A note on explicit solution in linear fractional programming

In this note we analyze the fractional interval programming problem (FIP) and find, explicitly, all its optimal solutions. Though our results are essentially the same as those in Charnes and Cooper [4], the proofs and analysis we provide here are considerably simpler.     

Flowshop sequencing problem with ordered processing time matrices: A general case

The ordered matrix flow shop problem with no passing of jobs is considered. In an earlier paper, the authors have considered a special case of the problem and have proposed a simple and efficient algorithm that finds a sequence with minimum makespan for a special problem. This paper considers a more general case. This technique is shown to be considerably more efficient than are existing methods for the conventional flow shop problems.     

An algorithm for solving general fractional interval programming problems

A Linear Fractional Interval Programming problem (FIP) is the problem of extremizing a linear fractional function subject to two-sided linear inequality constraints. In this paper we develop an algorithm for solving (FIP) problems. We first apply the Charnes and Cooper transformation on (FIP) and then, by exploiting the special structure of the pair of (LP) problems derived, the algorithm produces an optimal solution to (FIP) in a finite number of iterations.     

Ordering policies for an inventory system with three supply modes

This article explores ordering policies for inventory systems with three supply modes. This model is particularly interesting because the optimal ordering decision needs to balance the inventory and purchase costs, as well as the costs for earlier and later periods. The latter cost trade-off is present only in inventory systems with three or more supply modes. Therefore, the result not only offers guidelines for the operation of the concerned inventory systems, but also provides valuable insight into the complex cost trade-offs when more supply modes are available. We assume that the difference between the lead times is one period, and the inventory holding and shortage costs are linear. We analyze two cases and obtain the structure of the optimal ordering policy. Moreover, in the first case, explicit formulas are derived to calculate the optimal order-up-to levels. In the second case, although the optimal order-up-to levels are functions of the initial inventory state and are not obtained in closed form, their properties are discussed. We also develop heuristic ordering policies based on the news-vendor model. Our numerical experiments suggest that the heuristic policies perform reasonably well. © 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.     

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.     

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.     

A linear-programming-based method for determining whether or not n demand points are on a hemisphere

Whenever n demand points are located on a hemisphere, spherical location problems can be solved easily using geometrical methods or mathematical programming. A method based on a linear programming formulation with four constraints is presented to determine whether n demand points are on a hemisphere. The formulation is derived from a modified minimax spherical location problem whose Karush-Kuhn-Tucker conditions are the constraints of the linear program. © 1993 John Wiley & Sons, Inc.