The minmax multidimensional knapsack problem with application to a chance‐constrained problem

In this paper we present a new combinatorial problem, called minmax multidimensional knapsack problem (MKP), motivated by a military logistics problem. The logistics problem is a two‐period, two‐level, chance‐constrained problem with recourse. We show that the MKP is NP‐hard and develop a practically efficient combinatorial algorithm for solving it. We also show that under some reasonable assumptions regarding the operational setting of the logistics problem, the chance‐constrained optimization problem is decomposable into a series of MKPs that are solved separately. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Some aging properties of parallel and series systems with a random number of components

In this article, we study aging properties of parallel and series systems with a random number of components. We show that the decreasing likelihood ratio property is closed under the formation of random minima. We also show, by counterexamples, that other aging properties are not closed under the formation of random minima or maxima. Some mistakes in the literature are corrected. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 238–243, 2014     

Multiperiod resource allocation with a smoothing objective

We consider a multiperiod resource allocation problem, where a single resource is allocated over a finite planning horizon of T periods. Resource allocated to one period can be used to satisfy demand of that period or of future periods, but backordering of demand is not allowed. The objective is to allocate the resource as smoothly as possible throughout the planning horizon. We present two models: the first assumes that the allocation decision variables are continuous, whereas the second considers only integer allocations. Applications for such models are found, for example, in subassembly production planning for complex products in a multistage production environment. Efficient algorithms are presented to find optimal allocations for these models at an effort of O(T²). Among all optimal policies for each model, these algorithms find the one that carries the least excess resources throughout the planning horizon. © 1995 John Wiley & Sons, Inc.     

A many-on-many stochastic duel model for a mountain battle

Terrain plays a major role in mountain battle. The advancing (attacking) force is usually restricted to move in a single column—along a narrow, winding, and steep road. The defending force, on the other hand, which is static, can select its positions such that most of its firepower can be effective against the front unit(s) of the attacking force. This combat situation is modeled as a special type of the many-on-many stochastic duel. This duel is a series of many-on-one subduels where at each such subduel the defending force units simultaneously engage the single exposed front unit of the attacking force. This special type of many-on-many stochastic duel demonstrates the possibility of practical applications of stochastic duel theory.     

Printed circuit board family grouping and component allocation for a multimachine,open-shop assembly cell

This article considers a particular printed circuit board (PCB) assembly system employing surface mount technology. Multiple, identical automatic placement machines, a variety of board types, and a large number of component types characterize the environment studied. The problem addressed is that of minimizing the makespan for assembling a batch of boards with a secondary objective of reducing the mean flow time. The approach adopted is that of grouping boards into production families, allocating component types to placement machines for each family, dividing of families into board groups with similar processing times, and the scheduling of groups. A complete setup is incurred only when changing over between board families. For the environment studied, precedence constraints on the order of component placement do not exist, and placement times are independent of feeder location. Heuristic solution procedures are proposed to create board subfamilies (groups) for which the component mounting times are nearly identical within a subfamily. Assignment of the same component type to multiple machines is avoided. The procedures use results from the theory of open-shop scheduling and parallel processor scheduling to sequence boards on machines. Note that we do not impose an open-shop environment but rather model the problem in the context of an open shop, because the order of component mountings is immaterial. Three procedures are proposed for allocating components to machines and subsequently scheduling boards on the machines. The first two procedures assign components to machines to balance total work load. For scheduling purposes, the first method groups boards into subfamilies to adhere to the assumptions of the open-shop model, and the second procedure assumes that each board is a subfamily and these are scheduled in order of shortest total processing time. The third procedure starts by forming board subfamilies based on total component similarity and then assigns components to validate the open-shop model. We compare the performance of the three procedures using estimated daily, two-day, and weekly production requirements by averaging quarterly production data for an actual cell consisting of five decoupled machines. © 1994 John Wiley & Sons, Inc.     

A two-on-one stochastic duel with maneuvering and fire allocation tactics

The large body of work on stochastic duels represents an attempt to model combat situations, or parts of it, by means of formal probability models. Most, but not all, of the existing stochastic duel models, however, relate to static posture and fail to capture dynamic aspects as well as tactical considerations that may be present. In this article we propose a simple model of a two-on-one duel in which dynamic and tactical aspects are considered. The model represents a combat situation that is typical of a battle in which a maneuvering force attacks a smaller defending unit that is static.     

Minimizing the makespan in open‐shop scheduling problems with a convex resource consumption function

We consider open‐shop scheduling problems where operation‐processing times are a convex decreasing function of a common limited nonrenewable resource. The scheduler's objective is to determine the optimal job sequence on each machine and the optimal resource allocation for each operation in order to minimize the makespan. We prove that this problem is NP‐hard, but for the special case of the two‐machine problem we provide an efficient optimization algorithm. We also provide a fully polynomial approximation scheme for solving the preemptive case. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006     

The effect of training data set size and the complexity of the separation function on neural network classification capability: The two-group case

Classification among groups is a crucial problem in managerial decision making. Classification techniques are used in: identifying stressed firms, classifying among consumer types, and rating of firms' bonds, etc. Neural networks are recognized as important and emerging methodologies in the area of classification. In this paper, we study the effect of training sample size and the neural network topology on the classification capability of neural networks. We also compare neural network capabilities with those of commonly used statistical methodologies. Experiments were designed and carried out on two-group classification problems to find answers to these questions. The prediction capability of the neural network models are better than traditional statistical models. The learning capability of the neural networks is improving compared to traditional models because the discriminate function is more complex. For real world classification problems, the usage of neural networks is highly recommended, for two reasons: learning capability and flexibility. Learning capability: Neural network classifies better in sterile experiments as performed in this research. Flexibility: Real life data are rarely not contaminated with noise, such as unknown distributions, and missing variables, etc. Neural networks differ from a statistical model that it is not dependent on any assumption concerning the data set distribution. © 1997 John Wiley & Sons, Inc. Naval Research Logistics 44: 699–717, 1997     

Generalized linear programming and sensitivity analysis techniques

In this article we report on numerical experiments conducted to assess the performance of c-programming algorithms for generalized linear programming problems involving the maximization of composite-convex objective functions. The results indicate that the standard parametric sensitivity analysis techniques of the simplex method can play a central role in such algorithms. We also comment on issues concerning the use of commercial LP packages to solve problems of this type. © 1996 John Wiley & Sons, Inc.