A selective newsvendor approach to order management |
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Authors: | Kevin Taaffe Edwin Romeijn Deepak Tirumalasetty |
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Institution: | 1. Industrial Engineering, Clemson University, Clemson, South Carolina 29634;2. Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan 48109;3. TransSolutions, LLC, Fort Worth, Texas 76155 |
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Abstract: | Consider a supplier offering a product to several potential demand sources, each with a unique revenue, size, and probability that it will materialize. Given a long procurement lead time, the supplier must choose the orders to pursue and the total quantity to procure prior to the selling season. We model this as a selective newsvendor problem of maximizing profits where the total (random) demand is given by the set of pursued orders. Given that the dimensionality of a mixed‐integer linear programming formulation of the problem increases exponentially with the number of potential orders, we develop both a tailored exact algorithm based on the L‐shaped method for two‐stage stochastic programming as well as a heuristic method. We also extend our solution approach to account for piecewise‐linear cost and revenue functions as well as a multiperiod setting. Extensive experimentation indicates that our exact approach rapidly finds optimal solutions with three times as many orders as a state‐of‐the‐art commercial solver. In addition, our heuristic approach provides average gaps of less than 1% for the largest problems that can be solved exactly. Observing that the gaps decrease as problem size grows, we expect the heuristic approach to work well for large problem instances. © 2008 Wiley Periodicals, Inc. Naval Research Logistics 2008 |
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Keywords: | selective newsvendor demand selection Bernoulli demands |
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