OPTIMAL BATCH SIZING AND REPAIR STRATEGIES FOR OPERATIONS WITH REPAIRABLE JOBS

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 perfo rming one type of operation to a different type, Upon the completion o f a batch of jobs in the regular mode, each batch is subjected to a te st, where the entire batch (of jobs) will be classified accordingly as either nondefective, repairable, or nonrepairable. A nondefective bat ch 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 r epair policy for the bottleneck facility so that the long run average operating profit is maximized. We first characterize the optimal repai r policy by showing that the optimal repair policy must take one of th e two forms: a ''repair-none'' policy under which all repairable batch es are scrapped, or a ''repair-all'' policy under which all repairable batches are repaired. We then develop optimality conditions for the r epair-none policy and the repair-all policy. When the repair-all polic y 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 o n the optimal operating policy.