Cost analysis and extension of a simple maintenance-scheduling heuristic

Practitioners of maintenance scheduling sometimes use a simple analytic formula, derived based on inspection scheduling, as a heuristic to determine the length of the preventive maintenance period. The sensitivity of this heuristic solution is analyzed and the cost penalties are calculated compared to the exact solution that utilizes the lifetime distribution in the derivation of the optimal preventive maintenance period. A simple extension of the heuristic is suggested to improve the approximation with a slightly increased computational effort. The sensitivity and cost analysis of the improved heuristic are discussed as well. © 1994 John Wiley & Sons, Inc.     

Setting military reenlistment bonuses

The United States military frequently has difficulty retaining enlisted personnel beyond their initial enlistment. A bonus program within each service, called a Selective Reenlistment Bonus (SRB) program, seeks to enhance reenlistments and thus reduce personnel shortages in critical military occupational specialties (MOSs). The amount of bonus is set by assigning “SRB multipliers” to each MOS. We develop a nonlinear integer program to select multipliers which minimize a function of deviations from desired reenlistment targets. A Lagrangian relaxation of a linearized version of the integer program is used to obtain lower bounds and feasible solutions. The best feasible solution, discovered in a coordinate search of the Lagrangian function, is heuristically improved by apportioning unexpended funds. For large problems a heuristic variable reduction is employed to speed model solution. U.S. Army data and requirements for FY87 yield a 0-1 integer program with 12,992 binary variables and 273 constraints, which is solved within 0.00002% of optimality on an IBM 3033AP in less than 1.7 seconds. More general models with up to 463,000 binary variables are solved, on average, to within 0.009% of optimality in less than 1.8 minutes. The U.S. Marine Corps has used a simpler version of this model since 1986. © 1993 John Wiley & Sons, Inc.     

The conditional p-center problem in the plane

An algorithm is given for the conditional p-center problem, namely, the optimal location of one or more additional facilities in a region with given demand points and one or more preexisting facilities. The solution dealt with here involves the minimax criterion and Euclidean distances in two-dimensional space. The method used is a generalization to the present conditional case of a relaxation method previously developed for the unconditional p-center problems. Interestingly, its worst-case complexity is identical to that of the unconditional version, and in practice, the conditional algorithm is more efficient. Some test problems with up to 200 demand points have been solved. © 1993 John Wiley & Sons, Inc.     

A network reformulation of an electric utility expansion planning model

We reformulate a multiperiod capacity expansion model of electric utilities as a network model. We show how to reconstruct the dual solution of the original mathematical program from the network model solution. To formulate the network model, we use information about the properties of the optimal solution of the mathematical program to reduce the number of constraints. The remaining constraints are then readily converted into network constraints. © 1993 John Wiley & Sons. Inc.     

A parametric-based heuristic program for the quadratic assignment problem

In this article we study the quadratic assignment problem by embedding the actual data in a data space which satisfies an extension of the metric triangle property. This leads to simpler computations for the determination of heuristic solutions. Bounds are given for the loss of optimality which such heuristic solutions would involve in any specific instance. © 1993 John Wiley & Sons, Inc.     

Local search techniques for the generalized resource constrained project scheduling problem

In this article we address the problem of scheduling a single project network with both precedence and resource constraints through the use of a local search technique. We choose a solution definition which guarantees precedence feasibility, allowing the procedure to focus on overcoming resource infeasibility. We use the 110-problem data set of Patterson to test our procedure. Our results indicate a significant improvement over the best heuristic results reported to date for these problems (Bell and Han [1]). Two major advantages of the local search algorithm are its ability to handle arbitrary objective functions and constraints and its effectiveness over a wide range of problem sizes. We present a problem example with an objective function and resource constraints which include nonlinear and non-continuous components, which are easily considered by the procedure. The results of our algorithm are significantly better than random solutions to the problem. © 1993 John Wiley & Sons, Inc.     

On testing for decreasing mean residual life ordering

We consider the problem of testing for the decreasing mean residual life ordering introduced in Kochar and Wiens [14]. We treat both the one-sample and two-sample problems. The limiting distributions of the proposed test statistics are derived. © 1993 John Wiley & Sons, Inc.     

Optimal base stock policies and truck capacity in a two-echelon system

With the recent trend toward just-in-time deliveries and reduction of inventories, many firms are reexamining their inventory and logistics policies. Some firms have dramatically altered their inventory, production, and shipping policies with the goal of reducing costs and improving service. Part of this restructuring may involve a specific contract with a trucking company, or it may entail establishing in-house shipping capabilities. This restructuring, however, raises new questions regarding the choice of optimal trucking capacity, shipping frequency, and inventory levels. In this study, we examine a two-level distribution system composed of a warehouse and a retailer. We assume that demand at the retailer is random. Since the warehouse has no advance notice of the size of the retailer order, inventory must be held there as well as at the retailer. We examine inventory policies at both the warehouse and the retailer, and we explicitly consider the trucking capacity, and the frequency of deliveries from the warehouse to the retailer. Both linear and concave fixed transportation costs are examined. We find the optimal base stock policies at both locations, the optimal in-house or contracted regular truck capacity, and the optimal review period (or, equivalently, delivery frequency). For the case of normally distributed demand we provide analytical results and numerical examples that yield insight into systems of this type. Some of our results are counterintuitive. For instance, we find some cases in which the optimal truck capacity decreases as the variability of demand increases. In other cases the truck capacity increases with variability of demand. © 1993 John Wiley & Sons, Inc.     

A bivariate pareto model and its applications to reliability

We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed. © 1993 John Wiley & Sons, Inc.