Stochastic optimization models for service and manufacturing industry

Abstract

<p>We explore two novel applications of stochastic optimization inspired by real-world problems. The first application involves the optimization of appointments-based service systems. The problem here is to determine an optimal schedule of start times for jobs that have random durations, and a range of potential cost structures based on common performance metrics such as customer waiting and server idling . We show that the problem can be formulated as a two-stage stochastic linear program and develop an algorithm that utilizes the problem structure to obtain a near-optimal solution. Various aspects of the problem are considered, including the effects of job sequence, dependence on cost parameters, and job duration distributions. A range of numerical experiments is provided and some resulting insights are summarized. Some simple heuristics are proposed, based on relaxations of the problem, and evidence of their effectiveness is provided. The second application relates to inventory deployment at an integrated steel manufacturer (ISM). The models presented in this case were developed for making inventory design-choice (what to carry) and lot-size (how much to carry) decisions. They were developed by working with managers from several different functional areas at a particular ISM. They are, however, applicable to other ISMs and to other continuous-process industries with similar architectures. We discuss details of the practical implementation of the models, the structure of the problems, and algorithms and heuristics for solving them. Numerical experiments illustrate the accuracy of the heuristics, and examples based on empirical data from an ISM show the advantages of using such models in practice and suggest some managerial insights.</p>