Recommend-to-Match with Random Supply Rejections: Formulation, Approximation, and Analysis

TL;DR

This paper addresses the challenge of matching demand with supply in crowdsourcing logistics under uncertain worker participation, proposing a convex relaxation approach with strong performance guarantees and practical efficiency.

Contribution

It introduces a novel approximation method using convex relaxation and mixed-integer exponential cone programming for stochastic supplier rejections, with theoretical and empirical validation.

Findings

The proposed MIECP approach achieves near-optimal matching performance.

It reduces computation time by over 90% compared to benchmark methods.

Deterministic linear approximations can perform arbitrarily poorly in this setting.

Abstract

Matching demand with supply in crowdsourcing logistics platforms must contend with uncertain worker participation. Motivated by this challenge, we study a two-stage "recommend-to-match" problem under stochastic supplier rejections, where each demand is initially recommended to multiple potential suppliers prior to final matching decisions. We formulate a stochastic optimization model that explicitly captures uncertain supplier acceptance behavior. For the special case with homogeneous and independent acceptance responses, an exact mixed-integer linear program and LP formulations are achievable, but the general problem does not admit an efficient formulation. Particularly, our analysis reveals that deterministic linear approximation methods can perform arbitrarily poorly in such settings. To overcome this limitation, we propose a new approximation approach based on a convex relaxation of the original problem that admits a mixed-integer exponential cone program (MIECP) formulation. We analyze the structural properties of this approximation and establish its parametric performance guarantees. We also characterize conditions under which it can dominate a deterministic approximation. Extensive experiments on synthetic data and real-world freight data validate the effectiveness of our approach. Our MIECP-based solution achieves near-optimal matching performance while reducing computation time by over 90% compared to benchmark methods, which makes it particularly promising for large-scale matching problems.