Distributionally Robust Omnichannel Stocking Decisions in Quick Fulfillment Systems

40 Pages Posted: 3 Sep 2019 Last revised: 5 Dec 2019

See all articles by Louis Chen

Louis Chen

Massachusetts Institute of Technology (MIT), Operations Research Center, Students

Rong Jin

Alibaba Group

Hanzhang Qin

Massachusetts Institute of Technology (MIT) - Center for Computational Engineering

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering

Zirun Zhang

Alibaba Group

Date Written: September 1, 2019

Abstract

This work is inspired by the daily operations of Hema supermarket, which is a recently established “new retail” model by Alibaba Group, China. In a Hema supermarket store, a single SKU may be presented with demand in the form of multiple channels. The challenge facing Hema is to stock inventory between the warehouse and the store-front in advance of uncertain demand that arises in several consecutive time frames, each 30 minutes long. Using historical sales data provided by Alibaba, we construct a distributionally robust optimization model, wherein we are to make a stocking decision robust to an adversary's choice of coupling of (marginal) demand distributions by channel and by time frame. The adversary's decision amounts to designing a random mathematical program with equilibrium constraints (MPEC). And we provide both a structural analysis of the adversary's choice of coupling as well as an efficient procedure to find this coupling. Though the distributionally robust stocking problem is non-concave in general, we provide sufficient conditions on the cost parameters for which this problem is concave, and hence tractable. Finally, in data experiments, we compare and contrast the performance of our distributionally robust solution with the performance of a Newsvendor-like solution implemented at Alibaba on various SKUs of varying sales volume and number of channels. The results indicate that the distributionally robust solutions generally outperform the Newsvendor-like solution. Interestingly, in all experiments, the distributionally robust inventory problems presented by the historical data provided by Hema are in fact concave.

Keywords: Robust Optimization, Omnichannel Inventory Management, Optimal Transport, New Retail

Suggested Citation

Chen, Louis and Jin, Rong and Qin, Hanzhang and Simchi-Levi, David and Zhang, Zirun, Distributionally Robust Omnichannel Stocking Decisions in Quick Fulfillment Systems (September 1, 2019). Available at SSRN: https://ssrn.com/abstract=3383881 or http://dx.doi.org/10.2139/ssrn.3383881

Louis Chen

Massachusetts Institute of Technology (MIT), Operations Research Center, Students ( email )

77 Massachusetts Avenue
Bldg. E 40-149
Cambridge, MA 02139
United States

Rong Jin

Alibaba Group ( email )

Hanzhang Qin (Contact Author)

Massachusetts Institute of Technology (MIT) - Center for Computational Engineering ( email )

77 Massachusetts Avenue
50 Memorial Drive
Cambridge, MA 02139-4307
United States

David Simchi-Levi

Massachusetts Institute of Technology (MIT) - School of Engineering ( email )

MA
United States

Zirun Zhang

Alibaba Group ( email )

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