Numerical study of the optimality of a threshold policy in a batch service queue with operating costs

Abstract

Semiconductor manufacturing systems include multiple batch processing operations. In the case where a batch process machine becomes idle when there is an incomplete batch in queue, a decision should be made to either start processing a partial batch or to wait for more lots to come. The trade-off in this situation is that in the first scenario, there will be an underutilization of the Batch Processing Machine, and more operating costs (Run cost, setup cost..etc). However, choosing to wait for upcoming lots increases the queuing time for the existing ones, hence the total cycle time. This study will provide an optimal batching policy that helps make a load/wait decision considering the state of the system, and study the optimality of the threshold policy, a common policy in batch processing. The system is modeled as a Markov Decision Process described with two variables: The number of lots in queue and the number of lots in service. It is then solved using dynamic programming, and the performance of the result policy in terms of time and cost is evaluated, and compared to the performance of two other batching policies.