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

Abstract

Crowdsourced delivery (CSD), or crowd-shipping, 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 large-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 and efficient auction mechanism to the sub-problems, which enables the observation of privately perceived costs for each shipper/driver. Furthermore, by finding a theoretical link between the auction problems and random/perturbed utility theory, we succeed in accurately reflecting the information collected from the auctions to the master problem in a theoretically consistent manner. 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 representation. 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 the proposed approach drastically reduces the computational cost of the general and complex CSD matching problem ($\sim$ 700 times faster than a naive method) without sacrificing the accuracy of the optimal solution (mostly within 0.5% errors).