Financial planning using goal programming

112 Long Range Planning, Vol. 22, No. 5, pp. 112 to 120, 1989 0024-6301/89 $3.00 + .OO Printed in Great Britain Pergamon Press plc

Financial Planning Using Goal Programming

Robert G. Batson

Strategic planning applications of the resource allocation technique known as goal programming have proliferated during the past decade. This can be attributed to the overall growth in use of formal planning models. and the suitability of the multiple objective design of goal programming which permits experimentation with priority and trade-off among conflicting objectives. Ten actual applications are reviewed with enough detail to permit a manager or planner to decide if the approach followed might be adaptable to a current planning exercise. Goal programming’s benefits and limitations as a quantitative aid to strategic planning are summar- ized, based on the implementation experiences reported.

The use of computer models in strategic planning is a relatively new and expanding phenomenon. Corporate planners are being asked to make projections covering a whole range of variables such as profit, sales, growth, return on capital, and return on sales. The main approaches used are forecasting, and financial simulation. However, a surprisingly broad collection of organizations have reported use of goal programming as a technique for allocating resources. In this paper we aim to: (1) present a literature survey of applications of goal programming in strategic planning and (2) assess the benefits and limitations of goal programming as a planning aid.

Since the development of linear programming (LP) by George Dantzig in the mid-1940s, numerous applications in industry, military, and government have been reported. While LP applications have proliferated, managers and analysts alike have noted a limit to its effectiveness. Linear programming models incorporate only a single objective such as maximizing profits or minimizing costs whereas most managerial problems are more complex with multiple and conflicting objectives. In 1961, Charnes and Cooper’ developed the concept of goal programming to model resource allocation prob-

The author is Associate Professor in the Industrial Engineering Department at the University of Alabama.

lems with multiple and conflicting objectives. Included in their model was a provision that goals which may not be totally attainable can be reached ‘as close as possible’ through optimization of a stated objective. Later, Ijiri3 extended goal programming as defined by Charnes and Cooper to include ‘Pre-emptive Priority Factors’ in which priorities and weights are assigned to multiple goals according to their importance.

Goal programming (GP) is an extension of linear programming to model problems with multiple and conflicting objectives. Modern texts” illustrate the ease with which such models can be solved by a version of the two-phase simplex method. Charac- teristics of goal programming that make it appropriate for strategic planning are that it:

(1)

(2)

(3)

(4)

(5)

(6)

reveals the conflicting objectives of the organization and requires management to establish priorities among them.

Produces feasible compromise solutions, reveal- ing whether each objective can be achieved within resources, and if not, produces quantitative information about trade-offs among unachieved goals and resource constraints.

Does not require that goals be expressed in a common unit such as dollars (as would LP).

Permits ‘non-absolute’ or partial constraints. For example, even though total corporate employees may not be specified as a goal, it is likely some projection for the planning horizon is known. By permitting a number of employees to be a constraint, it is possible to tell how this variable is related to achievement of corporate goals.

Permits simultaneous assessment of a large number of feasible plans, rather than detailed assessment of a few (2-5) plans. Thus GP has a value as a screening tool.

There are two types of sensitivity analysis: analysis of discrete changes, and variations

Financial Planning Using Goal Programming 113

across a range. Important types of changes permitted are the addition of a new goal, addition of a new decision variable, and re- ordering and/or permutation of the original priority levels. Rapid reassessment of the effects of these structural changes provides strategic managers with valuable information that they cannot obtain from other sources, including corporate simulation models.

The journal Omegn has published three survey articles by Kornblutz,R Lit-r,’ and Zanaski and Gupta.‘” Kornblutz’s 1973 article was primarily a survey of solution procedures, though a few applications are discussed. The other two, written in 1979 and 1985, provide bibliographies of all reported applications. Lin uses the categories: Accounting, Finance, Operations Management, Marketing, Manpower Planning, and Other, along with subcategories to classify 84 applications. The survey presented in the next section differs from these in that the objective is to put those applications devoted to strategic planning in perspective.

Because most corporate executives have at least been exposed to financial forecasting and risk analysis, it is useful to compare linear programming and goal programming with simulation-based approaches to quantitative strategic planning studies. Simulation models utilize mathematical relationships to represent the process by which inputs get utilized and converted to outputs. Both inputs and parameters of the model may be, and typically are, probabilistic variables. For instance, interest rates and sales volume are time-dependent random variables-the further in the future they are projected, the wider the variance of the probability distribution. Simula- tion models, which by definition are time-driven, are a type of predictive model. They have high resolution in representing process flows (men, materials, money, etc.) but offer significant diffr- culty if one wants to represent goal-seeking behaviour.

LP and GP are optimizing approaches, as opposed to predictive. Both were created to model goal seeking behaviour, but have the weakness of treating decisions as one-time choices. Furthermore, all data used in the model formulation are taken as deterministic (often, an average); no random variation occurs as the model runs. Clearly, policy decisions evolve over an extended period in an environment that is at best representable as a family of dependent random variables. To pursue new business, build new facilities, start a new R & D thrust, and so on takes years to reach conclusion. Linear and goal programming have been adapted to handle discrete time periods, such as annual updates of the companies strategic and tactical plans or R & D port- folios. Still, within the ‘bIack box’ that exchanges resources for results, they generally represent the process activities in a very aggregated fashion; simulation models are more derailed in modelling such processes, even to the point that some provide continuous flows of resource utilization and process performance. A summary of the types of situations where goal programming is useful is given in column 2 of Table 1. These characteristics are found in the applications review which follows. In particular, none of the organizations (except, per- haps Texas Instruments) function in a competitive environment of rapid change.

Strategic Planning Case Studies

Corporate strategic planning involves the assessment and selection of various types of goals, e.g. financial, sales growth, manpower, and production, to support the corporate purpose. Allocation of resources to the various corporate divisions and business lines requires a corporation to set priorities and make trade-offs among these goals. This interplay between goal-setting and resource allocation, and the impact of introducing a goal programming model, are illustrated by the following descriptions of 10 applications of goal programming

Table 1. Situations where linear and goal programming apply

Linear programming Situation charateristic applicable

Decision type Operations management

Objective(s) of the decision Single, overarching

Individuals or groups interested, with One distinct value systems

Constraints on action (resource Rigid utilization, requirement satisfaction)

Desire of each group with respect to Optimize (maximize or minimize) objectives

Assumptions about environment Deterministic

Assumptions about change Slow, predictable

Goal programming applicable

Strategic management

Multiple, conflicting but can be prioritized

Several

Flexible

Simultaneous achievement of multiple targets

Deterministic

Slow, predictable

114 Long Range Planning Vol. 22 October 1989

in strategic planning. Public institutions also must make similar trade-offs in allocating resources.

Cities Service Company Cities Service is a vertically integrated oil, gas, and petrochemical company. In 1976, this company began using a formal planning process with activities divided among 22 strategic planning units (SPUs). The pl anning is done at the SPU level under corporate guidelines and approval. From two to five alternative plans are submitted to corporate planning, at which time a complex budget allocation process is required.

Difficult decisions have to be made about which business lines are assets to the company and what amount of funds should be allocated to each SPU. Part of the plans submitted to corporate were the expected financial results from each of several levels of funding. Corporate management was faced with assessing these multiple alternatives and selecting those that best met corporate goals.

A O-l linear programming model was developed to aid in this analysis, providing the option of specifying a single objective or weighted multiple objectives. This model selects from each SPU one plan and assigns a zero to all other plan’s income, cash, capital, and assets. The input data for each SPU plan is 10 years’ estimated Net Income, Net Cash, Capital Expenditures, Net Assets, and Return on Assets. Corporate input data include debt repay- ment schedules, borrowing limits, interest rates, dividend requirements, corporate overhead and non-operating assets and income.

The objectives which management could choose to optimize individually or as a weighted sum are: income, net worth, growth, and return on assets (ROA). Within each objective, annual weights permit more emphasis on near term objectives. A weakness of this original LP model is the fact that objectives are measured in incommensurate units (e.g., ROA is a fraction). To avoid difficulty in interpreting results, but still permit multiple objectives to be considered simultaneously, the model was reformulated as a GP.”

According to Rychel, I’ ‘the objectives and their accompanying bounds were replaced with prioritized goals and a solution sought that most nearly satisfied these goals. The process of choosing targets and ranking the goals more closely approximates the management decision process; and the interpre- tation of results is more concrete. The optimization model . . . allows management to explore a wide range of strategies to respond to a variety of external events’.

The Mutual Life Insurance Company Marosa13 describes an application of goal programming to strategic planning in an insurance company. The strategic planning priorities of the company are

evaluated by formulating and solving a goal programming model in which are represented both multiple objectives and multiple decision makers. The Analytic Hierarchy Method’” of Saaty is used to derive the weights assigned to subgoals within each objective. This method elicits from management a sequence ofpaired comparisons of goals at each level of the objectives hierarchy, and its use permits incorporation of various special interest groups’ values into the planning model. A comprehensive 15-year, time-staged linear goal programming model is used, illustrating that not all GP models are ‘static’.

U.S. Army Ballistic Missile Defense Agetlcy The classical capital budgeting problem is one of selecting a portfolio of investments (or projects) from a set of potential investments in order to maximize some benefit while remaining within a sequence of yearly budget limits. Ignizio’j extends the usual O-l linear programming formulation of this problem to include multiple objectives. The objectives of the Ballistic Missile Defense (BMD) Agency were not measurable by the same standard, hence GP was an ideal approach. These objectives were :

(1)

(2)

(3)

Maximize the defense capabilities of the U.S. against various types of enemy ballistic missile threats.

Minimize technical risks associated with the programs selected.

Maximize utilization of present personnel.

Appointed committees ranked and weighted these objectives. Budget constraints were formulated, and the entire problem was modelled as an integer goal program and solved. Depending on the problem size, either a branch and bound (exact) or a heuristic approach was used in the solution.

In 1978, the Ballistic Missile Defense Advanced Technology Center (BMDATC) began using a goal programming model developed by Mellichamp er a1.l6 to plan the allocation of research budgets to technology development programs. A goal representing ‘benefit to the organization’ of the completed projects was modelled. This approach required a subjective assessment of management of the value to the organization of each project if successfully completed and an assessment of the probability of success. Also included was a budget goal, which management wanted to exactly spend and a risk goal which stated that management desired at least 30 per cent of the budget to be allocated to low risk projects.

Example applications are given in the form of the sensitivity of the solution of a six-project selection model to variations in research budget, risk attitude, project availability, and goal preference. BMDATC management uses the model for S-year budget


analysis, using 45 projects and a budget in excess of SOeSbn.

City of Lincoln, Nebraska This article presents goal programming as a system- atic approach for performing zero base budgeting (ZBB) with multiple objectives. In 1977, President Carter established ZBB as the management tool to be used in the federal government. Allocating federal tax dollars efficiently and effectively involves multiple and frequently conflicting objectives. Since this type of problem cannot be easily solved by traditional budgeting procedures GP can be used to yield satisfactory simultaneous solution to this problem of various objectives. The paper first explains ZBB and then shows how it can be used with GP for a more effective solution. ZBB is a management tool in which the planners ‘start from base zero or scratch, analyse all activities and priorities afresh, and create a new and better set of allocations for the upcoming budget year’ rather than working on the basis of previous budgets.” In ZBB each decision unit is described as a decision package. The packages are then ranked in order of their priority and detailed budget material then evolves.

An example is given of a GP application to ZBB using budgeting data from the City of Lincoln, Nebraska. The city government activities are grouped into four categories: public work/utilities, parks/recreation, police/fire and library/health. Each category includes four decision packages. The budget limitation constraint is the first priority goal. The second most important goal is to achieve the first decision package in each category. The remainder of the nine goals each deal with achieving particular decision packages of the various categories and are ranked according to their importance. The GP model is developed including 33 constraints and 82 variables. The solution is obtained using a computer program employing Lee’s modified simplex method.J Solution of the model involves selection of three complete decision packages of the public works/utilities program, park/recreation program and police/fire program respectively and two packages of the library/health program. The first six goals are completely attained and the last three are not attained.

State University Hospital* The area of hospital budgeting and capital investment include unique problems to which the GP model is well-suited. Some of these problems include limitation of funds, unclear definition and measurement of output, various and conflicting objectives concerning quantity and quality of services, and the necessity of satisfying various governing and regulating groups. The hospital administration, board of trustees, and medical staff all have a voice in deciding how funds will be

‘The name is not revealed for reasons of confidentiality.

allocated. Each has their own interests and goals which are often in conflict with each other. Among these goals are efficient and effective institutional management, quality health care for the sick, prevention of disease, medical education, advance- ment of research, and meeting the needs of the community. If in addition the hospital is non-profit, it must ensure a balance in revenues and expenditures. Therefore, the hospital typically strives to achieve these various and conflicting goals within the confines of certain resource limitations.

This application l8 involves a 450 bed, state-university-based teaching hospital. The executive committee is made up of two groups: administration and the medical staff. This committee formulated a list of goals for the hospital which were as follows: facilitate teaching and research; create a centre for excellence in health care; maintain a skilled and motivated force of health care workers; elevate the standards of health care in the United States; satisfy the demand for health care in the community; improve the social and economic climate in the community; and provide effective management in order to achieve institutional efficiency and effectiveness.

Though the goals were jointly determined, each had different levels of importance for the two separate groups. Administration and the medical staff each assigned priority coefficients to individual goals based on their own self-interests. The goals were then designated as primary, secondary, or tertiary depending on their overall importance to both groups. Seven projects were submitted for consider- ation including: expansion of the surgical facility; expansion of the epidemiology department; brain scanner; hospital training office; hospital industrial engineering department; patient screening clinic; and office leased space. The cost and operating expenses of each complete project were included in the model. Next constraints were formulated by both the medical staff and administration which specified limits on project acceptance, staff-patient ratio, and available space and funds. The goals were assigned aspired levels of achievement and the objective function established using only negative deviations.

The formulations were solved with a strictly linear goal programming solution technique, first with the administration’s budget constraints and then with the medical staffs constraints. The results showed that a jointly amicable allocation of funds from the two separate runs was impossible. The two sets of budget constraints were then merged to form a forced compromise solution. This result solved the problem of unallocated funds and included at least a portion of all the projects in the budget. However, it violated the considerations of project mutual exclu- sivity and divisibility along with implying an average of priority values. Overall it was not likely to please either group. The problems with this


model were finally solved with a mixed integer programming solution technique which produces optimal allocation of funds assuming the two groups are equal in power. ‘The initial construction of each model and its subsequent revision offer significant managerial insights into both organiza- tional and operational realities, and thereby improve the resource allocation process.“8

Texas Instruments, Inc. In ‘Financial Planning Using Goal Programming’ Kvanli” observes that the task of formulating multi-year financial plans in corporations is vir- tually impossible because the planning guidelines severely over-constrain the feasible alternatives. ‘As the planner attempts to meet one objective, another variable becomes unacceptable . . . the familiar balloon-squeezing effect.’ He proposes goal programming as ‘the way out of this dilemma’. However, as discussed below, he does not believe that individual goals should be assigned a priority as is typical in goal programming applications. Rather, he suggests that priorities be explored during the subsequent sensitivity analyses.

Kvanli illustrates the concept of penalty functions for deviations about an acceptable interval, rather than a point target. He shows how penalty functions for sales, profit, number of employees, and year-end assets were constructed for l-year planning at TI. He explains that once a baseline problem has been solved, the financial planner concentrates on the output values of variables and ratios that he doesn’t like. He forces a particular variable to shift in a desirable direction by redefining the intervals or penalty exchange rates input to the model.

In the multi-year financial planning problem at TI, 14 key variables were used to construct the GP model. Besides the four yearly variables above, also included were earnings per share, net fixed assets, average assets, capital expenditures, depreciation, and payroll. Sales levels for each year were pre-specified by management. The values of the remaining variables were thereby driven by the forecasted sales. Also the number of shares was fixed over the 3-year planning horizon. The problem required 418 variables and 208 constraints, including constraints required to ‘tie’ two or more variables together:

(1) within time-period constraints (two for each time period)

(2) between time-period constraints (three for each

year)

A sequence of three solutions to the 3-year planning problem is presented. In the first, there were three unacceptable variable values: year-end asset (Year l), Sales/Average Assets (Year l), Year-end Assets (Year 3). In the second, only two variables were at unacceptable levels: Sales/Average Assets (Year l), Other Assets (per cent of Sales, 1980).

These variables were moved to acceptable levels in each case by modifying the slope of an input penalty function which corresponds to an increased priority or emphasis on that variable moving into its acceptance region.

Electrical Equipment Manufacturer* The remaining four applications deal with corporate research and development (R & D) planning. The first paper to be discussed is entitled ‘Allocation of Research and Development Funds: A Zero-One Goal Programming Approach.‘20 It begins by describing some of the problems management encounters in making R & D decisions. Among these are incommensurable units of measurement and indivisibility of projects. Another problem is the long time period between investment in basic R & D and payoff. This paper demonstrates a solution to these problems by presenting an application of a zero-one interger goal programming model to the R & D selection process.

The case study is based on a high technology electrical equipment manufacturer with two divisions: The Atomic, Defense and Space Division and Electric Utility Division. There are two research centres, one for each major division, located in different areas of the country. Limits are imposed on R & D funds and resources (laboratories and researchers). The problem is to select which of 16 projects to fund, accounting for a lo-year planning horizon. Decision variables for the model are the R & D projects being considered and are expressed as zero-one values.

There are five strict constraints which are all mutually exclusive projects. Nine goals are listed which were established and ranked by management to make up the priority structure. The R & D budget goal is the first priority since the resources available are limited by a budget constraint. The second priority is the physical facilities goal which states that the new projects should not require more research facilities than are already available at the two research centres. Third are the maximum manpower goals which state that the new projects should not require any increase in qualified researchers than what is already available at the two research centres. Other goals, continuing in order of priority include: priority project goals; offensive- defensive project balance goals; risk spreading goal; sales goal; market share growth goals; and maximization of net present values. This priority structure leads to the resulting objective function.

This model was solved by the Lee algorithm.J The solution resulted in acceptance ofeight projects. The model completely satisfied the first six goals; but failed to satisfy goals seven through nine. The sales goal of S500,OOO was underachieved by S172,400 (34 per cent). The market share goals were adding

‘The name is not given to preserve confidentiality.


28 per cent in atomic equipment and 2.2 per cent in steam-powered electric utility markets. These were underachieved by 0.201 per cent and O-2 per cent, respectively. The net present value of the projects selected was $860,000, however, the goal for this objective was set at an arbitrarily large value (SlOm) to force maximization.

Keown et ul.*O report that their model was used by management as a decision aid, not as a binding decision. The actual projects selected did closely parallel the ones recommended by the model. ‘The use of the model and its subsequent results were viewed favourably by management in that it forced them to define ‘and establish goals, required a quantification of the resulting benefits, and provided a guideline to the selection process.’

Lord Corporation Lord Corporation” is an adhesives and coatings manufacturer, headquartered in Erie, Pennsylvania. To assist in allocating funds to R & D projects, a O-l goal programming model was used. The 10 goals established by top management, in their (initial) priority order, are:

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

No program may consume more than 10 per cent of the resources.

Sales growth should exceed 15 per cent per year.

Discounted cash flow rate of return should exceed 30 per cent.

Projects have j-year capital limits.

Projects promote constructive change in the industry.

Company develops a leadership role.

Company develops new technology.

Advanced technology is interrelated.

Projects provide diversification of product and market.

Current balance of allocations between units is to be maintained.

There were 25 projects competing for resources in the program. The GP algorithm was run four separate times, each under slightly different condi- tions involving arrangement of priorities and discounting of financial inputs for uncertainty. Each run produced different results in relation to the extent each goal was achieved. Management at the Lord Corporation was involved in this program in an integral way since they were responsible for setting up the goal list. Goal programming was quite beneficial to them in the solution of this problem. It offered an advantage over other mathematical programming techniques because of its ability to accommodate a variety of variable types. It also provided management the opportunity

to assess the conflict between financial goals and corporate purpose goals.

Textile Manufacturing Company* The paper entitled ‘R & D Project Selection and Manpower Allocation With Integer Non-linear Goal Programming”’ begins by explaining that goal programming is a logical approach to be used for R & D project selection because of its multiple- objective feature. It also states, however, that GP treats the functional relationship between resource utilization and project outputs in a linear fashion. although often times they are more realistically non- linear. An example is given of a project being selected and researchers being assigned incremen- tally. This results in an increased probability of success but at a decreasing rate, which is a non-linear relationship. For this reason an integer non-linear goal programming model for R & D project selection and manpower allocation was chosen for the example in this paper. The example comes partly from the R 8r D division of a textile manufacturer in the Southeast and partly from the R & D department of an electronics corporation in the Southwest. The two operate similarly and the case example represents a combination of the R & D units of both companies.

The problem involves the selection of up to seven projects as well as the availability of 30 researchers to be assigned to the projects. The model will reflect the allocation of researchers to the R & D projects as well as project selection. The system constraints have to do with the number of researchers availabl: for allocation to each project. The goal constraints have to do with the firm’s goals for the projects and are listed in order of their priority: (1) Probability of success for individual projects; (2) Budget limitation; (3) Expected monetary return from selected projects; (4) J oint probability of success for all projects selected; (5) Time to project completion: (6) Total time allocated to all selected projects; (7) Computer capacity utilization; (8) Mutually exclusive projects; and (9) Preferred projects. The objective function then captures these ordered goals. The model was solved with a specially written FORTRAN program. The result included selection of five projects with rive researchers allocated to three projects and seven to the other two projects. Goals 1,2,3,5,8, and 9 were achieved and 4,6, and 7 were not. This paper illustrates how using an integer non-linear GP model for R & D project selection can help overcome the problems one would have with a strictly linear O-l GP model.

Goodyear Aerospace Corporation The paper of Madey and Dean2 examines the R & D project selection and budgeting decision of a division of Goodyear Aerospace in the strategic planning process. The model employed is a multi- attribute utility (MAU) representation of the value

‘Name withheld to preserve confidentiality.


system and risk attitude of the firm, based on orientation of the authors and the journals in which Madey’s dissertation.‘4 MAU is an advanced form of they wrote led to a lack of common format or scoring model,‘j in which the preferences and value information upon which a formal comparative trade-offs of management with respect to multiple analysis could be based. However, we can isolate measures (attributes) are elicitied via interviews, and common benefits and limitations experienced in the represented as a mathematical model. applications.

As part of the division’s strategic planning process, a portfolio of R & D projects for the next 5 years was required. Each project and its funding profile was identified, along with projections of return on investment, sales growth, and profit. Approxi- mately 50 projects, with a duration of from i-3 years, may be funded at any one time. A preliminary screening reduces the maximum number of potentially-funded projects to 80. The overall objective of the project selection process is to increase the number of contracts that are won and thereby to increase the firm’s ROI, sales, and profits. The ultimate outcome of a contract on each of these three decision criteria is uncertain because of technical risk, schedule risk, estimating errors, and changes in governmental policies and plans. In addition to the annual strategic plan update, this portfolio must be occasionally updated throughout the year to adjust to internal and external changes.

Benejits Observed All applications mentioned the integrative role of the goal programming model. It served as a means to structure the outputs of various processes, sub- models, and management committees. In some instances it showed precisely what information was missing in data bases, leading to other model development. In the diversified corporations, the model building effort indicated the need for a centralized, accurate data base.

A set of 15 attributes was used in formulating the objectives of the firm: ROI, sales growth, and profit in each of the 5 years. The objective of maximizing expected utility is non-linear, hence the basic model proposed is a O-l integer non-linear program. Using an exact method on a problem with 50 projects used 1 hour of CPU time. Approximate methods, including compromise programming” and goal programming, are evaluated and yield results which are reasonably close to the solution obtained by exact methods. In the goal programming method, target levels are specified for each attribute. Deviations from this ideal are minimized by taking each goal in priority sequence.

In each exercise, it was evident that the model served as an experirnentnl tool for management. Rather than starting with a few predetermined strategy alternatives for which a number of financial measures are calculated, the model permits incommensurate payoffs to be evaluated over the continuous feasible region of strategies. As a result, certain good compromise solutions can be isolated for closer analysis. Clearly, the applications pointed toward sensitivity information from repeated model runs under various assumptions as the primary information used by management. Precise, quantified trade-offs were provided concerning the link between resource allocation, strategy selection, and goal attainment. Also established were the relationships between goal levels and the cost to pursue them.

Although the goal programming solution approach produced generally unacceptable results in this modelling effort, there are two important lessons embedded in this paper. First, this company is maintaining an extensive, computerized data base to support R & D strategic planning. Included in this data base are each project’s funding requirements in several resource categories at each of three funding levels . . . along with the values for the probability of success and for ROI, sales, and profit for the project. These data are available and familiar to the decision-makers and used independently of the R & D planning model. Also, this paper highlights the value of using an R & D planning model intermittently as the need arises, not simply once-a-year.

Finally, in those instances where there are conflicting interest groups, each with their own goals and priorities, GP can serve as a conjlict resolution device. Each group must reveal to the others Lvhat are their objectives, goal levels, and priorities. The model then can be run using various group priorities, or some compromise, in order to show just how much each group is compromising its goals. Conflicts often arise over how a company should respond to external events. The model, where viewed as an operational tool, was used to help in deciding the appropriate response.

Limitations Goal programming, like any quantitative method, is an imperfect representation of reality. Model results have meaning relative to the model, but must be interpreted back to the real situation. Therefore in each application reported there was a competent model developer and user who was brought into the planning process by management. This individual always was of Ph.D.-level skills, and in half the applications was from outside the organization.

Conclusions

The 10 articles reviewed above were selected because they each reported a real application. The

The data required to build a goal programming model must be developed. Certain organizations within the corporation are required to respond with


what may require intense man-months of analysis, if not model development. Management must be willing to be interviewed either individually, collectively, or by questionnaire in order to establish a baseline set of priorities and weights within priorites. Furthermore, once these subjective data arc finalized they become a key part of the model. Usually these interview and encoding processes are neither too mentally demanding nor time-intensive, because the GP paradigm matches the thought processes managers must engage in order to select a strategic plan without modelling assistance.

Finally, most strategies involve some decisions that are ‘non-divisible’-either a project is funded (facility is built) or it is not. Non-divisibility of projects occurred in many of the applications cited. This in turn requires the use of integer-valued variables (actually binary variables) and so special solution procedures beyond those in a typical GP package must be invoked. Other model-specs@ problems that arose in a majority of the applications reported are that: (1) Initial problem formulations are highly over-constrained, so no feasible strategy exists; (2) once feasibility is attained by recasting the model, then there is seldom a strategy that satisfies all goals.

Summary Staternent Applications of goal programming prior to 1976 were predominantly oriented toward operational decisions. In the last decade, there has been a definite shift toward applications in strategic planning to answer the question ‘what shall we emphasize?’ This shift seems to be a natural result of the growth in formal planning processes, increased use of corporate planning models, and the recognized limitations of single objective resource allocation models. The advantage most often cited by those who have used goal programming in strategic planning is that it forced management to think hard about priorities and goals, to discuss these among themselves, and to commit the results of these discussions to paper. Another advantage is that GP permits management to quantitatively assess the impact of rearranging priorities and resetting goals, often as part of a process to reach compromise among themselves or to accommodate changes in the environment.

Goal programming can be a successful planning aid if it has high level support, management team participation, and if it is promoted as:

(1)

(2)

(3)

(4)

A regular tool to respond to decision situations, not a ‘once-a-year’ run.

A tool for policy experimentation, not optimization.

A communication aid that facilitates discussion and compromise.

A focus for the data gathering activities in planning.

(5) A companion, not replacement, of existing single objective models.

References

(1)

(2)

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(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19)

(20)

(21)

(22)

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M. J. Oglesby, An interactive, mixed-integer goal programming application of capital budgeting at Cities Service Corporation, Unpublished MBA Thesis, Oklahoma State University, Still- water, OK (1980).

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Biographic note

Robert G. Batson is an Associate Professor in the Industrial Engin- eering Department of the University of Alabama. For 5 years prior to this 1984 appointment he was a Senior Operations Research Analyst with Lockheed Corporation, where he was the principal investigator on two R & D projects; performed risk, decision, and statistical analysis in support of aircraft conceptual design; and sewed as an internal consultant to engineering management. Dr Batson holds an M.S.I.E. and a Ph.D. from the University of Alabama. His research interests are in operations research, systems engineering, quality assurance, and engineering management. He has published in journals, proceedings, and handbooks. He is a member of ORSA, TIMS. IIE, and ASQC.

Documents

Financial planning using goal programming