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

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, Chains, 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.