Differential Evolution to Solve the Lot Size Problem in Stochastic Production Systems

An Advanced Resource Planning model is presented to support optimal lot size decisions for performance improvement of a production system in terms of either delivery time or setup related costs. Based on a queueing network, a model is developed for a mix of multiple products following their own speci fic sequence of operations on one or more resources, while taking into account various sources of uncertainty, both in demand as well as in production characteristics. In addition, the model includes the impact of parallel servers and diff erent time schedules in a multi-period planning setting. The corrupting influence of variabilities from rework and breakdown is explicitly modeled. As a major result, the di fferential evolution algorithm is able to fi nd the optimal lead time as a function of the lot size. In this way, we add a conclusion on the debate on the convexity between lot size and lead time in a complex production environment. We show that differential evolution outperforms a steepest descent method in the search for the global optimal lot size. For problems of realistic size, we propose appropriate control parameters for the differential evolution in order to make its search process more efficient