From strategic to tactical carriers’ selection: A new SDDP algorithm to handle dynamic stochastic demand

This paper addresses a Carrier’s Selection and Shipment Assignment Problem (CSSAP) in a distribution network where a set of products need to be shipped from warehouses to distribution centers to satisfy the demand at each distribution center at each period of a tactical planning horizon. The demand at distribution centers is uncertain and back-ordering is permitted but penalized. Shipments are ensured by external carriers either strategic or spot ones. Strategic carriers are long-term contracts carriers with commitments to respect when solving the CSSAP. The problem is formulated as a multi-stage dynamic stochastic model. New variants of the Stochastic Dual Dynamic Programming (SDDP) algorithm are proposed to solve it. They consider novel cut removal techniques and new stopping criterion inspired by the concept of regret from the field of reinforcement learning. The concept of regret additionally enables evaluating the quality of the SDDP decisions, rarely addressed in the literature. We carried out experiments and evaluated our results against other cut removal strategies and stopping criteria reported in the literature. Our results first show that the SDDP algorithm is a good approach to solve the CSSAP under different contexts yielding good-quality solutions in a reasonable time. Second, some of the new variants we propose outperform existing ones and this is mostly due to the new techniques we propose to remove what we call the detrimental cuts. The new SDDP variants can be easily adapted to be used for any other problem to which a standard SDDP algorithm may apply. • SDDP is appropriate for tactical planning of transport decisions under uncertainty. • The standard SDDP algorithm may generate detrimental cuts resulting in bad results. • Detecting and removing detrimental cuts improve the SDDP performance. • The novel concept of regret helps better analyze the quality of the SDDP solutions. • A stopping criterion using the concept of regret deteriorates the SDDP performance.