Relative value function approximation for the capacitated re-entrant line scheduling problem

The problem addressed in this study is that of determining how to allocate the workstation processing and buffering capacity in a capacitated re-entrant line to the job instances competing for it, in order to maximize its long-run/steady-state throughput, while maintaining the logical correctness of the underlying material flow, i.e., deadlock-free operations. An approximation scheme for the optimal policy that is based on neuro-dynamic programming theory is proposed, and its performance is assessed through a numerical experiment. The derived results indicate that the proposed method holds considerable promise for providing a viable, computationally efficient approach to the problem and highlight directions for further investigation.