(Social) Pooling in Service, Capacity, and Demand

This manuscript examines three operational problems in pooling resources and productions in distinct contexts. Firstly, we delve into pooling restroom units as a response to the prevalent issue of potty imparity. The inequitable restroom access has mainly affected women and LGBTQ+ people in recent years. The proposal of converting gender-segregated restrooms into all-unisex restrooms might seem convincing due to the pooling of resources, ensuring fairness by having everyone wait in the same line. However, through an analytical framework that considers factors like wait time, users' gender identities, safety concerns in how users choose which restroom to join, and various fairness criteria, including totalitarian efficiency, Rawlsian, and distributive fairness, we illustrate that this intuition does not hold. Furthermore, we demonstrate that a more efficient and equitable solution involves converting some men's restrooms into unisex facilities, combining all three types of restrooms. This showcases that a certain level of flexibility outperforms a fully flexible system. Secondly, we investigate the decentralized pooling of resources within a social network inspired by platforms that facilitate sharing items like leftover food and idle tools. These platforms have recently gained popularity because it is perceived that they can reduce waste by allowing people to rely on borrowing items from their sharing network rather than owning all items. We construct a model of newsvendors over a social network to explore this concept. Newsvendors have limited information about the network structure and only know their number of connections, i.e., degree. We model sharing activity among newsvendors based on the amount and frequency of exchanging leftover items after they satisfy their own demand. We define two types of social networks: acquaintance networks and friendship networks. Our analysis showcases the degree of free-riding among newsvendors based on their network degree for these two types of social networks. Additionally, we examine the impact of sharing network expansion on these platforms. Interestingly, we show that as the sharing network becomes more connected, the overall stocking levels of newsvendors increase in a friendship network for certain types of products. Lastly, we tackle the demand estimation challenge using sales data from companies selling product bundles. Classic methods without considering the bundle promotion, such as customer choice models, can not solve this problem because they assume customer valuation independence. Our study employs a utility model for customer choices and aims to identify a joint demand distribution that optimally aligns with sales data. The Expectation-Maximization algorithm is employed to recover the estimation parameters. We demonstrate the conditions under which the problem is identifiable and establish the algorithm's convergence rate. We then assess the algorithm's effectiveness using a JD.com dataset, highlighting the efficacy of our approach.

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