Differential evolution to solve the lot size problem in stochastic supply chain management systems

An advanced resource planning model is presented to support optimal lot size decisions for overall performance improvement of real-life supply chain management systems in terms of either total delivery time or total setup costs. Based on a queueing network, a model is developed for a mix of products, which follow a sequence of operations taking place at multiple interdependent supply chain members. At the same time, various sources of uncertainty, both in demand and process characteristics, are taken into account. In addition, the model includes the impact of parallel servers for multiple resources with period dependent time schedules. The corrupting influence of variabilities from rework and breakdown is also explicitly modeled. This integer non-linear problem is solved by standard differential evolution algorithms. They are able to find each product's lot size that minimizes its total supply chain lead time. We show that this solution approach outperforms the steepest descent method, an approach commonly used in the search for optimal lot sizes. For problems of realistic size, we propose appropriate control parameters for an efficient differential evolutionary search process. Based on these results, we add a major conclusion on the debate concerning the convexity between lot size and lead time in a complex supply chain environment.