Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor

Forthcoming in Management Science

Ross School of Business Paper No. 1389

56 Pages Posted: 14 Jan 2019 Last revised: 1 Jul 2020

See all articles by Aravind Govindarajan

Aravind Govindarajan

Target Corporation

Amitabh Sinha

University of Michigan, Stephen M. Ross School of Business

Joline Uichanco

University of Michigan, Stephen M. Ross School of Business

Date Written: January 1, 2019

Abstract

We study a multi-location 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. This result extends the well-known Scarf (1958) bound for a single location. 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.

Keywords: Newsvendor networks, distribution-free optimization, inventory management

Suggested Citation

Govindarajan, Aravind and Sinha, Amitabh and Uichanco, Joline, Distribution-free Inventory Risk Pooling in a Multi-location Newsvendor (January 1, 2019). Forthcoming in Management Science, Ross School of Business Paper No. 1389, Available at SSRN: https://ssrn.com/abstract=3315439 or http://dx.doi.org/10.2139/ssrn.3315439

Aravind Govindarajan (Contact Author)

Target Corporation

Sunnyvale, CA 94086
United States

Amitabh Sinha

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Joline Uichanco

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

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