[论文解读] Two-sided Facility Location

Reza Alijani, Siddhartha Banerjee+3 more|arXiv (Cornell University)|Nov 30, 2017

Transportation and Mobility Innovations参考文献 13被引用 3

一句话总结

本文提出双面设施选址（Two-sided Facility Location），一种针对电子商务市场平台的新型优化框架，通过联合确定定价、设施选址与代理路径规划，在质量与可用性约束下最大化社会剩余。该框架提出一种线性规划（LP）舍入算法，对任意 ε>0 实现社会剩余的 (1+ε) 近似解，同时将匹配距离放宽一个常数因子，并可扩展至利润与吞吐量等目标。

ABSTRACT

Recent years have witnessed the rise of many successful e-commerce marketplace platforms like the Amazon marketplace, AirBnB, Uber/Lyft, and Upwork, where a central platform mediates economic transactions between buyers and sellers. Motivated by these platforms, we formulate a set of facility location problems that we term Two-sided Facility location. In our model, agents arrive at nodes in an underlying metric space, where the metric distance between any buyer and seller captures the quality of the corresponding match. The platform posts prices and wages at the nodes, and opens a set of facilities to route the agents to. The agents at any facility are assumed to be matched. The platform ensures high match quality by imposing a distance constraint between a node and the facilities it is routed to. It ensures high service availability by ensuring flow to the facility is at least a pre-specified lower bound. Subject to these constraints, the goal of the platform is to maximize the social surplus (or gains from trade) subject to weak budget balance, i.e., profit being non-negative. We present an approximation algorithm for this problem that yields a $(1 + ε)$ approximation to surplus for any constant $ε> 0$, while relaxing the match quality (i.e., maximum distance of any match) by a constant factor. We use an LP rounding framework that easily extends to other objectives such as maximizing volume of trade or profit. We justify our models by considering a dynamic marketplace setting where agents arrive according to a stochastic process and have finite patience (or deadlines) for being matched. We perform queueing analysis to show that for policies that route agents to facilities and match them, ensuring a low abandonment probability of agents reduces to ensuring sufficient flow arrives at each facility.

研究动机与目标

• 建模并求解双面在线市场中定价、调度与设施选址的联合问题。
• 通过代理与设施间距离的有界约束，确保高匹配质量。
• 通过在每个设施上强制执行最小流量（下界 L）来保障服务可用性。
• 在弱预算平衡（非负利润）条件下，最大化社会剩余（总买家价值减去总卖家成本）。
• 将该框架扩展至最大化利润或交易量等目标。

提出的方法

• 提出一类新型设施选址问题——双面设施选址，其中代理根据度量距离被路由至设施。
• 使用线性规划松弛来建模问题，整合距离上限 R 与最小流量约束 L。
• 应用一种新颖的 LP 舍入框架，对任意 ε>0 实现社会剩余目标的 (1+ε) 近似解。
• 通过放宽匹配质量约束（最大距离）实现该近似，放宽幅度为常数因子。
• 通过排队论进行模型合理性论证，表明在动态市场中低放弃概率可归约为设施处的充分流量。
• 通过基于代理耐心程度与到达率设定设施权重与下界，将动态调度策略简化为设施选址问题。

实验结果

研究问题

• RQ1 市场平台如何联合优化定价、设施选址与代理路径规划以最大化社会剩余？
• RQ2 在距离与流量约束下，社会剩余最大化可实现何种近似保证？
• RQ3 引入代理耐心程度（截止时间）如何影响设施选址与匹配性能？
• RQ4 能否将设施选址模型扩展至通过价格与工资的彩票机制，实现对代理截止时间的诚实披露？
• RQ5 在动态市场中，设施流量、放弃概率与系统性能之间存在何种关系？

主要发现

• 所提出的 LP 舍入框架对任意 ε>0 实现社会剩余的 (1+ε) 近似解，同时将匹配距离约束放宽一个常数因子。
• 该框架可自然扩展至最大化利润或交易量等目标，且保持相同的近似保证。
• 排队分析表明，为使放弃概率低于 η，到达率 λ 必须满足 λ(�D + �S) ≥ 2/η，其中 �D 与 �S 分别为平均买家与卖家截止时间。
• 采用下界 L = 2/η 的设施选址模型可捕捉动态市场策略，相较于忽略耐心程度的模型，将下界依赖关系从 1/η² 改进为 1/η。
• 该模型为基于设施的路径规划作为动态、随机市场中具有截止时间意识代理的最优调度策略的代理提供了理论依据。
• 结果表明，即使仅掌握部分代理耐心信息，也能显著提升系统性能，实现在更低放弃率下更高的匹配质量。