Stochastic Dual Dynamic Programming for Multiechelon Lot Sizing with Component Substitution

This work investigates lot sizing with component substitution under demand uncertainty. The integration of in an uncertain context is important because the consolidation for components naturally allows risk-pooling and reduces operating costs. considered problem relevant not only a production context, but also distribution planning. We propose stochastic programming formulation static–dynamic type uncertainty, which setup decisions are frozen consumption quantities decided dynamically. To tackle scalability issues commonly encountered multistage optimization, this paper use dual dynamic (SDDP). In addition, we consider various improvements SDDP, including strong cuts, fast generation cuts by solving linear relaxation problem, retaining average scenarios. Finally, two heuristics, namely, hybrid progressive hedging SDDP heuristic version SDDP. Computational experiments conducted on well-known instances from literature show that outperforms other methods. proposed method can plan up to 10 decision stages 20 scenarios per stage, results scenario paths total. Moreover, as replan account new information less than second, it convenient context. Summary Contribution: believe our suitable mission scope IJOC design efficient algorithms solve operations research problem. More precisely, investigate (SDDP) work, framework, good approximation expected costs requires us large number future demand. As computationally intensive, decomposes stage. study several enhancements such incorporation lower bound computed scenario, multicut sampling randomized quasi–Monte Carlo. Despite these improvements, convergence remains slow. Consequently, present extensive computational performed literature. state-of-the-art methods Besides, analysis shows pool risk, maintaining same service level inventory. presented methodology be used practitioners size their lots, subsequent researchers build upon uncertainty parameters, lead times, yields, capacities. History: Accepted Andrea Lodi, Area Editor Design & Analysis Algorithms – Discrete. Funding: was supported Mitacs Institut de Valorisation des Données (IVADO). Supplemental Material: online supplement available at https://doi.org/10.1287/ijoc.2022.1215 .