Capacity improvement,penalties, and the fixed charge transportation problem

Capacity improvement and conditional penalties are two computational aides for fathoming subproblems in a branch‐and‐bound procedure. In this paper, we apply these techniques to the fixed charge transportation problem (FCTP) and show how relaxations of the FCTP subproblems can be posed as concave minimization problems (rather than LP relaxations). Using the concave relaxations, we propose a new conditional penalty and three new types of capacity improvement techniques for the FCTP. Based on computational experiments using a standard set of FCTP test problems, the new capacity improvement and penalty techniques are responsible for a three‐fold reduction in the CPU time for the branch‐and‐bound algorithm and nearly a tenfold reduction in the number of subproblems that need to be evaluated in the branch‐and‐bound enumeration tree. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 341–355, 1999     

Response surface analysis of two‐stage stochastic linear programming with recourse

We apply the techniques of response surface methodology (RSM) to approximate the objective function of a two‐stage stochastic linear program with recourse. In particular, the objective function is estimated, in the region of optimality, by a quadratic function of the first‐stage decision variables. The resulting response surface can provide valuable modeling insight, such as directions of minimum and maximum sensitivity to changes in the first‐stage variables. Latin hypercube (LH) sampling is applied to reduce the variance of the recourse function point estimates that are used to construct the response surface. Empirical results show the value of the LH method by comparing it with strategies based on independent random numbers, common random numbers, and the Schruben‐Margolin assignment rule. In addition, variance reduction with LH sampling can be guaranteed for an important class of two‐stage problems which includes the classical capacity expansion model. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 753–776, 1999     

The open shop scheduling problem with a given sequence of jobs on one machine

The paper considers the open shop scheduling problem to minimize the make-span, provided that one of the machines has to process the jobs according to a given sequence. We show that in the preemptive case the problem is polynomially solvable for an arbitrary number of machines. If preemption is not allowed, the problem is NP-hard in the strong sense if the number of machines is variable, and is NP-hard in the ordinary sense in the case of two machines. For the latter case we give a heuristic algorithm that runs in linear time and produces a schedule with the makespan that is at most 5/4 times the optimal value. We also show that the two-machine problem in the nonpreemptive case is solvable in pseudopolynomial time by a dynamic programming algorithm, and that the algorithm can be converted into a fully polynomial approximation scheme. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 705–731, 1998     

Inventory management under random supply disruptions and partial backorders

We explore the management of inventory for stochastic-demand systems, where the product's supply is randomly disrupted for periods of random duration, and demands that arrive when the inventory system is temporarily out of stock become a mix of backorders and lost sales. The stock is managed according to the following modified (s, S) policy: If the inventory level is at or below s and the supply is available, place an order to bring the inventory level up to S. Our analysis yields the optimal values of the policy parameters, and provides insight into the optimal inventory strategy when there are changes in the severity of supply disruptions or in the behavior of unfilled demands. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 687–703, 1998     

Minimizing weighted mean absolute deviation of flow times in single machine systems

We discuss the problem of scheduling several jobs on a single machine with the objective of minimizing the weighted mean absolute deviation of flow times around the weighted mean flow time. We first show that the optimal schedule is W-shaped. For the unweighted case, we show that all optimal schedules are V-shaped. This characterization enables us to show that the problem is NP-hard. We then provide a pseudopolynomial algorithm for the unweighted problem. Finally, we consider three heuristic algorithms for the unweighted problem and report computational experience with these algorithms. © 1998 John Wiley & Sons, Inc. Naval Research Logistics 45: 297–311, 1998     

A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

This article generalizes the model for the economic design of x̄-control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in-control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull-distributed in-control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in-control periods having an increasing failure rate is assumed and the possibility of age-dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.     

Minimizing quality control costs for laboratory instruments using information delays

This paper proposes the use of a cost-based statistical process control system for monitoring the quality of an unreliable analytical machine. In this environment the accuracy of the process cannot be determined by inspecting the output, but must be verified by analyzing standards of known values. The results demonstrate that a significant cost savings can be obtained if analytical results are placed in a “buffer” and their release delayed until the accuracy of the test can be assured. Results suggest the approach not only dramatically improves the quality of results reported but also significantly reduces the expected total cost of testing. © 1996 John Wiley & Sons, Inc.     

Reliability models and inference for systems operating in different environments

We consider a class of models for the reliability function of a series system. The models incorporate dependence of the function on environmental covariates. On the basis of censored data obtained by monitoring several series systems operating under various sets of values of the covariates, estimators are derived of the reliability function of a series system operating under a different set of values of the covariates. Estimators of various functionals of the reliability function, such as the trimmed mean and quantiles, are also presented. Asymptotic properties of the estimators are obtained with the use of the framework of counting processes and martingales. The loss in efficiency in estimating the regression parameters and the reliability function is also examined when one assumes a more general semiparametric model, when in fact the true model belongs to a more restricted model. We illustrate these procedures with the use of accelerated failure-time data. © 1996 John Wiley & Sons, Inc.     

The single period procurement problem where dedicated supplier capacity can be reserved

In this article we consider the single period procurement strategy for an item with uncertainty in its demand and uncertainty in the capacity of the supplier. Dedicated capacity can be ensured by paying a premium charge to the supplier. The other decision variable is the replenishment quantity to request. It turns out to be very easy to select the best value of this latter quantity. On the other hand, we are only able to characterize the general behavior of the expected profit as a function of the level of dedicated capacity. In general, there can be multiple local maxima as a function of the dedicated capacity. However, for the special, but important, case of normally distributed demand, normally distributed capacity and a linear cost for reserving capacity, an algorithm is developed for finding the best level of dedicated capacity. Some preliminary insights regarding the extension to multiple periods are presented. © 1995 John Wiley & Sons, Inc.     

Component part stocking policies

This article presents research designed to aid firms who assemble many components into a final product. We assume that purchase quantities are fixed, and that all parts and components are assembled at one stage in a short time. Demand for the final product is represented by a stationary independent and identically distributed random variable; and unmet demand is backordered. Ordering is done on a periodic review basis. We develop infinite horizon, approximate expected cost, and expected service level functions, and we present an algorithm for finding approximately minimum cost reorder points for each part subject to a service level constraint. Extensive results on the accuracy of the approximations are presented. Due to the size of the problem, we present only limited results on the performance of the optimization algorithm.