Assembly Line Balancing with Resource Dependent Task Times*

Paced assembly lines are widely used in repetitive manufacturing applications. Most previous research on the design of paced lines has assumed that each task along the line can be performed by only one worker (or a fixed number of workers). In many cases, however, task duration times may be reduced by increasing the number of workers or changing the equipment assigned to work stations. Thus, the problem becomes one of assigning resource alternatives (e.g., workers and/or equipment) and tasks to work stations to minimize total cost for a desired production rate. For this problem, we present three procedures. The first formulates the problem as a shortest path problem and guarantees optimality. The second and third are heuristic adaptations of the shortest path procedure that are capable of solving large problems. The procedures are compared in terms of solution quality and computation time on a set of 128 randomly generated problems for which optimal solutions could be found. Our simulation results indicate that the choice of procedure depends on problem complexity and resource costs.     

Analyzing and Modeling the Maximum Diversity Problem by Zero-One Programming*

The problem of maximizing diversity deals with selecting a set of elements from some larger collection such that the selected elements exhibit the greatest variety of characteristics. A new model is proposed in which the concept of diversity is quantifiable and measurable. A quadratic zero-one model is formulated for diversity maximization. Based upon the formulation, it is shown that the maximum diversity problem is NP-hard. Two equivalent linear integer programs are then presented that offer progressively greater computational efficiency. Another formulation is also introduced which involves a different diversity objective. An example is given to illustrate how additional considerations can be incorporated into the maximum diversity model.     

A NOTE ON USER SOLUTION STRATEGY FOR MIXED-INTEGER LINEAR PROGRAMMING MODELS

Large-scale mixed-integer linear programming (MILP) models may easily prove extraordinarily difficult to solve, even with efficient commercially implemented MILP solution codes. Drawing on experience gained in solving and analyzing three intertemporal investment planning MILP models for electric power supply, this note offers several practical suggestions for reducing computer solution times for general production-allocation MILP models. Solution time reduction stems from judicious use of the powerful computational capabilities of existing commercial linear programming codes in conjunction with information known or to be learned by the practitioner about the model's structure.     

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.     

Minimizing Misclassifications in Linear Discriminant Analysis*

A procedure is developed for determining two-group linear discriminant classifiers that misclassify the fewest number of observations in the training sample. An experimental study confirms the value of this approach.     

AN IMPLICIT/EXPLICIT APPROACH TO MULTIOBJECTIVE OPTIMIZATION WITH AN APPLICATION TO FOREST MANAGEMENT PLANNING*

Implicit utility/value maximization and explicit utility/value maximization are identified as two major classes of multiobjective optimization methods. Explicit methods have the advantage of being able to fully exploit the power of existing mathematical programming algorithms. A disadvantage is the high information burden they place on the decision maker. Implicit (i.e., interactive) methods have complementary strengths and weaknesses: they require less extensive information but do not lend themselves as easily to use with optimizing algorithms. We develop a hybrid implicit/explicit approach that attempts to combine the advantages of both by embedding within the implicit method a procedure that periodically formulates an approximate explicit representation of the multiobjective problem and then solves it optimally without user interaction. Operationally, this requires the frequent solution of two nonlinear programs. We also report on the implementation of this method in a forest management decision support system. This is a completely microcomputer-based implementation currently undergoing field testing for use in planning the timing and intensity of timber harvests on non-industrial forests in the southeastern United States. The system has been selected as a replacement for an earlier multiobjective program (Harrison and Rosenthal [28]) used by over 1,800 landowners.     

Discrete Sequential Search with Group Activities*

Equipment failures can have significant implications in terms of cost and customer satisfaction. Reducing the time required to find the cause of a failure can provide large cost savings and help preserve customer goodwill. Single‐item discrete sequential search models can be used to sequence the tasks in diagnostic search to minimize the expected time required to find the cause of the failure. We increase the utility of the single‐item discrete sequential search model by developing a formulation that includes simple precedence relationships as well as sequence dependent relationships defined by group activities. This formulation can be applied to a number of other problems including determining the sequence for multiple quality control tests on an item, scheduling oil well workovers to maximize the expected increase in oil production, and sequencing tasks in a research project where there is a technological risk associated with each task.     

MODELS OF PARTS-ORIENTING SYSTEMS*

An analytical model to estimate, evaluate, and compare the behavior and performance of parts-orienting systems for automated manufacturing systems is developed. The model can be applied to parts-orienting systems for both traditional series-structured manufacturing systems and nontraditionally structured flexible manufacturing systems. Numerical examples are given for typical system configurations such as the pure series system, the pure parallel system, and the pure feedback system.     

Theoretical Distributions of Optima for Univariate Discrimination of Random Data*

Optimal linear discriminant models maximize percentage accuracy for dichotomous classifications, but are rarely used because a theoretical framework that allows one to make valid statements about the statistical significance of the outcomes of such analyses does not exist. This paper describes an analytic solution for the theoretical distribution of optimal values for univariate optimal linear discriminant analysis, under the assumption that the data are random and continuous. We also present the theoretical distribution for sample sizes up to N= 30. The discovery of a statistical framework for evaluating the performance of optimal discriminant models should greatly increase their use by scientists in all disciplines.     

Concepts,Theory, and Techniques PRINCIPLES OF MULTIOBJECTIVE OPTIMIZATION*

This paper attempts to isolate and analyze the principal ideas of multiobjective optimization. We do this without casting aspersions on single-objective optimization or championing any one multiobjective technique. We examine each fundamental idea for strengths and weaknesses and subject two—efficiency and utility—to extended consideration. Some general recommendations are made in light of this analysis. Besides the simple advice to retain single-objective optimization as a possible approach, we suggest that three broad classes of multiobjective techniques are very promising in terms of reliably, and believably, achieving a most preferred solution. These are: (1) partial generation of the efficient set, a rubric we use to unify a wide spectrum of both interactive and analytic methods; (2) explicit utility maximization, a much-overlooked approach combining multiattribute decision theory and mathematical programming; and (3) interactive implicit utility maximization, the popular class of methods introduced by Geoffrion, Dyer, and Feinberg [24] and extended significantly by others.     

A Note on “Discrete Sequential Search with Group Activities”

This note comments on a paper published by Wagner and Davis [Decision Sciences (2001), 32(4), 557–573]. These authors present an integer‐programming model for the single‐item discrete sequential search problem with group activities. Based on their experiments, they conjecture that the problem can be solved as a linear program. In this note, we provide a counterexample for which the optimal value of the linear program they propose is different from the optimal value of the integer‐programming model, hence contradicting their conjecture for the specific linear program that they specify. To the best of our knowledge, the conjecture settled in this note was still an open question.     

An Information Theoretic Framework for Exploratory Multivariate Market Segmentation Research*

State-of-the-art market segmentation often involves simultaneous consideration of multiple and overlapping variables. These variables are studied to assess their relationships, select a subset of variables which best represent the subgroups (segments) within a market, and determine the likelihood of membership of a given individual in a particular segment. Such information, obtained in the exploratory phase of a multivariate market segmentation study, leads to the construction of more parsimonious models. These models have less stringent data requirements while facilitating substantive evaluation to aid marketing managers in formulating more effective targeting and positioning strategies within different market segments. This paper utilizes the information-theoretic (IT) approach to address several issues in multivariate market segmentation studies. A marketing data set analyzed previously is employed to examine the suitability and usefulness of the proposed approach [12]. Some useful extensions of the IT framework and its applications are also discussed.     

A PREEMPTIVE VALUE-FUNCTION METHOD APPROACH FOR MULTIOBJECTIVE LINEAR PROGRAMMING PROBLEMS

Many common decision-making situations require integration of a number of objectives or goals into a single objective function to be optimized. A number of techniques for performing this analysis are presented in the literature. These procedures generally require a tradeoff between realism and tractability. The present approach uses the idea of preemptive priority levels with an approximate value function at each level. An efficient experimental design is used to assess directly a quadratic approximation of the multiattribute value functions. An existing algorithm is then used to solve the resulting problem. This procedure is shown to give good results when compared to both the value-function method and goal programming.     

MARKET PENETRATION AND LOCATIONAL CONFLICT IN FRANCHISE SYSTEMS*

This paper addresses the questions of market penetration and locational conflict in a franchise system of distribution. The models developed provide a means to evaluate alternative scenarios and the effects of various franchise policies. It is shown that the market penetration and location goals of the members of a franchise system coincide only under a very limited set of circumstances.     

The Minimum-Covering/Shortest-Path Problem*

Due to the inherent multiobjective nature of many network design and routing problems, there has been a tremendous increase in multiobjective network modeling in recent years. In this article we introduce one such model, the minimum-covering/shortest-path (MinCSP) problem, and formulate several variations of the problem. The MinCSP problem is a two-objective path problem: minimization of the total population negatively impacted by the path and minimization of the total path length. A population is considered to be negatively impacted by the path if the path comes within some predetermined distance of the population. Consequently, the MinCSP problem extends the concept of coverage from facility location modeling to network design. Additionally, several existing solution methods for the problem are briefly discussed and potential applications presented.     

Notes and Communications ON SENSITIVITY ANALYSIS IN DECISION THEORY*

This note points out a crucial flaw in Evans's recent article [1] on decision sensitivity analysis which was published in this journal. This flaw leads to errors in the majority of his formulae and examples. Correct distance formulae in “probability space,” easily computed from the problem data, are provided. After a critical discussion of some of the concepts Evans employed, we bring to the reader's attention a body of prior work in this area that apparently was overlooked.     

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.     

SOCIAL LEARNING THEORY AND THE IMPLEMENTATION OF PRODUCTION INNOVATION*

In a study of the implementation of production innovation using a social learning theory focus, four organizations were monitored with a real-time study design. The following propositions were strongly supported: (1) During the initial implementation period (3–4 months), the stress felt by personnel in new user organizations was significantly higher (p < .01) than for organizations previously experienced with technology; (2) Firms experienced with the new technology obtain early success when compared with inexperienced firms (p < .01). Moderate support was found for the proposition that new users rely heavily on original equipment manufacturers for demonstration to acquire new skills, but gradually models within the user organization emerge as the dominant influence. The proposition that new users have significantly higher imitation scores than users experienced with the technology was only weakly supported. No substantive or significant changes in the attitudes of users toward the innovation were found during the first three to four months of the implementation period. These and other results suggest that longitudinal studies of this type ought to be carried out over periods in excess of 2 1/2 years. Implications for the management of change are presented.     

An Efficient Optimal Solution Algorithm for the Classification Problem

A new LP-based algorithm is developed to determine the optimal solution to the two-group classification problem. The procedure is efficient when compared to current research in a simulation study.     

APPLICATION OF AN EXPECTED COVERING MODEL TO EMERGENCY MEDICAL SERVICE SYSTEM DESIGN*

The Emergency Medical Service (EMS) Act specifies the fraction of all demands for service that must be reached in a given amount of time for urban and rural areas. The conditions have traditionally been interpreted to apply to the case in which all EMS vehicles are available to respond to demands. A model that considers the probability of a vehicle being busy is formulated and model properties are briefly discussed. The model is then applied to two problems: a 55-node test case and a 33-node census tract representation of Austin, Texas. The implications of the new model for EMS system design are discussed as are the limitations of the modeling approach.