Minimizing absolute and squared deviations of completion times with different earliness and tardiness penalties and a common due date

We consider a single-machine scheduling problem in which all jobs have the same due date and penalties are assessed for both early and late completion of jobs. However, earliness and tardiness are penalized at different rates. The scheduling objective is to minimize either the weighted sum of absolute deviations (WSAD) or the weighted sum of squared deviations (WSSD). For each objective we consider two versions of the problem. In the unconstrained version an increase in the due date does not yield any further decrease in the objective function. We present a constructive algorithm for the unconstrained WSAD problem and show that this problem is equivalent to the two-parallel, nonidentical machine, mean flow-time problem. For the unconstrained WSSD and the constrained WSAD and WSSD problems we propose implicit enumeration procedures based on several dominance conditions. We also report on our computational experience with the enumeration procedures.     

The validity of assumptions underlying current uses of Lanchester attrition rates

This study examines critically the various assumptions, results, and concepts that exist to date in the literature and scientific community concerning the relationships among the Lanchester, stochastic Lanchester, and the general renewal models of combat. Many of the prevailing understandings are shown to be erroneous.     

A branch-and-bound algorithm for flow-path design of automated guided vehicle systems

An algorithm for determining the optimal, unidirectional flow path for an automated guided vehicle system with a given facility layout is presented. The problem is formulated as an integer program. The objective is to minimize the total distance traveled by vehicles subject to the constraint that the resulting network consists of a single strongly connected component. A specialized branch-and-bound solution procedure is discussed in detail.     

Minimizing flow time on a single machine with job classes and setup times

We examine the static sequencing problem of ordering the processing of jobs on a single machine so as to minimize the average weighted flow time. It is assumed that all jobs have zero ready times, and that the jobs are grouped into classes with the property that setup tasks are only required when processing switches from jobs of one class to jobs of another class. The time required for each setup task is given by the sum of a setdown time from the previous class and a setup time for the new class. We show that an algorithm presented in the literature for solving a special case of this problem gives suboptimal solutions. A number of properties of the optimal solution are derived, and their use in algorithms is evaluated. Computational results are presented for both a branch-and-bound procedure and a simpler depth-first search.     

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.