Multi-cycle production network design under supply uncertainty

Abstract

This study addresses a novel production network design problem with an expanded scope inspired by a real-world business context. The problem involves strategic decisions for a long-term horizon regarding production sites’ location and capacity, suppliers’ selection, and transportation modes choice, given in-house vs external service providers’ options. To support these decisions, we integrate key tactical decisions for a large set of planning periods, involving flows between origin–destination pairs, production levels based on bill of materials, and inventory levels. Additionally, we consider uncertainty in raw material availability at suppliers, disruption in production capacities, and perturbation in transportation flows. First, we develop a multi-stage stochastic program that re-optimizes strategic decisions at each design period. Then, this program is reformulated into a multi-cycle two-stage stochastic model. Uncertainty is modeled through a finite set of scenarios generated using the Latin hypercube sampling technique, and the sample average approximation method is used to calibrate the sample size. Given the challenging solvability of the model, we proposed an advanced solution approach that builds on the recently introduced Partial Benders Decomposition (PBD) technique with new scenario creation strategies. Our experiments highlight the superiority of the proposed PBD’s variant in terms of solution quality and time reaching the best solution, compared to classical approaches. Furthermore, we demonstrate the benefits of enlarging the scope of the production network design problem by integrating all strategic decisions, which can yield gains of up to 36% compared to addressing them separately. Finally, we underscore the importance of stochastic modeling, contributing to cost reductions of over 3% compared to the deterministic counterpart.