A fluid–particle decomposition approach to matching market design for crowdsourced delivery systems

This paper considers a crowdsourced delivery (CSD) system that effectively utilizes the existing trips to fulfill parcel delivery as a matching problem between CSD drivers and delivery tasks. This matching problem has two major challenges. First, it is a large-scale combinatorial optimization problem that is hard to solve in a reasonable computational time. Second, the evaluation of the objective function for socially optimal matching contains the utility of drivers for performing the tasks, which is generally unobservable private information. To address these challenges, this paper proposes a hierarchical distribution mechanism of CSD tasks that decomposes the matching problem into the task partition (master problem) and individual task-driver matching within smaller groups of drivers (sub-problems). We incorporate an auction mechanism with truth-telling and efficiency into the sub-problems so that the drivers’ perceived utilities are revealed through their bids. Furthermore, we formulate the master problem as a fluid model based on continuously approximated decision variables. By exploiting the random utility framework, we analytically represent the objective function of the problem using continuous variables, without explicitly knowing the drivers’ utilities. The numerical experiment shows that the proposed approach solved large-scale matching problems at least 100 times faster than a naive LP solver and approximated the original objective value with errors of less than 1%. The code of this work is available at https://github.com/yuki-oyama/fluid-particle-csd.