Journal
MANAGEMENT SCIENCE
Volume 67, Issue 4, Pages 2272-2291Publisher
INFORMS
DOI: 10.1287/mnsc.2020.3719
Keywords
newsvendor networks; distribution-free optimization; inventory management
Funding
- National Science Foundation [CMMI-1561791]
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The study focuses on inventory optimization in a multilocation newsvendor network using a distributionally robust model. Tight bounds on expected costs and computationally tractable upper bounds on worst-case expected costs are identified under certain conditions. An algorithm is proposed for approximating fulfillment cost structures, yielding a computationally tractable heuristic for distributionally robust inventory optimization.
We study a multilocation newsvendor network when the only information available on the joint distribution of demands are the values of its mean vector and covariance matrix. We adopt a distributionally robust model to find inventory levels that minimize the worst-case expected cost among the distributions consistent with this information. This problem is NP-hard. We find a closed-form tight bound on the expected cost when there are only two locations. This bound is tight under a family of joint demand distributions with six support points. For the general case, we develop a computationally tractable upper bound on the worst-case expected cost if the costs of fulfilling demands have a nested structure. This upper bound is the optimal value of a semidefinite program whose dimensions are polynomial in the number of locations. We propose an algorithm that can approximate general fulfillment cost structures by nested structures, yielding a computationally tractable heuristic for distributionally robust inventory optimization on general newsvendor networks. We conduct experiments on networks resembling U.S. e-commerce distribution networks to show the value of a distributionally robust approach over a stochastic approach that assumes an incorrect demand distribution.
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