronted by most economic entities concerns allocation of scarce budgetary funds among competing activities and functions. This problem is exacerbated in governmental and nonprofit environments by the presence of multiple conflicting objectives, multiple restricted funding sources, and, most importantly, the inability to statistically estimate the contribution of each activity to the organization's goals. Further confounding the issue are the ever-changing funding levels confronted by such organizations, in particular, decreasing funding levels frequently require the difficult tasks of program reduction or elimination, and budget reallocation.

Past research in public sector decision making has often recommended adaptive mathematical programming techniques to assist in the planning process, e.g. [7-9]. A priori, these methods would appear quite useful when allocating scarce resources in a dynamic environment. However, straightforward application of such tools is often hindered since performance data needed to specify certain elements of the models are often inadequate or unknown.

The purpose of this research is thus to develop and apply a multiobjective budgeting approach that attempts to alleviate these problems. In an actual governmental budgeting situation, we use the eigenvalue scaling method of the Analytical Hierarchy Process (AHP) [I l, 12], to subjectively estimate selected components of a budget model where the required historical data are non-existent. Next, multiple restricted funding sources are incorporated into the model. Finally, Steuer's interactive interval criterion weights algorithm (ICWA) [17, 18] is used to generate alternative feasible budgets and assist the decision-maker (DM) in selecting a preferred budget allocation.

The remainder of the paper is organized as follows. The next section delineates the nature of the governmental budgeting process and discusses selected obstacles to implementation of multiobjective programming methods in governmental organizations. The multiobjective budgeting model of an existing governmental organization is then developed. Following this, results of the budgeting process are reported.

Practical implementation issues are then considered after which we offer some brief concluding remarks.

tAuthor to receive correspondence.

SEI~ ~ ..~-E 197

198 Ro~Ear R. GREENBERG and THOMAS R. NLNAMAKER

THE GOVERNMENTAL BUDGETING PROCESS

The multiple objecth'e em'ironment

Multiple objectives tend to predominate in governmental and nonprofit organizations [2]. Focusing on a single criterion as a basis for allocating scarce funds may thus produce a budget allocation resulting in suboptimal achievement on other important objectives. Some form of multiple objective budgeting model is therefore required.

In the present study, the multiobjective budget allocation problem of a university-sponsored public radio/TV facility is examined. The general model is as follows:

Maximize: z~(x), k = I, 2 . . . . . p objectives, (I)

Subject to: g,(x) ~< 0, / = I, 2 . . . . . m constraints,

where x is an (n x / ) vector of decision variables (e.g. departmental budgets) and p is the number of objectives. The p objectives are defined as z = Cx, where C is a (p x n) matrix of contribution coefficients that are assumed known and measurable. When elements of C are estimable, they can then be multiplied by x* to obtain anticipated achievement levels for each budgeted amount.

Past research has generally focused on selection of appropriate preference weights to be used in converting (I) to a single objective problem (e.g. see the review in Ref. [9]). Advances include incorporating AHP into the multiobjective procedure to simplify, yet enhance, the search for a preferred alternative [3, 8]. However, the power of AHP has not been fully exploited in public sector budgeting situations. In public sector environments, operationalizing (i) is difficult since historical performance data needed to statistically estimate C are often unavailable. That is, extant data may be insufficient to estimate the causal relationships between departmental expenditures (inputs) and measurable organizational objectives (outputs) with any acceptable degree of precision.

This difficulty is pervasive in public organizations since output and performance statistics arc not routinely produced by existing governmental fund accounting systems [15]. Management information systems, even when they exist, may be incapable of providing relevant, reliable output data (e.g. [4]). Moreover, the historical time series of relevant output data that are available may be fairly short since output measurement is constantly evolving for many public sector activities. Further, the outputs most relevant to the current period decision may be quite different from those used in prior periods. Thus, an adequate base of the most pertinent output data may not exist at the current time. Such was the case for the public radio/TV facility being examined in the present study.

Absence of objective, measurable data does not preclude the making of resource allocation decisions. However, the ad hoc nature of these decisions often results in a suboptimal allocation of organizational (and, thus, social) resources. This is illustrated in the property rights literature initiated by Alchian and Demsetz [i] which includes analysis of the incentives for goal-maximizing behavior, given differing degrees of ownership attenuation.

In the profit-oriented firm, producing outputs at the efficient price/quantity combination desired by consumers results (or, at least should result) in increased profits to the firm. Unattenuated ownership suggests that shareholders can capture these profits. Computing the manager's compensation as a function of profits mitigates certain agency problems resulting from separation of owner and manager. Accordingly, profit-oriented managers will generally seek to make decisions that meet consumer approval and simultaneously maximize firm profits.

In contrast, managers in the public sector environment would appear to have less incentive to act in an efficiency- or effectiveness-maximizing fashion [16]. The absence of residual claimants (e.g. stockholders), combined with legal constraints on distribution of the firm's resources to manage- ment, suggests that motivating managers to act in a socially-desirable manner is more difficult and ambiguous in the public sector. Absence of the wealth maximization criterion implies that managers will often exhibit dysfunctional behavior since the cost to monitor the social-desirability of their actions (e.g. measure the social contribution of the firm's outputs) is high [5].

As noted by Clarkson [6], nonprofit managers will ignore valuable market information on the use of resources more often than their for-profit counterparts. For example, nonprofit managers tend to use simple rules of thumb in setting salary increases for employees, rather than engaging

Integrating the analytic hierarchy process 199

in costly calculations (to the manager), even though the rules of thumb result in higher total costs to the organization.

Similar observations can be made concerning the prevalence of incremental budgeting techniques in the public sector. Rose-Akerman [10] indicates that mechanistic budgeting approaches and simple rules of thumb used in the United Way resource allocation process should be expected, given the extreme difficulties encountered in measuring the social benefits provided by United Way agencies.

These observations suggest that implementation of model (I) in a public sector organization will require a method enabling the manager to subjectively calculate the matrix of contribution coefficients (C) in a systematic and relatively low cost manner. Achieving this will encourage the use of cost/benefit budgeting methods in public sector organizations.

Saaty and Vargas [13, 14] addressed a similar problem in subjectively estimating input--output coefficients for a national economy by using the eigenvalue scaling method associated with AHP. Their success suggested we employ the same method here to estimate the elements of C.

The multiobjecth'e sohaion technique

Though faced with multiple objectives, most public sector organizations have historically prepared annual budgets in a fairly stable and predictable environment [2]. Recently, however, the financial environment of these organizations has become more challenging. Long-term changes in funding levels from different sources often require both local governmental and nonprofit officials to reassess their priorities and adjust budget allocations accordingly. Prior years' consistently- offered programs and services (and their expenditures) must now be re-evaluated. For instance, reduced federal support for public expenditures such as education, highways and social services has required many public sector organizations to find new funding sources (e.g. raise taxes, obtain new grants, etc.), reduce expenditure budgets for existing departments and programs, or both. Moreover, identification of benefits generated from each expenditure is desirable in order to fully evaluate the effects of budget (re)allocations.

This process requires that measurable organizational objectives (outputs) be defined and causal relationships between inputs and outputs be identified. Additionally, spending priorities must be monitored and revised as political and economic conditions change. As discussed previously, we propose that AHP be used in estimating the causal relationships between inputs and outputs [i.e. to estimate C in (I)]. The specific solution technique used to assist the decision-maker in choosing a preferred alternative must in turn reflect the complex, dynamic environment of public budgeting.

A myriad of adaptive multiobjective techniques might be employed for solving (I). However, as suggested by Reeves and Franz [9], no single solution method is likely to dominate across all decision contexts and individuals. Considering their suggested criteria for selecting an interactive solution approach, we elected the interval criterion weights algorithm (ICWA) developed by Steuer [17, 18] although other adaptive approaches, e.g. [8, 9], could be considered. Note that use of AHP to estimate elements of C addresses the general problem of data insufficiency in public sector decision environments although its use is not restricted by the particular solution procedure chosen for (I).

Rather than relying on prespecified importance weights for each objective (as in, e.g. goal programming), the ICWA employs an iterative search and learning process. Using the ICWA, the DM can examine several budget plans, each of which is developed assuming a different preference function over the set of objectives. Through this process, the DM may gain insight into the feasible combinations of goal achievement and, accordingly, refine his/her subjective importance weights.

The ICWA commences by generating sets of trial weights that span the feasible region in objective space. At each iteration, the DM selects a preferred solution from the trial solutions and the algorithm produces a new set of trial weights centered on the previously preferred weights. In this way, the algorithm focuses on incrementally smaller portions of the feasible region, thereby assisting the DM in selecting a final budget allocation. Moreover, use of the algorithm allows the DM to learn about the possible solutions in the feasible region. The adaptive nature of the procedure thus allows the DM to "'change directions" as additional information regarding the feasible space is received.

200 ROBERT R. GREENBERG and THOMAS R. NUNAMAKER

Table I. Organizational performance m©asures

Performance measure (:~) Abbr¢viation

Cumulative radio audience" (.-~) Average quarter hour radio audience" (.-:) Cumulative television audience b (_-~) Average quarter hour television audience b (:4) Hours of local television programming (:~) Hours of local radio programming (-'6) Hours of instructional programming ( :0

CumRadAud AceQHRad CumTVAud AveQHTV HrsLocTV HrsLocRad HrslnsPro

"Number of listeners (or viewers) aged 12 and over. ~'Numbcr of hou.~holds.

MODEL DEVELOPMENT

As noted, the study organization here is a university-based radio/TV service, composed of the following seven departments:

(I) Public radio. (2) Public television. (3) Television operations. (4) Engineering. (5) Marketing. (6) Business office. (7) Instructional telecommunications.

The organization provides public television and radio services as well as instructional telecommu- nications services for branch campus operations. Some of the organization's seven departments are directly related to these services (such as public TV and public radio), while others serve several areas (such as engineering and marketing).

The organization's general manager (DM) identified p = 7 performance measures (or objectives) as critical to the organization's success (see Table I).t In the budget model, each of the seven performance measures is an objective to be maximized.

Funding necessary to support the organization's activities comes from many sources including private and federal grants, state tax revenues and public donations. In many eases, contributors restrict the use of funds to certain activities and departments of the organization. The DM's problem is to allocate resources from five funding sources among the seven departments in a manner that maximizes the DM's preference weighting over the seven objectives. Each departmen- tal budget is the sum of its budgeted resources from all funds, and is thus defined as:

5

xj= Z x,,, j = l . . . . . 7, i - I

where x,j represents the resource flow to department j from fund i (i = I to 5). Development of the budget model commences with specification of the seven objective functions.

Objective functions Each objective function is a linear combination of the form:

7

".k=~'.CjkXs, k = l . . . . . 7, 1-1

where xj is the total dollars allocated to department j ( j = I . . . . . 7) and c~, is the j th department's marginal contribution per dollar to objective Zk.

AS indicated previously, historical data were unavailable for statistical estimation of the c,k. Instead, the eigenvalue scaling method associated with AHP was used to subjectively measure the DM's relative contribution weights ( ~ ) ; these were, in turn. scaled to yield the c~. For a given objective, the DM considered all pairwise departmental comparisons and, for each pair, evaluated the relative contribution of the departments in attaining the stated objective. This procedure was

1"1t is only coincidence that the number o f performance measures equals the number o f departments in the organization.

I n t e g r a t i n g the ana ly t i c h i e r a r c h y p rocess

Table 2. Contributions to objectives by ,departments' (w,,) I I I I I I I I I I I

Objet:tive k

Department j CumRadAud AveQHRad CumTVAud AveQHTV HrLOCTV HrLocRad HrlnsPro

201

Public radio 47.6% 57.3% 2.8% 2.6% 2.6% 48.4% 3.3% Public "IV 6.7 10.3 50.4 48.2 46.8 2.7 3.3 "IV operations 2.2 4.0 12.5 21. I 2.8 2.7 3.3 Engineering 13.2 10.3 I 1.2 10.2 26.4 23.0 2 I. I Marketing 20.3 10.3 13.8 8.5 9.5 10. I 3.2 Business office 7.9 4.0 7.2 3.5 9.5 10.6 13.0 Instructional

telecommunications 2.2 4.0 2.0 1.8 2.5 2.5 52.8

'Columns may not sum to 100% due to rounding. Key to objectives (see also Table I): CumRadAud = Number of listeners aged 12 and over. AveQHRad - Number of households listening. CumTVAud I= Number of viewers aged 12 and over. AvcQHTV = Number of households watching. HrsLocTV = Hours of local (non-network) programming. HrsLocRad = Hours of local (non-network) programming. HrsInsPro = Hours of instructional support programming.

repeated for each of the seven objectives. The resulting relative contribution weights, t,~ (expressed in percentages), are reported in Table 2.

Note that the w~ differ markedly across the seven criteria. No single department emerges as dominant on all criteria and, with the exception of the business office, all departments rank at least second on one or more criteria. The resulting profiles are quite diverse and demonstrate the complexity of the DM's task.

Reasonable consistency was achieved by the DM in determining the w~ for each objective. In the eigcnvalue scaling technique, consistency is measured by the dominant eigenvalue of the ratio weights matrix. Maximum consistency is indicated by an eigenvalue equal to the rank of the matrix (7, in this case) with less consistency indicated by a larger eigenvalue [I I]. An eigenvalue of less than 8 was obtained for all objectives with the average being 7.6. Consistent results were obtained on the first trial for all objectives except AveQHTV, which required a second evaluation by the DM.

Consider that the H~ in Table 2 are different from the c~ required to estimate the z, and hence solve equation (I). Recall that the c~ represent the change in objective :~ for each dollar change in the budget allocated to a particular department, x s. The ~,~, are simply relative contribution percentages rather than marginal contribution coefficients.

To allow computation of goal achievement levels for each budget generated by the ICWA, the following procedure was thus used to convert the w~ to c,~. Current performance information was used to scale the weights t,,~ such that, given the current departmental funding levels x ; , the linear combination "-'k would equal the current performance on each objective (..- ~,). The scaling factor:

• fk m 7

Y [(w~)(x;)] j - I

was then used to compute department j ' s marginal contribution per dollar to :,:

c,~ = ( s , ) ( , ~ ) .

To illustrate the scaling procedure, consider a budgeting case for an organization with a single performance measure (service hours) and two departments with the following current departmental funding levels: x ; = $100,000 and x~ = $200,000. Given these levels, 5000 service hours (: ;) have been achieved. Using AHP, the DM generates the following relative contribution weights: wl! = 0.4 and ,'2, = 0.6. These weights must be scaled to express each department's contribution to the performance measure (i.e. service hours) for each marginal budget dollar. The scaling procedure computes the hours per budget dollar (HPD) which is then used to determine the scaled contribution weights (c~t and c:t) as follows:

5000 hr s~ = (0.4) ($100,000) + (0.6) ($200,000) = 0.03125 HPD

202 ROBERT R. GRBENBERG and THOMAS R. NUNAMAKER

and

c,j = (0.03125 HPD) (0.4) = 0.0125 HPD,

c:f = (0.03125 HPD)(0 .6 )=0 .01875 HPD.

Note that after scaling, the current funding levels produce the currently achieved performance:

: i = (0.0125 HPD) ($100,000) + (0.01875 HPD) ($200,000) = 5000 hr.

max:

s.t.

C o n s t r a i n t s

The DM expressed a desire to include minimum and maximum attainment levels (.- ~,m and : ~'~') for each objective in order to represent practical ranges over which goal achievement might be desired, or could be expected, based on previous experience. In other applications of the model. goal minima and/or maxima may not be needed, but were included here in response to the DM's wishes.

To assure a minimum level of continuing operations, the DM further specified minimum funding levels (x~ ~") for each department. Additional funding constraints were also required to account for the restricted nature of some funding sources. In this regard, five funds (four restricted, one unrestricted) provide monetary resources to the seven departments. As indicated in Table 3, the restricted funds (i = I . . . . . 4) provide resources to but a subset of the departments.

The DM stipulated that each fund must be fully allocated, resulting in five equality constraints: 7

t,jx,, = f , , i = I . . . . . 5, t - I

where t , is a binary variable (with t,i = I indicating that department j can receive resources from fund i, zero otherwise), and f, is total dollars expected to be available from fund i in the budget period. Note that t,, = I corresponds to these department fund combinations marked with a * in Table 3.

Recall that the departmental budget xj is the sum of its budgeted resources from all funds:

5

x i = Z x , ~, j = l . . . . . 7. i - I

Thus, the final form of the proposed model is as follows:

7

:~ = Z c,,x,, k = I . . . . . 7 , (2) I - I

7

Z ClkX,<~:~ "~, k = I . . . . . 7, I ' 1

7

c,Ax, t> :~ i " k = l . . . . . 7, i - I

T u b l c 3. D e p a r t m e n t a l f u n d i n g by r cs t r i c l cd funds

F u n d ( i )

D~parlmen! ( i ) I 2 .1 4 5

( I J Pub l i c r a d i o " " (2 ) Pub l i c te lev is ion " " (3 ) T c l c v i s h ) n o l ~ r a t i o n s • " (4) E n g i n e e r i n g * * " " • (5) M a r k c i i n 8 " " " " (6J Bu~ines~i

o l l i ce * • • • • (7) In' , t r u c t i o n a l

le le¢, l )mmunx:at ion~, * " •

No te : D e p a r t m e n t s t h a i can rece ive funds a re m a r k e d by *,

Integrating the analytic hierarchy process

Table 4. First iteration budget options

203

I-I

Trial solution

I-2 I-3 I-4

Performance measures (:~): Cure RadAud 52.000 52.000 41,593 44.135 AveQHRad 5100 5019 3995 4410 CumTVAud 44.930 36.645 49.050 48.635 AveQHTV 784 660 850 850 HrLocTV 322 287 368 347 HrLocRad 17,738 19,487 15,066 15.085 HrlnsPro 1438 1800 1200 1800

Departmental budgets ($) (x,): Public radio 278,446 276.351 167.200 214.929 Public TV 436,609 308,442 479,022 493,210 "IV operations 7315 52.872 7315 7315 Engineering 209.000 330.810 314.937 209.000 Marketing 120.705 83.61)0 83.600 83.600 Business office 52.250 52.250 52.250 52.250 Instructional telecommunications 15.675 15.675 15.675 59.689

Key to performance measures: CumRadAud = Number of listeners aged 12 and over. AveQHRad = Number of households listening. CumTVAud = Number of viewers aged 12 and over. AveQHTV = Number of households watching. HrsLocTV = Hours of local (non-networkl programming. HrsLocRad = Hours of local (non-network) programming. HrslnsPro = Hours of instructional support programming.

xj>~xT i", j = l . . . . . 7,

{, t,/x~/=f,, i = l . . . . . 5, t,j= j - I

if./;, can fund department j, 0 otherwise,

x,/~>O, i = l . . . . . 5 ; j = l . . . . . 7.

The interval criterion weights algorithm (ICWA) used in solving (2) consisted of the following steps:

Step !.

Step 2. Step 3.

Step 4. Step 5.

Generate 2p + ! (i.e. 15) sets of trial weights for combining the objectives. Thus, 15 trial linear programs (LPs) with a common feasible region are defined. The 15 trial LPs are solved. Of the 15 trial solutions, select the four maximally dispersed solutions to be presented to the decision-maker. This filtering process allows the DM to focus on a representative subset of solutions rather than requiring comparison of all 15 trial solutions. Filtering was accomplished using the furthest point outside the neighborhoods method [I 8]. The DM selects a preferred solution from the trial subset. If the DM is satisfied with the solution from Step 5, the process terminates. If not, the ICWA specifies 15 sets of new trial weights that are in the region of, and centered on, the previously preferred solution. The process continues with Step 2.

RESULTS

First iteration

The initial solution and filtering process (steps I-3) produced departmental budgets and the corresponding performance measure estimates as displayed in Table 4.

As indicated, each performance measure differed substantially across the four trial solutions. The departmental budget amounts show less variance but each of the four solutions represents a distinct

204 ROaERT R. GREENBERG and THOMAS R. NUNAMAKER

budget profile, Only the business office allocation remains unchanged across all solutions. Trial solution I-I was preferred by the DM.

Second iteration

New trial weights, centering on solution 1-1 (from Table 4), were generated by the ICWA. Again, 15 trial LPs were solved and the new solutions filtered. The four maximally dispersed solutions are presented in Table 5.

Note that solution 2 appears in both Tables 4 and 5. Solutions 1, 3 and 4, however, are new in the second iteration. This is not unexpected since, in the second iteration, the trial solutions span a smaller subset of the feasible region. It may also be noted that the preferred solution in the first iteration (solution I-I in Table 4) does not appear in the second iteration. This solution was indeed generated in the second iteration but eliminated in the filtering process.

The DM preferred solution 2-4 (Table 5), indicating that he was reasonably satisfied with it as a final solution. The process thus terminated at this point.

PRACTICAL IMPLEMENTATION ISSUES

We believe that the general methodology employed here should be usable by most public sector organizations with multiple restricted funding sources and data bases inadequate to statistically estimate necessary output-input relationships. The model's usefulness can, however, be constrained by the organization's size and complexity. If a large number of measurable objectives and/or departments are present, for example, the sheer number of priority comparisons required may overwhelm the decision-maker. If J equals the number of departments involved in the budgct allocation plan and P is the total number of organizational objectives, then the decision- maker must evaluate J P ( P - I ) / 2 comparisons using AHP. Thus, for highly complex budget allocation tasks, model implementation should generally proceed at lower organizational levels. Our restricted applicatum of the model to only the radio/TV services portion of the larger university-wide budget allocation problem is an example of focusing model implementation at lower organizational levels.

Further complicating model development is the possible presence of multiple decision-makers. Use of our technique is enhanced when only a single decision-maker is involved, although, as indicated in the next section, it is possible to generate priority rankings when multiple decision-

Tablc 5. Second iteration budget oplions

Trial solution

2-1 2-2 2-3 2-4

Performance measures (:L): CumRadAud 50.800 52,000 49,403 52.000 AvcQ|I Rad 5100 5019 4958 5100 CamTVAud 47,168 36.645 48.288 41.161 AveQHTV 832 660 850 724 t l rLocTY 337 287 344 298 HrLocRad 17,511 19.487 16.966 17.930 HrlnsPro 1439 1800 1200 1800

Dcpartmcmal budgets ($) (x,): Public radio 278.446 276.351 264.125 2X4.348 Public "IV 473.709 308.442 488.035 389.887 TV opcfalions 7315 52.872 7315 7315 Engineering 209.001) 330.I~ I 0 209,000 2(F),O(Y) Markcling 83.6(R) 83,fX}O 83.600 I 17,47 I Busincss ol6cc 52.250 52.250 52.250 52.250 Inslruclional Iclccommunicalions 15.675 15.675 15.675 59.728

Key Io i~:ri'orman¢¢ measure~: CumRadAud = Number of listener, aged 12 and o~cr. AveQHRad = Number of hou~holds listening. CumTVAud = Number of viewer~ aged 12 and over. AvcOHTV = Number of households walehing HrsLocTV = Hours o f local (non-network) programming. Hr.*LocRad ~ Hours of local (non-nclwork) programming. HrslnsPro ~ Hours of inslruclional support programming.

206 ROBEgT R. GRI~NnEIIG and THOMAS R. NUNAMXKER

(Tables 4 and 5) were helpful in choosing a preferred allocation (implying that A H P was useful in construct ing meaningful indicators o f goal attainment).

Extending the current experience suggests that A H P could be useful in virtually any budgeting planning situation (e.g. capital budgeting, performance budgeting, etc.) where data needed to estimate various ou tpu t - inpu t relationships are generally not available. A H P could be completed by a single person (e.g. a town mayor , the city manager , etc.) then reviewed and approved by a larger legal body (e.g. the city council). For larger governmental organizations, the model would be implemented at lower organizational levels (e.g. police depar tment , fire department , parks and recreation, etc.) as suggested previously. Sensitivity analysis could also be provided by calculating expected at ta inment levels under a variety o f resource allocation plans.

R E F E R E N C E S

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Integrating the analytic hierarchy process 205

makers are present. However, the model is more easily implemented for the single decision-maker situation.

Another difficulty occurs when the organization's total dollars available for allocation changes significantly from year to year. Even after adjusting for inflation, the study organization experienced a sizable increase in total allocable resources over the previous year. This situation led to several goal constraints binding in (2), resulting in unrealistic budget allocations, Upon consultation with the DM, the goal maximums were adjusted upward to account for the expected real increase in total funding.

The DM reported that after viewing the different budget profiles and contemplating the results, the goal achievement levels indicated for each budget were probably attainable. Our adjustment of the goal maximum constraints thus appeared successful in permitting the ICWA to produce a diverse, yet reasonably acceptable set of budget profiles. Conversely. in situations where total budgeted dollars are decreased, some downward adjustment of the goal minimums may be needed to allow for a sufficient range of feasible solutions.

An added complication involves the potential inability of the ICWA to identify a sufficient number of solutions at each iteration so that the DM is provided a reasonable range of choice. That is, the ICWA generates corner-point solutions only. As noted in previous studies [8], depending upon the geometry of the feasible region in certain applications, the number and diversity of solutions produced by the ICWA may be inadequate to allow the DM to find a preferred, or even satisfying, budget allocation. Attempts to alleviate this problem come in at least two forms. First, the ICWA can be discarded in favor of an alternative solution method such as described by OIson et al. [8]; this allows for the DM's utility function to be non-linear. Secondly, given that the ICWA is used as the primary solution technique, intra-set point generation could be performed by constructing linear combinations of corner-point solutions [19]. Used in conjunction with filtering procedures, intra-set point generation should increase the range of candidate solutions and permit a non-linear utility function, In this study, such point generation was not employed since the DM expressed satisfaction with the diversity of solutions presented at each iteration. Moreover, we recall that the generality of our approach is not limited by the multiobjective solution technique (ICWA) employed here. AHP can still be used to overcome data availability problems and generate the basic budget allocation model of (2), independent of the solution technique employed.

A related issue concerns model validation. Since public sector organizations are characterized by an absence of market-based output prices, reference to an external market for model validation is not possible. A more feasible validation procedure would be to ascertain the model's deciMon usefulne.~'s within a variety of judgment situations, in the current study, the DM remarked that the process of prioritizing goals and ranking them against each other was particularly useful in articulating the organization's current goal structure and judging its suitability. Further, the entire process of model building, including final selection of a preferred budget allocation, was not viewed as overly time-consuming, implying its acceptability in aiding preparation of the annual budget.

The DM was comfortable with the final budget allocation. He indicated that certain minor adjustments would be needed prior to its final acceptance. This "fine tuning" is consistent with our intended use of the proposed model as a decision aid rather than a "'panacea" for solving the resource allocation problem. Our experience within the single decision context is thus supportive of the model's usefulness and suggests that additional applications in other contexts would be appropriate.

CONCLUDING REMARKS

In this study, we have utilized multiobjective techniques in developing a budget allocation model for a university-sponsored public radio/TV facility. In doing so, we have successfully confronted the issue of data (un)availability often found in public sector organizations. This was accom- plished by integrating AHP into the budgeting process. Indeed, remarks from the study organiz- ation's DM indicated that the estimated goal achievement levels shown for each budget