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Zhang Jie (jiezhangvt.edu) Abstract: This work studies a Robust Multiproduct Newsvendor Model with Substitution (RMNMS), where the demand and the substitution rates are stochastic and are subject to cardinalityconstrained uncertainty sets. The goal of this work is to determine the optimal order quantities of multiple products to maximize the worstcase total profit. To achieve this, we first show that for given order quantities, computing the worstcase total profit, in general, is NPhard. Therefore, we derive the closedform 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 RMNMS, we formulate it as a mixedinteger linear program with an exponential number of constraints and develop a branch and cut algorithm to solve it. For largescale problem instances, we further propose a conservative approximation of RMNMS and prove that under some certain conditions, this conservative approximation yields an exact optimal solution to RMNMS. The numerical study demonstrates the effectiveness of the proposed approaches and the robustness of our model. Keywords: Newsvendor Model, Robust, Cardinalityconstrained Uncertainty Set, Mixed Integer Program, Branch and Cut Algorithm Category 1: Applications  OR and Management Sciences Category 2: Robust Optimization Citation: Download: [PDF] Entry Submitted: 10/26/2018 Modify/Update this entry  
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