面向众包配送系统匹配市场设计的流体-粒子分解方法
A fluid-particle decomposition approach to matching market design for crowdsourced delivery systems
AI总结：
针对众包配送中大规模匹配与司机效用私有信息两大难题，本文提出流体-粒子分解方法，通过拍卖机制揭示效用并以流体模型加速求解，实现百倍以上提速且误差低于1%。
摘要：
本文将众包配送（CSD）系统视为CSD司机与配送任务之间的匹配问题，该系统有效利用现有行程来完成包裹配送。该匹配问题面临两大挑战。首先，它是一个大规模组合优化问题，难以在合理的计算时间内求解。其次，社会最优匹配的目标函数评估包含司机执行任务的效用，而这通常是不可观测的私有信息。为应对这些挑战，本文提出了一种CSD任务的分层分配机制，将匹配问题分解为任务划分（主问题）和较小司机群体内的个体任务-司机匹配（子问题）。我们在子问题中引入具有真实报价激励和效率属性的拍卖机制，使司机感知的效用通过其出价得以揭示。此外，我们将主问题建模为基于连续近似决策变量的流体模型。通过利用随机效用框架，我们在不显式获知司机效用的情况下，用连续变量解析地表示问题的目标函数。数值实验表明，所提方法求解大规模匹配问题的速度比朴素LP求解器至少快100倍，并且对原始目标值的近似误差小于1%。
英文摘要：
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%.
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