Multiproduct Newsvendor Problem with Customer-Driven Demand Substitution: A Stochastic Integer Program Perspective

Jie Zhang (), Weijun Xie () and Subhash C. Sarin ()
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Jie Zhang: Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061
Weijun Xie: Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061
Subhash C. Sarin: Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, Virginia 24061

INFORMS Journal on Computing, 2021, vol. 33, issue 3, 1229-1244

Abstract: This paper studies a multiproduct newsvendor problem with customer-driven demand substitution, where each product, once run out of stock, can be proportionally substituted by the others. This problem has been widely studied in the literature; however, because of nonconvexity and intractability, only limited analytical properties have been reported and no efficient approaches have been proposed. This paper first completely characterizes the optimal order policy when the demand is known and reformulates this nonconvex problem as a binary quadratic program. When the demand is random, we formulate the problem as a two-stage stochastic integer program, derive several necessary optimality conditions, prove the submodularity of the profit function, and also develop polynomial-time approximation algorithms and show their performance guarantees. We further propose a tight upper bound via nonanticipativity dual, which is proven to be very close to the optimal value and can yield a good-quality feasible solution under a mild condition. Our numerical investigation demonstrates effectiveness of the proposed algorithms. Moreover, several useful findings and managerial insights are revealed from a series of sensitivity analyses.

Keywords: newsvendor problem; demand substitution; stochastic program; submodularity; approximation algorithm (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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