TITLE: Multi-Product Newsvendor Model with Substitutions

ABSTRACT: We study a multi-product newsvendor model with customer-driven demand substitutions, where each product, once run out of stock, can be proportionally substituted by the others. This model has been widely studied in the literature, however, due to its nonconvexity and intractability, only very limited analytical properties have been discovered nor efficient solution approaches. This paper first completely characterizes the optimal order policy when the demand is known and recasts the model as a discrete submodular maximization problem. When the demand is stochastic, we first reformulate this nonconvex model as a two-stage stochastic integer program, where the recourse decision variables are mixed integers. We further study a tight upper bound via nonanticipativity dual, which is proven to be close to the true optimal and can be computed as a linear program. Finally, numerical studies demonstrate the effectiveness of the algorithms.


Dr. Weijun Xie graduated from Georgia Tech in 2017 and is Assistant Professor in the Department of Industrial and Systems Engineering at Virginia Tech.