An exact algorithm for the maximal covering problem

This article develops a robust, exact algorithm for the maximal covering problem (MCP) using dual-based solution methods and greedy heuristics in branch and bound. Based on tests using randomly generated problems with problem parameters similar to those in the existing literature, the hybrid approach developed in this work appears to be effective over a wide range of MCP model parameters. The method is further validated on problems constructed from three real-world data sets. The extensive computational study compares the new method with other existing exact methods using problems that are as big, or larger than, those used in previous work on MCP. The results show that the proposed method is effective in most instances of MCP. In particular, it is shown that bounding schemes using Lagrangian relaxation are effective on MCP as a method of obtaining both exact and heuristic solutions. © 1996 John Wiley & Sons, Inc.     

General solution to many-on-many heterogeneous stochastic combat

Stochastic combat models are more realistic than either deterministic or exponential models. Stochastic combat models have been solved analytically only for small combat sizes. It is very difficult, if not impossible, to extend previous solution techniques to larger-scale combat. This research provides the solution for many-on-many heterogeneous stochastic combat with any break points. Furthermore, every stage in stochastic combat is clearly defined and associated aiming and killing probabilities are calculated. © 1996 John Wiley & Sons, Inc.     

The advantage of deeper pockets in Silverman's game on intervals

Silverman's game on (1, B) × (1, B) was analyzed by R. J. Evans, who showed that optimal strategies exist (and found them) only on a set of measure zero in the parameter plane. We examine the corresponding game on (1, B) × (1, D) with D > B, and show that optimal strategies exist in about half the parameter plane. Optimal strategies and game value are obtained explicitly. © 1995 John Wiley & Sons, Inc.     

Expressions for item fill rates in periodic inventory systems

We examine the problem of estimating the item fill rate in a periodic inventory system. We show that the traditional expressions for line item fill rate, found in many operations management textbooks, perform well for high fill rates (above 90%), but they consistently underestimate the true fill rate. The problem of underestimation becomes significant as the fill rate falls below 90% and is greatly amplified in cases with very low fill rates (below 50%). We review other more accurate expressions for fill rate, discussing their relative merits. We then develop an exact fill rate expression that is robust for both high and low fill rates. We compare the new expression to others found in the literature via an extensive set of simulation experiments using data that reflect actual inventory systems found at Hewlett-Packard. We also examine the robustness of the expressions to violations in the underlying assumptions. Finally, we develop an alternative fill rate expression that is robust for cases of high demand variability where product returns are allowed. © 1995 John Wiley & Sons, Inc.     

Criteria and approximate methods for path-constrained moving-target search problems

A search is conducted for a target moving in discrete time among a finite number of cells according to a known Markov process. The searcher must choose one cell in which to search in each time period. The set of cells available for search depends upon the cell chosen in the last time period. The problem is to find a search path, i.e., a sequence of search cells, that either maximizes the probability of detection or minimizes the mean number of time periods required for detection. The search problem is modelled as a partially observable Markov decision process and several approximate solutions procedures are proposed. © 1995 John Wiley & Sons, Inc.     

Facility location and capacity acquisition: An integrated approach

The facility location and capacity acquisition decisions are intertwined, especially within the international context where capacity acquisition costs are location dependent. A review of the relevant literature however, reveals that the facility location and the capacity acquisition problems have been dealt with separately. Thus, an integrated approach for simultaneous optimization of these strategic decisions is presented. Analytical properties of the arising model are investigated and an algorithm for solving the problem is devised. Encouraging computational results are reported. © 1995 John Wiley & Sons, Inc.     

An exact aggregation/disaggregation algorithm for large scale markov chains

Many Markov chain models have very large state spaces, making the computation of stationary probabilities very difficult. Often the structure and numerical properties of the Markov chain allows for more efficient computation through state aggregation and disaggregation. In this article we develop an efficient exact single pass aggregation/disaggregation algorithm which exploits structural properties of large finite irreducible mandatory set decomposable Markov chains. The required property of being of mandatory set decomposable structure is a generalization of several other Markov chain structures for which exact aggregation/disaggregation algorithms exist. © 1995 John Wiley & Sons, Inc.     

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.     

Jointly constrained order quantities with all-units discounts

In this article we investigate situations where the buyer is offered discounted price schedules from alternative vendors. Given various discount schedules, the buyer must make the best buying decision under a variety of constraints, such as limited storage space and restricted inventory budgets. Solutions to this problem can be utilized by the buyer to improve profitability. EOQ models for multiple products with all-units discounts are readily solvable in the absence of constraints spanning the products. However, constrained discounted EOQ models lack convenient mathematical properties. Relaxing the product-spanning constraints produces a dual problem that is separable, but lack of convexity and smoothness opens the door for duality gaps. In this research we present a set of algorithms that collectively find the optimal order vector. Finally, we present numerical examples using actual data. to illustrate the application of the algorithms. © 1993 John Wiley & Sons, Inc.