Application of disjunctive programming to the linear complementarity problem

In this article we address the question of developing deep cuts for disjunctive programs using rectilinear distance measures. The method is applied to linear complementarity problems where the matrix M need not be copositive plus. Some modifications that are needed as a computational expediency are discussed. The computation results for matrix M of size up to 30 × 30 are discussed.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

Computational results with a branch-and-bound algorithm for the general knapsack problem

In this paper, a branch-and-bound procedure is presented for treating the general knapsack problem. The fundamental notion of the procedure involves a variation of traditional branching strategies as well as the incorporation of penalties in order to improve bounds. Substantial computational experience has been obtained, the results of which would indicate the feasibility of the procedure for problems of large size.     

Maximal nash subsets for bimatrix games

In this work maximal Nash subsets are studied in order to show that the set of equilibrium points of a bimatrix game is the finite union of all such subsets. In addition, the extreme points of maximal Nash subsets are characterized in terms of square submatrices of the payoff matrices and dimension relations are derived.     

Multiobjective fractional programming duality theory

Results of Geoffrion for efficient and properly efficient solutions of multiobjective programming problems are extended to multiobjective fractional programming problems. Duality relationships are given for these problems where the functions are generalized convex or invex.     

Compromise allocation in multivariate stratified sampling: An integer solution

The problem of determining the sample sizes in various strata when several characteristics are under study is formulated as a nonlinear multistage decision problem. Dynamic programming is used to obtain an integer solution to the problem. © 1997 John Wiley & Sons, Inc.     

Volume discount decisions: Wealth maximization or EOQ approach?

A recent paper finds that when volume discounts are available, in some cases, reliance on the Economic Order Quantity (EOQ) model can induce purchasers to make wealth reducing decisions, and the Present Value (PV) approach should be preferred. While this finding is theoretically correct, the magnitudes of wealth reductions suggested by the paper's numerical examples seem to be questionable. Furthermore, the paper also finds that, in some other cases, a purchaser using the EOQ approach realizes a net increase in current wealth compared to a purchaser using the PV approach. Logic suggests that such a finding cannot be correct, since by its very definition, it is the PV approach that seeks to maximize the current wealth. We offer an alternative frame of comparison and a modified model to show that, under the paper's assumptions, the EOQ approach can never realize a net increase in current wealth compared to the current wealth generated by the PV approach. On the other hand, we also show that when typical values of the relevant parameters prevail, the additional costs imposed by the EOQ approach are not significant. Finally, we suggest that insofar as the PV approach requires greater administrative costs to implement, it may even be counterproductive to the goal of wealth maximization. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 377–389, 1998     

Exploiting symmetry in the reliability analysis of coherent systems

Components in a complex system are usually not structurally identical. However, in many cases we may find components that are structurally symmetric, and one should make use of this additional information to simplify reliability analysis. The main purpose of this article is to define and study one such class of systems, namely, those having symmetric components, and to derive some reliability-related properties. © 1996 John Wiley & Sons, Inc.     

The individual station technique for the analysis of cyclic polling systems

Polling systems are used to model a wide variety of real-world applications, for example, telecommunication and material handling systems. Consequently, there is continued interest in developing efficient algorithms to analyze the performance of polling systems. Recent interest in the optimization of these systems has brought up the need for developing very efficient techniques for analyzing their waiting times. This article presents the Individual Station technique for cyclic polling systems. The technique possesses the following features: (a) it allows the user to compute the mean waiting time at a selected station independent of the mean waiting time computations at other stations, and (b) its complexity is low and independent of the system utilization. In addition the technique provides explicit closed-form expressions for (i) the mean waiting times in a system with 3 stations, and (ii) the second moment of the waiting times in a system with 2 stations, for an exhaustive service system. © 1996 John Wiley & Sons, Inc.