Zhang, JieXie, WeijunSarin, Subhash C.2021-09-242021-09-242021-08-160377-2217http://hdl.handle.net/10919/105059This work studies a Robust Multi-product Newsvendor Model with Substitution (R-MNMS), where the demand and the substitution rates are stochastic and are subject to cardinality-constrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worst-case total profit. To achieve this, we first show that for given order quantities, computing the worst-case total profit, in general, is NP-hard. Therefore, we derive the closed-form optimal solutions for the following three special cases: (1) if there are only two products, (2) if there is no substitution among different products, and (3) if the budget of demand uncertainty is equal to the number of products. For a general R-MNMS, we formulate it as a mixed-integer linear program with an exponential number of constraints and develop a branch and cut algorithm to solve it. For large-scale problem instances, we further propose a conservative approximation of R-MNMS and prove that under some certain conditions, this conservative approximation yields an exact optimal solution to R-MNMS. The numerical study demonstrates the effectiveness of the proposed approaches and the robustness of our model.Pages 190-20213 page(s)application/pdfenIn CopyrightSocial SciencesTechnologyManagementOperations Research & Management ScienceBusiness & EconomicsStochastic programmingRobustCardinality-constrained uncertainty setMixed-integer programBranch and cut algorithmOperations ResearchArticle - Refereed2021-09-24https://doi.org/10.1016/j.ejor.2020.12.0232931Xie, Weijun [0000-0001-5157-1194]1872-6860