OPTIMAL OPERATING POLICY FOR A BOTTLENECK WITH RANDOM REWORK

This paper presents a model of a bottleneck facility that performs two distinct types of operations: ''regular'' and ''rework.'' Each job is subjected to a test after completing the regular operation at the bot tleneck. If the job passes the test, then it continues its process dow nstream. Otherwise, the job will cycle back to the bottleneck stage fo r rework operation. Upon the completion of a batch of regular jobs, Me decision maker observes the amount of rework and decides on whether t o switch over to process the reworks or continue to process another ba tch of regular jobs. It is assumed that both switch-over time and cost are incurred when the facility switches from performing one type of o peration to a different type. The goal of the analysis is to character ize Me optimal operating policy for the bottleneck so that the average operating cost is minimized. In order to characterize the optimal ope rating policy, we first formulate the problem as a semi-Markov decisio n process. Then we show that there exists an optimal ''threshold'' ope rating policy that can be described as follows: upon completion of a b atch of regular jobs, switch over to process the reworks only if the n umber of reworks exceeds a critical value. In addition, we develop a s imple procedure to compute the critical value that specifies the optim al threshold policy. Moreover, we evaluate the impact of batch sizes, yield, and switch-over time on the optimal threshold policy.