Designing Sparse Graphs for Stochastic Matching with an Application to Middle-Mile Transportation Management

69 Pages Posted: 7 Jun 2022

See all articles by Yifan Feng

Yifan Feng

National University of Singapore (NUS)

Rene Caldentey

University of Chicago - Booth School of Business

Linwei Xin

University of Chicago - Booth School of Business

Yuan Zhong

University of Chicago - Booth School of Business

Bing Wang

Alibaba Group

Haoyuan Hu

Alibaba Group

Date Written: May 30, 2022

Abstract

Given an input graph Gin =(V,E_in), we consider the problem of designing a sparse subgraph G = (V, E) with E ⊆ E_in that supports a large matching after some nodes in V are randomly deleted. We study three families of sparse graph designs (namely, Clusters, Rings, and Erdős-Rényi graphs) and show both theoretically and numerically that their performance is close to the optimal one achieved by a complete graph. Our interest in the stochastic sparse graph design problem is primarily motivated by a collaboration with a leading e-commerce retailer in the context of its middle-mile delivery operations. We test our theoretical results using real data from our industry partner and conclude that adding a little flexibility to the routing network can significantly reduce transportation costs.

Suggested Citation

Feng, Yifan and Caldentey, Rene and Xin, Linwei and Zhong, Yuan and Wang, Bing and Hu, Haoyuan, Designing Sparse Graphs for Stochastic Matching with an Application to Middle-Mile Transportation Management (May 30, 2022). Available at SSRN: https://ssrn.com/abstract=4123410 or http://dx.doi.org/10.2139/ssrn.4123410

Yifan Feng

National University of Singapore (NUS) ( email )

1E Kent Ridge Road
NUHS Tower Block Level 7
Singapore, 119228
Singapore

Rene Caldentey

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://www.chicagobooth.edu/faculty/directory/c/rene-caldentey

Linwei Xin (Contact Author)

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

Yuan Zhong

University of Chicago - Booth School of Business ( email )

5807 S. Woodlawn Avenue
Chicago, IL 60637
United States

HOME PAGE: http://faculty.chicagobooth.edu/Yuan.Zhong/

Bing Wang

Alibaba Group ( email )

Haoyuan Hu

Alibaba Group ( email )

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