Optimal Batch Sizing and Repair Strategies for Operations with Repairable Jobs

Kut C. So and Christopher S. Tang
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Kut C. So: Graduate School of Management, University of California, Irvine, California 92717
Christopher S. Tang: Anderson Graduate School of Management, University of California, Los Angeles, California 90024

Management Science, 1995, vol. 41, issue 5, 894-908

Abstract: This paper presents a model of a bottleneck facility that performs two distinct types of operations: "regular" and "repair." Both switch-over time and cost are incurred when the facility switches from performing one type of operation to a different type. Upon the completion of a batch of jobs in the regular mode, each batch is subjected to a test, where the entire batch (of jobs) will be classified accordingly as either nondefective, repairable, or nonrepairable. A nondefective batch continues its process downstream, a nonrepairable batch is scrapped, and a repairable batch can be cycled back to the bottleneck facility for repair. The objective of this paper is to determine the optimal repair policy for the bottleneck facility so that the long run average operating profit is maximized. We first characterize the optimal repair policy by showing that the optimal repair policy must take one of the two forms: a "repair-none" policy under which all repairable batches are scrapped, or a "repair-all" policy under which all repairable batches are repaired. We then develop optimality conditions for the repair-none policy and the repair-all policy. When the repair-all policy is optimal, we further show that there exists an optimal "threshold" operating policy that can be described as follows: upon completion of a regular batch, switch over to the repair mode only if the number of available repairable batches exceeds a certain threshold value. We also evaluate the impact of batch sizes, yield, and switch-over cost on the optimal operating policy.

Keywords: bottleneck with yield loss; bottleneck with repairable jobs; optimal repair policy; optimal processing policy; dynamic policy; static policy; optimal batch size (search for similar items in EconPapers)
Date: 1995
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