Single machine scheduling with a restricted rate‐modifying activity

In this paper we consider the problem of scheduling a set of jobs on a single machine on which a rate‐modifying activity may be performed. The rate‐modifying activity is an activity that changes the production rate of the machine. So the processing time of a job is a variable, which depends on whether it is scheduled before or after the rate‐modifying activity. We assume that the rate‐modifying activity can take place only at certain predetermined time points, which is a constrained case of a similar problem discussed in the literature. The decisions under consideration are whether and when to schedule the rate‐modifying activity, and how to sequence the jobs in order to minimize some objectives. We study the problems of minimizing makespan and total completion time. We first analyze the computational complexity of both problems for most of the possible versions. The analysis shows that the problems are NP‐hard even for some special cases. Furthermore, for the NP‐hard cases of the makespan problem, we present a pseudo‐polynomial time optimal algorithm and a fully polynomial time approximation scheme. For the total completion time problem, we provide a pseudo‐polynomial time optimal algorithm for the case with agreeable modifying rates. © 2005 Wiley Periodicals, Inc. Naval Research Logistics, 2005     

Two heuristics for the economic lot scheduling problem: An experimental study

In this article we present and test two heuristics for the economic lot scheduling problem. The first heuristic was developed by one of us (P.C. Geng) during Ph.D. research, while the other is a convergent implementation of an algorithm due to Doll and Whybark. We study the performance of these heuristics on a large set of test problems constructed using a new form of problem generation that yields random problems within an experimental design.     

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     

Probabilistic analysis of an asymptotically optimal solution for the completion time variance problem

Scheduling a set of n jobs on a single machine so as to minimize the completion time variance is a well‐known NP‐hard problem. In this paper, we propose a sequence, which can be constructed in O(n log n) time, as a solution for the problem. Our primary concern is to establish the asymptotical optimality of the sequence within the framework of probabilistic analysis. Our main result is that, when the processing times are randomly and independently drawn from the same uniform distribution, the sequence is asymptotically optimal in the sense that its relative error converges to zero in probability as n increases. Other theoretical results are also derived, including: (i) When the processing times follow a symmetric structure, the problem has 2^{⌊(n−1)/2⌋} optimal sequences, which include our proposed sequence and other heuristic sequences suggested in the literature; and (ii) when these 2^{⌊(n−1)/2⌋} sequences are used as approximate solutions for a general problem, our proposed sequence yields the best approximation (in an average sense) while another sequence, which is commonly believed to be a good approximation in the literature, is interestingly the worst. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 373–398, 1999     

Optimal interdiction policy for a flow network

This paper analyzes the problem faced by a field commander who, confronted by an enemy on N battlefields, must determine an interdiction policy for the enemy's logistics system which minimizes the amount of war material flowing through this system per unit time. The resource utilized to achieve this interdiction is subject to constraint. It can be shown that this problem is equivalent to determining the set of arcs Z* to remove subject to constraint from a directed graph G such that the resulting maximal flow is minimized. A branch and bound algorithm for the solution to this problem is described, and a numerical example is provided.     

Longitudinal manpower planning models

A manpower planning model is presented that exploits the longitudinal stability of manpower cohorts. The manpower planning process is described. An infinite horizon linear program for calculating minimum cost manpower input plans is presented and found to have a straightforward solution in a great many cases and to yield an easily implemented approximation technique in other cases.