Yield uncertainty is an important issue in various industries such as agriculture, food, and textile where the production output relies on uncontrollable factors and fluctuating raw material quality. To systematically leverage data to deal with uncertainty cost-effectively, distributionally robust optimization combines the strengths of stochastic programming and robust optimization by optimizing the expected costs against an ambiguity set that defines possible distributions. In this work, we leverage a data-driven robust optimization framework and formulate a mixed-integer distributionally robust multi-item lot-sizing model with uncertain production yield to determine a robust production plan. To this end, we use a scenario-wise formulation that partitions the available data into scenarios that define different patterns influencing the quality of the product and production process. In addition, we apply the proposed approach to real-world data of a case study to demonstrate the effectiveness of the proposed framework in dealing with yield uncertainty. Our experimental results show that distributionally robust plans lead to more effective cost-saving strategies and decreased risk of stock-outs. Additionally, our findings suggest that the proposed model exhibits lower sensitivity to variations in production yield realizations and it is more proficient in incorporating historical data into the decision-making process. This results in a more effective response to challenges encountered within the production system under yield uncertainty. Note to Practitioners–In a production context with various sources of uncertainty for which the mathematical estimation of the uncertain parameter can be complex or hard to perform, it would be better to use the proposed robust approach. Here, any information, accurate or not, new or historical, can be integrated into the system to improve the quality of the obtained production plan, yet still robust and mitigate nervousness. For the reduction of conservatism, the proposed approaches indicate how the manufacturer risk aversion could be integrated into the decision models to respond to the strategic need for robustness for production planning under uncertainty.

This work investigates lot sizing with component substitution under demand uncertainty. The integration of component substitution with lot sizing in an uncertain demand context is important because the consolidation of the demand for components naturally allows risk-pooling and reduces operating costs. The considered problem is relevant not only in a production context, but also in the context of distribution planning. We propose a stochastic programming formulation for the static–dynamic type of uncertainty, in which the setup decisions are frozen but the production and consumption quantities are decided dynamically. To tackle the scalability issues commonly encountered in multistage stochastic optimization, this paper investigates the use of stochastic dual dynamic programming (SDDP). In addition, we consider various improvements of SDDP, including the use of strong cuts, the fast generation of cuts by solving the linear relaxation of the problem, and retaining the average demand scenarios. Finally, we propose two heuristics, namely, a hybrid of progressive hedging with SDDP and a heuristic version of SDDP. Computational experiments conducted on well-known instances from the literature show that the heuristic version of SDDP outperforms other methods. The proposed method can plan with up to 10 decision stages and 20 scenarios per stage, which results in 2010 scenario paths in total. Moreover, as the heuristic version of SDDP can replan to account for new information in less than a second, it is convenient in a dynamic context. Summary of Contribution: We believe our paper is suitable for the mission and scope of IJOC because we design efficient algorithms to solve an operations research problem. More precisely, we investigate the use of stochastic dual dynamic programming (SDDP) for lot sizing with component substitution under demand uncertainty. In this work, we consider the static–dynamic decision framework, and a good approximation of the expected costs in this context requires us to solve the problem with a large number of scenarios of future demand. As solving the considered problem is computationally intensive, we investigate the use of SDDP, which decomposes the problem per decision stage. We study several enhancements of SDDP, such as the use of strong cuts, the incorporation of a lower bound computed with the average demand scenario, the multicut version of SDDP, and scenario sampling with randomized quasi–Monte Carlo. Despite these improvements, the convergence of SDDP remains slow. Consequently, we propose a heuristic version of SDDP and a hybrid of progressive hedging and SDDP. We present the results of an extensive computational study performed on well-known instances from the literature. The results show that the heuristic SDDP outperforms the hybrid of progressive hedging with SDDP and state-of-the-art methods from the literature. Besides, our analysis shows that component substitution can pool the risk, and it allows maintaining the same service level with less inventory. The presented methodology can be used by practitioners to size their production lots, and subsequent researchers can build upon our results to consider uncertainty in other parameters, such as lead times, yields, and production capacities. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms – Discrete. Funding: This work was supported by Mitacs and the Institut de Valorisation des Données (IVADO). Supplemental Material: The online supplement is available at https://doi.org/10.1287/ijoc.2022.1215 .