Planning accelerated life tests for censored two‐parameter exponential distributions

We consider optimal test plans involving life distributions with failure‐free life, i.e., where there is an unknown threshold parameter below which no failure will occur. These distributions do not satisfy the regularity conditions and thus the usual approach of using the Fisher information matrix to obtain an optimal accelerated life testing (ALT) plan cannot be applied. In this paper, we assume that lifetime follows a two‐parameter exponential distribution and the stress‐life relationship is given by the inverse power law model. Near‐optimal test plans for constant‐stress ALT under both failure‐censoring and time‐censoring are obtained. We first obtain unbiased estimates for the parameters and give the approximate variance of these estimates for both failure‐censored and time‐censored data. Using these results, the variance for the approximate unbiased estimate of a percentile at a design stress is computed and then minimized to produce the near‐optimal plan. Finally, a numerical example is presented together with simulation results to study the accuracy of the approximate variance given by the proposed plan and show that it outperforms the equal‐allocation plan. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 169–186, 1999     

The residual life of the renewal process: A simple algorithm

We develop a simple algorithm, which does not require convolutions, for computing the distribution of the residual life when the renewal process is discrete. We also analyze the algorithm for the particular case of lattice distributions, and we show how it can apply to an inventory problem. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 435–443, 1999     

A heuristic for the two‐machine no‐wait openshop scheduling problem

In this paper the problem of minimizing makespan in a two‐machine openshop is examined. A heuristic algorithm is proposed, and its worst case performance ratio and complexity are analyzed. The average case performance is evaluated using an empirical study. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 129–145, 1999     

Heuristic procedures for scheduling job families with setups and due dates

This paper examines heuristic solution procedures for scheduling jobs on a single machine to minimize the maximum lateness in the presence of setup times between different job families. It reviews the state of knowledge about the solution of this problem, which is known to be difficult to solve in general, and examines natural solution approaches derived from some of the underlying theory. The emphasis is on the design and computational evaluation of new heuristic procedures. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 978–991, 1999     

Expected waiting time rankings in extended machine-repair models

The present paper studies the relative magnitudes of expected waiting times in extended machine-repair models, when processing times are of two Erlang types. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 864–870, 1999     

Value added analysis for army equipment modernization

This paper describes the Value Added Analysis methodology which is used as part of the U.S. Army's Planning, Programming, Budgeting, and Execution System to assist the Army leadership in evaluating and prioritizing competing weapon system alternatives during the process of building the Army budget. The Value Added Analysis concept uses a family of models to estimate an alternative system's contribution to the Army's effectiveness using a multiattribute value hierarchy. A mathematical optimization model is then used to simultaneously determine an alternative's cost‐benefit and to identify an optimal mix of weapon systems for inclusion in the Army budget. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 233–253, 1999     

A multiple‐shift workforce scheduling model under annualized hours

Many manufacturing and service organizations in Europe have used annualized hours, also known as flexiyear, to successfully tackle seasonal demand. Under annualized hours, the employer has a certain number of labor hours available in a year and the employer can allocate the hours over the year according to manpower need. A problem in planning for annualized hours is the scheduling of the workforce over the year. We present an algorithm to generate an annual schedule for a scenario in which a facility operates one or more shifts and manpower need may vary from week to week. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 726–736, 1999     

Estimating the point availability with right‐censored data

The point availability of a one‐unit system at a specified time is defined as the probability that the component is operating at that time. When both operating time and repair time are subject to random (right) censorship, we propose an asymptotic nonparametric approach for constructing confidence intervals for the point availability of the system. The technique is based on the fact that a product limit estimator converges to a Gaussian process. The method is also extended to finding confidence intervals for the point availability of a complex system using the δ‐Method. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 119–127, 1999     

Note: Two rendezvous search problems on the line

A new upper bound is obtained for the two‐person symmetric rendezvous value on the real line when the distribution function of their initial distance apart is bounded. A second result shows that if three players are placed randomly on adjacent integers on the real line facing in random directions and able to move at a speed of at most 1, then they can ensure a three‐way meeting time of at most 7/2; the fact that 7/2 is a best possible result follows from work already in the literature. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 335–340, 1999     

Approximation algorithms for the capacitated traveling salesman problem with pickups and deliveries

We consider the Capacitated Traveling Salesman Problem with Pickups and Deliveries (CTSPPD). This problem is characterized by a set of n pickup points and a set of n delivery points. A single product is available at the pickup points which must be brought to the delivery points. A vehicle of limited capacity is available to perform this task. The problem is to determine the tour the vehicle should follow so that the total distance traveled is minimized, each load at a pickup point is picked up, each delivery point receives its shipment and the vehicle capacity is not violated. We present two polynomial‐time approximation algorithms for this problem and analyze their worst‐case bounds. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 654–670, 1999     

The value of observing the condition of a deteriorating machine

We examine a small lot production setting in which a machine may go out of control and begin producing defective units. Traditionally, managers have had to rely upon observations of the quality of the output to determine whether the machine is in or out of control. However, with advances in technology such as vibration analysis, it is increasingly possible to obtain much more accurate information about the state of the machine. In this paper, we model and analyze a deteriorating machine in order to gain insight into the conditions under which investments in such technology are most beneficial. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 790–808, 1999     

Lagrangian relaxation approach to the targeting problem

In this paper, we consider a new weapon–target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model. We applied Lagrangian relaxation and a branch‐and‐bound method to the problem after transforming the nonlinear constraints into linear ones. An efficient primal heuristic is developed to find a feasible solution to the problem to facilitate the procedure. In the branch‐and‐bound method, three different branching rules are considered and the performances are evaluated. Computational results using randomly generated data are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 640–653, 1999     

Scheduling customer arrivals to a stochastic service system

An efficient algorithm for determining the optimal arrival schedule for customers in a stochastic service system is developed. All customers arrive exactly when scheduled, and service times are modeled as iid Erlang random variables. Costs are incurred at a fixed rate per unit of time each customer waits for service, and an additional cost is incurred for every unit of time the server operates beyond a scheduled closing time. The objective is to minimize total operating cost. This type of problem arises in many operational contexts including transportation, manufacturing, and appointment‐based services. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 549–559, 1999     

A genetic algorithm methodology for complex scheduling problems

This paper considers the scheduling problem to minimize total tardiness given multiple machines, ready times, sequence dependent setups, machine downtime and scarce tools. We develop a genetic algorithm based on random keys representation, elitist reproduction, Bernoulli crossover and immigration type mutation. Convergence of the algorithm is proved. We present computational results on data sets from the auto industry. To demonstrate robustness of the approach, problems from the literature of different structure are solved by essentially the same algorithm. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 199–211, 1999     

System availability in a gamma alternating renewal process

We measure the effectiveness of a repairable system by the proportion of time the system is on, where on-time and off-times are assumed independent and both gamma-distributed. This measure is helpful for system planning and control in the short term, before the steady-state is reached, and its mean value is intermediary between instantaneous and steady-state availabilities. We also present other significant results concerning the Gamma Alternating Renewal Process. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 822–844, 1999     

Measures of component importance for markov chain imbeddable reliability structures

In this article we study the reliability importance of the components for the wide class of Markov chain imbeddable systems (MIS). Methods for the evaluation of Birnbaum importance are developed for a general MIS, and some generating function techniques are demonstrated for the special case of homogeneous MISs. As an application, the reliability ordering for the components of a k‐out‐of‐n and consecutive‐k‐out‐of‐n structure is examined in some detail. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 613–639, 1999     

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     

Lateral stock transshipments in a two‐location inventory system with fixed and joint replenishment costs

We address the problem of inventory management in a two‐location inventory system, in which the transshipments are carried out as means of emergency or alternative supply after demand has been realized. This model differs from previous ones as regards its replenishment costs structure, in which nonnegligible fixed replenishment costs and a joint replenishment cost are considered. The single period planning horizon is analyzed, with the form and several properties of the optimal replenishment and transshipment policies developed, discussed and illustrated. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 525–547, 1999     

Two exact algorithms for the vehicle routing problem on trees

This article describes a heuristic and two exact algorithms for several classes of vehicle routing problems defined on tree networks. These include capacitated and time‐constrained vehicle routing problems. One of the exact algorithms is based on the computation of bin packing lower bounds. The other uses column generation. The first algorithm performs better on problems containing small customer demands and in which all vehicles are identical. Otherwise, the second algorithm is more powerful and more versatile. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 75–89, 1999     

Designing a degradation experiment

Degradation experiments are widely used to assess the reliability of highly reliable products which are not likely to fail under the traditional life tests. In order to conduct a degradation experiment efficiently, several factors, such as the inspection frequency, the sample size, and the termination time, need to be considered carefully. These factors not only affect the experimental cost, but also affect the precision of the estimate of a product's lifetime. In this paper, we deal with the optimal design of a degradation experiment. Under the constraint that the total experimental cost does not exceed a predetermined budget, the optimal decision variables are solved by minimizing the variance of the estimated 100pth percentile of the lifetime distribution of the product. An example is provided to illustrate the proposed method. Finally, a simulation study is conducted to investigate the robustness of this proposed method. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 689–706, 1999