Robust multi-product newsvendor model with uncertain demand and substitution

Jie Zhang, Weijun Xie and Subhash C. Sarin

European Journal of Operational Research, 2021, vol. 293, issue 1, 190-202

Abstract: This 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.

Keywords: Stochastic programming; Robust; Cardinality-constrained uncertainty set; Mixed-integer program; Branch and cut algorithm (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:293:y:2021:i:1:p:190-202

DOI: 10.1016/j.ejor.2020.12.023

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