EVALUATING ALTERNATIVE LINEAR PROGRAMMING MODELS TO SOLVE THE TWO-GROUP DISCRIMINANT PROBLEM

The two-group discriminant problem has applications in many areas, for example, differentiating between good credit risks and poor ones, between promising new firms and those likely to fail, or between patients with strong prospects for recovery and those highly at risk. To expand our tools for dealing with such problems, we propose a class of nonpara-metric discriminant procedures based on linear programming (LP). Although these procedures have attracted considerable attention recently, only a limited number of computational studies have examined the relative merits of alternative formulations. In this paper we provide a detailed study of three contrasting formulations for the two-group problem. The experimental design provides a variety of test conditions involving both normal and nonnormal populations. Our results establish the LP model which seeks to minimize the sum of deviations beyond the two-group boundary as a promising alternative to more conventional linear discriminant techniques.     

Applications and Implementation A SEPARABLE PROGRAMMING APPROACH TO EXPECTED COVERAGE: AN APPLICATION TO AMBULANCE LOCATION

The maximum expected covering location problem (MEXCLP) is reformulated using a separable programming approach. The resulting formulation—nonlinear maximum expected covering location problem (NMEXCLP)—guarantees optimality and also solves more quickly than previous heuristic approaches. NMEXCLP allows two important extensions. First, minor formulation changes allow the specification of the minimum number of times each node is to be covered in order to satisfy expected coverage criteria. Second, coverage matrices can be constructed that consider two different types of coverage simultaneously. Both extensions are useful for ambulance location problems and are demonstrated in that setting.     

A DISCRETE DYNAMIC OPTIMIZATION MODEL FOR MADE-TO-ORDER COST ANALYSIS

A model is presented that yields optimal production rates for a firm producing a contracted order. The model is unique in that it considers the influence of production rate and learning on total program cost. An application to the specific characteristics of two military production programs is presented. As demonstrated by the application, models of this type may be used as decision-making tools when negotiating the cost impact of contract modifications.     

SPECIFICATION AND ESTIMATION OF LOGICALLY CONSISTENT LINEAR MODELS

The implications of constrained dependent and independent variables for model parameters are examined. In the context of linear model systems, it is shown that polyhedral constraints on the dependent variables will hold over the domain of the independent variables when a set of polyhedral constraints is satisfied by the model parameters. This result may be used in parameter estimation, in which case all predicted values of the dependent variables are consistent with constraints on the actual values. Also, the implicit constraints that define the set of parameters for many commonly used linear stochastic models with an error term yield values of the dependent variables consistent with the explicit constraints. Models possessing these properties are termed “logically consistent”.     

USING AN UNCERTAINTY MODEL TO ASSESS SALES RESPONSE TO ADVERTISING*

Implications of a probabilistic “random walk” model of incremental sales response to advertising are developed for various timing patterns of advertising expenditures. Maximum likelihood procedures for assessing advertising effectiveness and for estimating a decay (forgetting) rate are developed and applied to artificial data of known configuration and are used to assess the impact over time of a brochure program on mail-order sales. Results are also compared to those from alternative models involving various lag patterns in advertising effects.     

Applications and Implementation

We propose an alternative solution to the discriminant problem, one that requires little more than a minimum familiarity with linear programming. The approach shows promise for eliminating the complexities of conventional statistical approaches without sacrificing the essential power of existing methods.     

A VARIANCE-REDUCTION STRATEGY FOR RSM SIMULATION STUDIES

The application of optimization techniques in digital simulation experiments is frequently complicated by the presence of large experimental error variances. Two of the more widely accepted design strategies for the resolution of this problem include the assignment of common pseudorandom number streams and the assignment of antithetic pseudorandom number streams to the experimental points. When considered separately, however, each of these variance-reduction procedures has rather restrictive limitations. This paper examines the simultaneous use of these two techniques as a variance-reduction strategy in response surface methodology (RSM) analysis of simulation models. A simulation of an inventory system is used to illustrate the application and benefits of this assignment procedure, as well as the basic components of an RSM analysis.     

A Learning Curve Analysis of Expert System Use*

In this article, we study how an expert system affects novice problem solving in a financial risk analysis domain. We demonstrate that novice performance is improved after exposure to an expert system. Further, we show that novice performance continues to improve when the system is withdrawn. By comparing learning curves for people with exposure to those without, we can assess how much the system has benefitted its users. We demonstrate a quantitative methodology to measure the increment of learning due to the use of an information technology. We also explore the issue of how expertise is transferred from the system to the user.     

Integrating Neural Networks and Semi-Markov Processes for Automated Knowledge Acquisition: An Application to Real-time Scheduling*

Recently, artificial neural networks (ANN) have gained attention as a promising modeling tool for building intelligent systems. A number of applications have been reported in areas varying from pattern recognition to bankruptcy prediction. In this paper, we present a creative methodology that integrates computer simulation, semi-Markov optimization, and ANN techniques for automated knowledge acquisition in real-time scheduling. The integrated approach focuses on the synergy between operations research and ANN in eliciting human knowledge, filtering inconsistent data, and building competent models capable of performing at the expert level. The new approach includes three main components. First, computer simulation is used to collect expert decisions. This step allows expert knowledge to be obtained in a non-intrusive way and minimizes the difficulties involved in interviewing experts, constructing repertory grids, or using other similar structures required for manual knowledge acquisition. The data collected from computer simulation are then optimized using a semi-Markov decision model to remove data redundancies, inconsistencies, and errors. Finally, the optimized data are used to build ANN-based expert systems. The integrated approach is evaluated by comparing it with the human expert and using ANN alone in the domain of real-time scheduling. The results indicate that ANN-based systems perform worse than human experts from whom the data were collected, but the integrated approach outperforms human experts and ANN models alone.     

A Comment on Second-Order Polynomial Regression Models

In a recent article, Chatterjee and Greenwood [1] addressed the problem of multicollinearity in polynomial regression models. They noted that there is a high correlation between X and X²; therefore, a second-order polynomial model suffers the consequences of collinearity. Chatterjee and Greenwood [1] suggested a method they believe will overcome the problem. The contention of the present comment is that the suggested method accomplishes nothing and, indeed, has the potential to lead the unwary researcher to the wrong inference and misinterpretation of his results.