IMPLICIT OPTIMAL AND HEURISTIC LABOR STAFFING IN A MULTIOBJECTIVE,MULTILOCATION ENVIRONMENT*

This paper presents a tractable set of integer programming models for the days-off scheduling of a mix of full- and part-time employees working α to β days/week (cycle) in a multiple-objective, multiple-location environment. Previous models were formulated to specifically schedule part-time employees working either two or three days per week. These models were intractable because they required complete employee schedule information. The new models are deemed implicit optimal since they are required to supply only essential information. While the number of variables in previous models is an exponential increasing function of β-α, the size of three of the new models is independent of α and β. The first three models developed here (as in [18]) deal with the trade-offs between idle time, the number of employees required to work at multiple “locations,” and the size of the total labor pool. The inherent flexibility of the implicit modeling approach is illustrated by the presentation of various modifications of the basic models. These modifications permit the use of preference weights on the number of employee work days/week (cycle) or the minimization of payroll costs where differential pay rates exist. These latter models may also be formulated such that idle time is ignored, constrained or minimized. The execution time for the implicit models (on a CDC CYBER 730 computer with commercially available software) averaged well under five seconds on 1200 trial problems for the type of application considered in [18]. A solution was obtained in less than 46 seconds of CPU time for a trial problem which would have required over 1.4 million integer variables with previous models. The availability of optimal solutions was invaluable in the development of two heuristics designed to deal with the trade-offs of [16]. In an experimental analysis a previous heuristic produced results which averaged from 74 to 508 percent above optimum across six experimental conditions. The comparable new heuristic produced results which averaged from 3 to 8 percent above optimum for the same experimental conditions. The paper concludes by developing a framework to integrate the results of this research with the tour scheduling problem and by identifying several other areas for related research.     

A NEW CLASS OF MODELS FOR THE DISCRIMINANT PROBLEM

Discriminant analysis is relevant to business decision making in a variety of contexts, such as when one decides to make or buy a specified component, fund a venture project, or hire a particular person. Potential applications in artificial intelligence, particularly in the area of pattern recognition, have further underscored the importance of the field. A recent innovation in discriminant analysis is provided by special linear programming (LP) models, which offer attractive alternatives to classical statistical approaches. The scope of application in which discriminant analysis can be advantageously employed is broadened by the flexibility to tailor parameters in the LP approaches to reflect diverse goals and by the power to explore the sensitivity of these parameters. In spite of the promise of the LP formulations, however, limitations to their effectiveness have been uncovered in certain settings. A recent advance involving a normalization construct removes some of the limitations but entails solving the LP model twice (to allow for different signs of a normalization constant) and does not yield equivalent solutions for different rotations of the problem data. This paper introduces a new model and a new class of normalizations that remedy both remaining limitations, making it possible to take advantage of the modeling capabilities of the LP formulations without the attendant shortcomings encountered by earlier investigations. Our development shows by empirical testing and illustrative analysis that the quality of solutions from LP discriminant approaches is more favorable (relative to the classical model) than previously supposed.     

SCHEDULING PARALLEL PROCESSORS WITH SETUP COSTS AND RESOURCE LIMITATIONS

An integer linear programming model is presented for the scheduling of n products on m identical machines. The particular problem studied is one that occurs frequently in the fiberglass and textile industries. The model incorporates setup costs, lost production costs, and overtime costs. Due to the structure of the model, integer solutions can be obtained by explicitly restricting only a small number of the integer variables. This allows those responsible for scheduling to solve realistically sized problems in an efficient manner. Computational results are provided for a set of generated test problems.     

USING CONJOINT ANALYSIS TO PREDICT TRIAL AND REPEAT-PURCHASE PATTERNS OF NEW FREQUENTLY PURCHASED PRODUCTS*

A new approach is proposed to evaluate new-product opportunities. This approach uses the distribution of brand-purchase probability of the new product over a population of potential customers and the outputs from conjoint analysis. The heterogeneous distribution of brand-purchase probability is expressed by a beta binomial brand-choice model compounded with a negative binomial product-class purchase-incidence model. The resulting model provides a way to predict trial and repeat-purchase patterns of new-product concepts. The paper discusses the development of the model. It also discusses issues of measurement, estimation, testing, and implementation of the proposed approach based on actual empirical data.     

AFFECTIVE RESPONSES WITHIN A COMPLEX DECISION-MAKING TASK: THE INFLUENCE OF “PERCEPTUALLY” ILL-STRUCTURED PROBLEMS

The perceptual effects of varying levels of expert advice for potentially improving on strategic decisions were examined in conjunction with goals. The amounts of advice about decision alternatives, as well as assigned goals ranging from “nearly impossible” to “easy,” were manipulated. The task used was complex and functioned perceptually as an “ill-structured” problem. Mixed results indicated that more advice significantly affected satisfaction but advice in general had little influence on effort. On the other hand, as goal difficulty decreased, satisfaction and effort significantly increased. Easy goals were superior to more difficult ones within this perceptually ill-structured decision-making situation.     

DIVERSIFICATION GAINS FROM INCLUDING REAL ESTATE IN MIXED-ASSET PORTFOLIOS*

Diversification gains in mean-variance efficiency derived from including real estate in financial asset portfolios are examined. Optimal financial and mixed-asset portfolios were generated by selecting from an investment universe including several distinct financial and real estate media. Deficiencies of previous studies were overcome by employing data with improved representativeness and comparability. The efficient mixed-asset portfolios dominated the efficient financial asset portfolios implying that purely financial asset diversification is inefficient. The optimal mixed-asset portfolio prescribed that approximately two-thirds of the investment wealth be allocated to real estate and one-third to the financial media.     

INSTRUCTING OPERATIONS DESIGN: AN EXPERIENTIAL APPROACH

Teaching an operations design course has major pedagogical challenges. (1) The design topics—output, process, facility, and work design—are necessarily taught sequentially, yet the decisions are integrative. (2) Instruction must be generic to service or product producers. (3) Discussing output design is difficult since students typically have had no exposure to the “product language” of engineering graphics. (4) No text is available which examines in sufficient depth all the operations design decisions. (5) Cases necessarily depict historical situations—process technologies and economic data—while operations managers must plan future directions for their productive systems. (6) While the commercial world contains fresh information and data, students are inexperienced in obtaining knowledge from the real world. (7) While the course presents an operations management perspective, students must recognize the information, data, and cooperation necessary from the other functional areas to successfully complete the operations design. To help overcome these seven pedagogical challenges, the students in the undergraduate and graduate operation design courses complete a comprehensive feasibility study for a new product or service and the entire productive system.     

Order Promising and the Master Production Schedule*

Previous research on material requirements planning (MRP) systems has rarely considered the impact of the master production scheduling method used to promise customer orders and to allocate production capacity. Based on a simulation study of an MRP environment, we show that the correct selection of a master production schedule (MPS) method depends on the variance of end-item demand. In addition, we find evidence that the effectiveness of a particular MPS method can be enhanced by holding buffer inventory at the same level in the product structure as in the MPS.     

Open Order Rescheduling in Job Shops with Demand Uncertainty: A Simulation Study

This paper addresses the problem of open order rescheduling in a job shop. Results are reported of experiments conducted in a simulation model of an 8-machine job shop. Four different order updating policies are examined. The due-date process is modeled to include several realistic features about the pattern of due-date variability. These features are parameterized and tested at several levels. Tardiness results indicate that open order rescheduling is beneficial only when allowances are loosely set. The results indicate that inventory performance is improved by order rescheduling, particularly in cases when due dates are revised to earlier times than originally forecast.     

A Variable Selection Criterion in the Linear Programming Approaches to Discriminant Analysis*

There are numerous variable selection rules in classical discriminant analysis. These rules enable a researcher to distinguish significant variables from nonsignificant ones and thus provide a parsimonious classification model based solely on significant variables. Prominent among such rules are the forward and backward stepwise variable selection criteria employed in statistical software packages such as Statistical Package for the Social Sciences and BMDP Statistical Software. No such criterion currently exists for linear programming (LP) approaches to discriminant analysis. In this paper, a criterion is developed to distinguish significant from nonsignificant variables for use in LP models. This criterion is based on the “jackknife” methodology. Examples are presented to illustrate implementation of the proposed criterion.