A market-based efficient matching mechanism for crowdsourced delivery systems with demand/supply elasticities

TL;DR

This paper introduces a scalable, market-based matching mechanism for crowdsourced delivery systems that efficiently handles demand/supply elasticity, heterogeneous preferences, and task-bundling, significantly reducing computational costs.

Contribution

It extends fluid-particle decomposition to large-scale CSD matching, integrating auction mechanisms and traffic assignment to improve efficiency and accuracy.

Findings

Achieves approximately 700x faster computation than naive methods.

Maintains solution accuracy within 0.5% error margin.

Provides a theoretically guaranteed, efficient solution framework.

Abstract

Crowdsourced delivery (CSD) is an emerging business model that leverages the underutilized or excess capacity of individual drivers to fulfill delivery tasks. This paper presents a general formulation of a larege-scale two-sided CSD matching problem, considering demand/supply elasticity, heterogeneous preferences of both shippers and drivers, and task-bundling. We propose a set of methodologies to solve this problem. First, we reveal that the fluid-particle decomposition approach of Akamatsu and Oyama (2024) can be extended to our general formulation. This approach decomposes the original large-scale matching problem into a fluidly-approximated task partition problem (master problem) and small-scale particle matching problems (sub-problems). We propose to introduce a truthful auction mechanism to sub-problems, which enables the observation of privately perceived costs for each shipper/driver. Furthermore, by finding a theoretical link between auction problems and parturbed utility theory, we succeed in accurately reflecting the information collected from auctions to the master problem. This reduces the master problem to a smooth convex optimization problem, theoretically guaranteeing the computational efficiency and solution accuracy of the fluid approximation. Second, we transform the master problem into a traffic assignment problem (TAP) based on a task-chain network. This transformation overcomes the difficulty in enumerating task bundles. Finally, we formulate the dual problem of the TAP, whose decision variable is only a price/reward pattern at market equilibrium, and develop an efficient accelerated gradient descent method. The numerical experiments clarify that our approach drastically reduces the computational cost of the matching problem (~700 times faster than a naive method) without sacrificing accuracy of the optimal solution (mostly within 0.5% errors).