A MATHEMATICAL PROGRAMMING MODEL FOR FACULTY COURSE ASSIGNMENTS

This paper describes an integer programming model that we believe has advantages over other models for determining faculty teaching assignments. Unlike previously proposed models, in this model the decision variables represent the assignment of complete teaching schedules rather than courses to faculty members. The paper compares the proposed model with previous models for application in an academic department.     

EXPLORING MARKET PRICING STRATEGIES VIA DYNAMIC PROGRAMMING

Price determinants as well as strategies can be studies by use of simulation, particularly if cost and price relationships can be related to market activity [1] [9] [11]. But, through the use of dynamic programming, given the market conditions, one can extend the analysis to include an optimal strategy. This paper describes a dynamic programming approach to studying price strategy. A model is developed to show that in a market characterized by cost/volume and price/volume relationships, profitability can be extended beyond that resulting from a dominant market strategy to an optimal maximizing strategy. Extension of the model is suggested for studying (a) sensitivity of a strategy (solution) to price level and cost changes, (b) optimal timing of withdrawal, and (c) present value analysis.     

SCHEDULING JOBS ON PARALLEL PROCESSORS WITH DYNAMIC PROGRAMMING

The problem of scheduling jobs on M-parallel processors is one of selecting a set of jobs to be processed from a set of available jobs in order to maximize profit. This problem is examined and a dynamic programming solution is presented which decomposes it into a sequencing problem within an allocation problem. The computation required for solution is found to depend on the sequencing problem as it is affected by the waiting cost function. Various forms of the waiting cost function are considered. The solution procedure is illustrated by an example, and possible extensions of the formulation are discussed.     

A DYNAMIC PROGRAMMING MODEL FOR PERIODICAL SELECTION

This paper presents a model for choosing the periodical collection in a reading room. The model consists of two stages. In the first stage the probability distribution of contacts by users with a given periodical is developed and employed to determine the utility of the periodical. In the second stage the problem of choosing an optimum periodical collection is formulated as a capital budgeting problem and solved with the aid of dynamic programming. The implementation of this model at the University of Connecticut is described in detail.     

MANAGEMENT OF COLLEGE STUDENT RECRUITING ACTIVITIES USING GOAL PROGRAMMING*

A shrinking pool of potential students, due to a declining birthrate as well as uncertain economic times, is creating the need for more effective recruiting of college students. One approach using a goal programming model has been developed and is currently being used to manage recruitment activities in a small four-year college in Nebraska. The model identifies both the type and number of activities that must be completed each quarter in order to reach an enrollment goal for a given year. Factors such as budget, time, manpower, and marketing strategies are highlighted in the model. The results of the goal programming model encouraged more field activities in the first two quarters with emphasis on new-candidate identification. The third-quarter recruiting strategy is more balanced while the fourth-quarter emphasis is placed on follow-up activities that occur chiefly in the office. Use of this model will enable recruiters to meet enrollments while managing recruiting resources and activities in order to remain within the recruiting budget.     

ASSESSMENT OF MULTIATTRIBUTED MEASURABLE VALUE AND UTILITY FUNCTIONS VIA MATHEMATICAL PROGRAMMING*

A major restriction on the use of decision analysis in practice is the frequent difficulty of determining a decision maker's multiattribute utility function. The assessment process can be complex and tedious and generally involves: (1) identifying relevant independence conditions, (2) assessing conditional utility functions, (3) assessing scaling constants, and (4) checking for consistency. Some of the assessment and modeling complexities encountered include an assessor's inability to respond in a quantitatively meaningful and consistent way to hypothetical gambles and an analyst's problem in selecting an appropriate functional form that accurately characterizes the conditional utility assessments. A simplified procedure that mitigates these difficulties is proposed. This procedure facilitates the determination of scaling constants by obtaining (via mathematical programming) a multiattributed measurable value function which is converted to a multiattributed utility function. The methodology can be developed advantageously to produce an interactive software package for use as an assessment aid.     

MATHEMATICAL PROGRAMMING FOR THE STATE EARMARKING PROCESS*

In state and local government, earmarking occurs when specific revenues from one or more tax imposts are set aside to fund specific expenditure programs. Problems arise in this dedication process when the theoretical link between the tax and expenditure program is doubtful or when tax receipts do not grow in proportion to desired expenditure patterns. This paper suggests that a long-range mathematical programming model may be useful in ameliorating this latter “distortionary” aspect of the earmarking process. Extensions of the model, which permit exogenous financial assistance to the special fund, external lending and borrowing, intertemporal transfers of tax revenues or expenditure requirements, or constraints on tax increases or tax-share burdens, are explored as ways to achieve an equitable as well as flexible tax policy.     

A DYNAMIC PROGRAMMING MODEL FOR OPTIMAL ALLOCATION OF DECISION TIME

Recurrent decision making by a lower-level manager can be viewed as a sequential decision process in which time and uncertainty are limiting factors. Under these conditions, the manager must determine how to best utilize his decision making time consistent with his own particular set of decision values. A dynamic programming model was devised to determine the optimal (consistent) allocation of decision time among five different types of problems for a sequence of simulated recurrent decision situations. Fifty-one lower-level managers were interviewed about their use of decision time and decision procedures. The model was validated by comparing model assumptions and results with the findings from the interviews. The model was used to determine the effects of variations in the levels of time available and uncertainty upon the optimal allocation of decision time.     

PRACTICE‐FOCUSED RESEARCH ISSUES FOR SCHEDULING SYSTEMS*

Scheduling research has had relatively little impact on manufacturing practice, yet within the last several years, there has been an explosive growth in the development and implementation of computer‐based scheduling systems in industry. Changes in the environment have increased the stakes and the opportunities for the results of scheduling research to influence manufacturing competitiveness. This paper draws on field‐related experiences with the development and implementation of scheduling systems to propose high‐impact research topics.     

THE ACADEMIC FLOW MODEL: A MARKOV-CHAIN MODEL FOR FACULTY PLANNING*

A Markov-chain faculty planning model to be used with institution-specific data is presented to describe and better understand the complex phenomena of faculty movement through an institution and on its relationship to salary costs, composition of the faculty, and faculty turnover rate. The model updates the earlier work done at Stanford University and Oregon State University by the addition of states for fixed-term appointments and for part-time FTEs to reflect accurately the current hiring trends at many institutions. The model is implemented and tested at two different institutions. The findings suggest that the model is a viable means of gaining useful insights and quantitative data on the faculty profile, salary costs, expected departures, and part-time trends. And further, when used as a planning tool, and the model apparently is comprehensive and flexible enough to analyze the probable effects, both in the short and long run, of alternative personnel policies on the faculty composition.     

MODELING LEARNING CURVE AND LEARNING COMPLEMENTARITY FOR RESOURCE ALLOCATION AND PRODUCTION SCHEDULING*

Research on learning effects in mathematical programming models for optimum resource allocation has called attention to the difficulty in solving such models in their original nonlinear form. In this paper, systematically varying sizes of linear segments are designed to approximate productivity changes along the learning curve, and a single separable linear programming model is developed. With production complementarity and learning transmission between products, a more realistic resource allocation and production scheduling problem emerges. Two cases of learning transmissions are considered, and the model design process, which defines a decision problem that can be solved by a simplex algorithm, is demonstrated.     

ON FUZZY GOAL PROGRAMMING*

This paper illustrates how the goal programming problem with fuzzy goals having linear membership functions may be formulated as a single goal programming problem. Also, a previously defined method for dealing with fuzzy weights for each of the goals is re-examined.     

DYNAMIC LOCATION MODELING FOR PUBLIC-SECTOR FACILITIES: A MULTICRITERIA APPROACH*

A major complication in the planning of facility systems and in the analysis of their locational configurations is the fluctuating nature of the systems they serve. Locations identified now, based on current conditions, may be undesirable in the future, and those based on future conditions may be undesirable now. This paper proposes a general methodology using multiobjective analysis to plan public-sector facility systems operating in a dynamic environment. A model is developed for the specific case of locating emergency services and an illustrative example is presented.     

LINEAR PROGRAMMING WITH DISCRETE STOCHASTIC RESOURCES: AN ALTERNATIVE APPROACH ACCOUNTING FOR INFEASIBILITY*

In this paper an alternative to, or extension of, the chance-constrained method of stochastic programming is presented whereby an expected cost of infeasibility is included in the objective function. The problem is to select a solution to implement before the available resources are known where the adaption of a non-feasible solution to the resources available involves a system cost. While increasing the amount of computation required, the model enables the decision maker to more effectively trade off increased payoff for decreased likelihood of feasibility.     

AN OPTIMIZATION-BASED METHODOLOGY FOR RELEASE SCHEDULING

Operational-level scheduling decisions on the factory floor include the release policy and the dispatching rule. Recent work by researchers suggests that factory performance depends heavily on the release policy. Several heuristic factory release rules have been developed that generate release decisions based on the status of the bottleneck machine. The heuristic rules perform very well in reducing the work-in-process inventory. However, factory output schedules generated by these rules generally fail to match the demand pattern, creating excessive finished goods inventory and/or excessive backorders. To overcome these difficulties, a computationally efficient integer programming model is proposed for release scheduling.     

CONFLICT RESOLUTION IN INVESTMENT DECISIONS: IMPLEMENTATION OF GOAL PROGRAMMING METHODOLOGY FOR DUAL-PURPOSE FUNDS*

Goal programming (GP) is designed to resolve allocation problems with conflicting goals. Both goals and constraints are incorporated in the allocational decision, and the objective function is stated in a way that, upon solution, yields a result “as close as possible” to the priority-weighted goals. The present paper applies GP methodology to the investment decision of dual-purpose funds (DPFs), that are required by law to pursue allocational decisions with potentially conflicting objectives. It provides an empirical demonstration that DPF managers could have improved their investment selection and subsequent performance by the use of GP methodology. Finally the paper stresses the importance of sensitivity analysis to improve both the goal-ranking and target-selection aspects of the methodology and provides a limited but illuminating empirical demonstration of post-optimality analysis.     

A MATHEMATICAL PROGRAMMING APPROACH TO THE SELECTION OF ACCESS PATHS FOR LARGE MULTIUSER DATA BASES*

The selection of an efficient set of access paths is critical to the design of large multiuser data bases. This task is formulated as an integer, linear mathematical program, and an approach to its solution is presented. A series of experiments support the assertion that this approach is sufficient for quickly producing an efficient, if not optimal, set of access paths for data-base problems of practical significance.     

SCHEDULING HYBRID FLOWSHOPS IN PRINTED CIRCUIT BOARD ASSEMBLY LINES*

We treat a three‐stage hybrid flowshop for the production of printed circuit boards (PCB), suggested to us by a real‐life production situation. The problem is to determine a schedule that minimizes the makespan for a given demand profile over a finite planning horizon. We propose a global procedure that utilizes genetic algorithms and three subproblems. The performance of the procedure is evaluated via experimentation over thousands of problem realizations that are randomly generated. The experimental results show the efficiency of the global procedure and provides qualitative answers to the allocation of machines to the various stages.