Optimal Batch Sizing and Repair Strategies for Operations with Repairable Jobs
研究瓶颈设施在同时处理常规作业和修复作业时的最优修复策略，通过分析批次测试结果（合格、可修复、不可修复），提出“不修复”或“全部修复”两种最优策略，并给出阈值操作策略，以最大化长期平均运营利润。
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.