Optimal Lot Sizing in a Two-Stage System with Auto-Correlated Arrivals

Most research on lot-size optimization has concentrated on single-stage batch production systems. However, in practice it is of interest to optimize performance over multiple processing stages, where stages are not independent. The models in this study consider two stages, where multiple products are produced using the processing stages sequentially. The objective is to minimize total lot flow times across both stages by selecting the optimal lot sizes for each product, subject to these remaining constant across both stages. Analytical relationships can be developed but rely on the assumption of lot interarrival time independence. This is clearly not the case in most manufacturing problems. Better solutions can be obtained experimentally using simulation and response surface methods. Alternatively, an approach has been developed that allows dynamic feedback to be used in adjusting analytical relations to compensate for auto-correlation. Results using this approach compare well with those obtained experimentally.