Optimal Job Sequencing Control in a Benchmark Reentrant Line with Finite Capacity Buffers

This paper presents the optimality condition, Bellman’s equation, and an optimal job sequencing policy for a benchmark reentrant line (RL) with finite capacity buffers. The optimal policy is obtained for an infinite horizon discounted cost criterion, and is characterized by an index which is a function of the one-stage cost function and system’s parameters. In addition, when the buffer levels are below its maximum capacity, necessary and sufficient conditions for optimality are obtained, and the optimal policy is independent of the discount factor. Therefore, the policy exhibits characteristics similar to Blackwell optimal policies. Numerical examples are presented on which the optimal policy is obtained for both quadratic and linear one-stage cost functions. Keywords— Optimal control, dynamic programming, reentrant lines, finite capacity buffers.