An efficient heuristic procedure for the capacitated warehouse location problem

This paper introduces an efficient heuristic procedure for solving a special class of mixed integer programming problem called the capacitated warehouse (plant) location problem. This procedure parallels the work reported earlier in [9] on the uncapacitated warehouse location problem. The procedure can be viewed as tracing a judiciously selected path of the branch and bound tree (from the initial node to the terminal node) to arrive at a candidate solution. A simple backtracking scheme is also incorporated in the procedure to investigate possible improvement in the solution. Computational results on problems found in the literature look quite encouraging.     

A heuristic network procedure for the assembly line balancing problem

Proposed is a Heuristic Network (HN) Procedure for balancing assembly lines. The procedure uses simple heuristic rules to generate a network which is then traversed using a shortest route algorithm to obtain a heuristic solution. The advantages of the HN Procedure are: a) it generally yields better solutions than those obtained by application of the heuristics, and b) sensitivity analysis with different values of cycle time is possible without having to regenerate the network. The rationale for its effectiveness and its application to problems with paralleling are presented. Computational experience with the procedure on up to 50 task test problems is provided.     

An exact branch-and-bound procedure for the quadratic-assignment problem

The quadratic-assignment problem is a difficult combinatorial problem which still remains unsolved. In this study, an exact branch-and-bound procedure, which is able to produce optimal solutions for problems with twelve facilities or less, is developed. The method incorporates the concept of stepped fathoming to reduce the effort expended in searching the decision trees. Computational experience with the procedure is presented.     

The optimal burn-in testing of repairable equipment

The subject of this paper is the utilization of the “infant mortality” or decreasing failure rate effect to improve the reliability of repairable devices. Decreasing failure rate implies the possibility that devices which exhibit it can be improved by “burn-in testing” of each unit. Such a test serves to accumulate operating time while shielded from the full costs and consequences of failure. A general formulation of the burn-in test decision for repairable devices is presented and some special cases are solved. A class of models, indexed by the degree of partial replacement present in the repair process, is considered and numerical results for the optimal policy are given for several members of that class. A comparison of those results reveals the profitability of testing increases with the complexity of the repairable device.     

Probabilistic models of decreasing failure rate processes

The “infant mortality” effect observed in the statistical treatment of reliability consists of a decreasing with age of the conditional probability of equipment failure (failure rate). One widely applicable explanatory hypothesis is that of population heterogeneity. This is developed here as a basis for several specific models of decreasing failure rate processes. Since, in the case of repairable devices, decreasing failure rate is often observed after the occurrence of failure and repair, consideration is extended to include repair in an explicit way. This union of failure and repair models is a fruitful one in view of the interaction between the two processes and gives a complete picture of the life of the device in terms of a stochastic process, usually with non-independent interfailure times. Four models, of particular significance due to their plausibility, mathematical tractability, and frugality of parameterization, are presented.     

The fixed charge problem

A fundamental unsolved problem in the programming area is one in which various activities have fixed charges (e.g., set-up time charges) if operating at a positive level. Properties of a general solution to this type problem are discussed in this paper. Under special circumstances it is shown that a fixed charge problem can be reduced to an ordinary linear programming problem.     

Integer points on the Gomory fractional cut (hyperplane)

In this paper we show that the Gomory fractional cut (hyperplane) for the integer program is either void of integer points or contains an infinite number of them. The conditions for each case are presented. Also, we derive a stronger cut from the hyperplane which does not intersect integer points.     

On the busy period of the M/G/1 retrial queue

The M/G/1 queue with repeated attempts is considered. A customer who finds the server busy, leaves the service area and joins a pool of unsatisfied customers. Each customer in the pool repeats his demand after a random amount of time until he finds the server free. We focus on the busy period L of the M/G/1$ retrial queue. The structure of the busy period and its analysis in terms of Laplace transforms have been discussed by several authors. However, this solution has serious limitations in practice. For instance, we cannot compute the first moments of L by direct differentiation. This paper complements the existing work and provides a direct method of calculation for the second moment of L. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 115–127, 2000     

Makespan minimization in the two‐machine flowshop batch scheduling problem

In this paper we consider a practical scheduling problem commonly arising from batch production in a flexible manufacturing environment. Different part‐types are to be produced in a flexible manufacturing cell organized into a two‐stage production line. The jobs are processed in batches on the first machine, and the completion time of a job is defined as the completion time of the batch containing it. When processing of all jobs in a batch is completed on the first machine, the whole batch of jobs is transferred intact to the second machine. A constant setup time is incurred whenever a batch is formed on any machine. The tradeoff between the setup times and batch processing times gives rise to the batch composition decision. The problem is to find the optimal batch composition and the optimal schedule of the batches so that the makespan is minimized. The problem is shown to be strongly NP‐hard. We identify some special cases by introducing their corresponding solution methods. Heuristic algorithms are also proposed to derive approximate solutions. We conduct computational experiments to study the effectiveness of the proposed heuristics. © 2000 John Wiley & Sons, Inc. Naval Research Logistics 47: 128–144, 2000