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New Operations Research Models for Emerging Problems in Service Operations

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Abstract

With the goal of exploiting theoretical and practical advancements in operations research to solve important problems in production, service, and sports, this dissertation studies two problems in particular using optimization: proposing a plan to conclude a suspended sports league in a shortened time frame, and analyzing pricing mechanisms in resource exchange economic models.

First, we study the problem of concluding a suspended sports league in a shortened time frame. Professional sports leagues may be suspended due to various reasons such as the recent COVID-19 pandemic. A critical question arises when the league decides to select a subset of the remaining games to conclude the season in a shortened time frame. Despite the rich literature on scheduling an entire season starting from a blank slate, concluding an existing season is quite different. Our approach attempts to achieve rankings similar to that which would have resulted had the season been played out in full. We propose a data-driven model which exploits predictive and prescriptive analytics to produce a schedule for the remainder of the season comprised of a subset of originally-scheduled games in anticipation of the future outcomes. This not only requires us to introduce novel rankings-based objectives, but also requires us to consider stochastic modeling approaches as well as a predictive model for estimating the parameters in the stochastic optimization model. In comparison, all of the sports scheduling optimization models in the literature are deterministic. We study the efficacy of our approach through comprehensive computational and simulation experiments. We present simulation-based numerical experiments from previous National Basketball Association (NBA) seasons 2004-2019, and show that our models are computationally efficient and produce interpretable results. Our approach provides a data-driven decision-making framework for concluding suspended sports leagues by taking uncertainties into account. We also provide suggestions on how to conclude the 2019-20 NBA season. As an addition to this chapter, we study the problem of concluding a season after a suspension while there are no prior games played. In other words, when the hiatus happens to be at the beginning of the season, and the league starts late which makes a shortened season inevitable, a natural question is that which games or matchups should be included in the shortened season. The main challenge in this scenario is the fact that there are no prior games played in the same year and the idea of employing a predictive model does not work, unless we find a way to use past season(s) games to train a predictive model. In order to overcome this challenge, we add player-level features to the training dataset which enables us to train a predictive model using only the previous season games to predict the outcome of the new season. Once we have a predictive model, we can use a similar approach as presented at the beginning of this chapter.

Second, we study an economic system where there are multiple agents each endowed with certain amount of resources, aiming to make profit either by producing their unique product and selling it to the spot market or by trading their endowed resources to other agents. All agents use the same type of resources for production (and exchange) purposes, possibly with different usage rates. The total profit in the system depends on the allocation of resources among agents and the production quantity of all agents. This problem can be studied from two lenses: centralized and decentralized. From a central planner's perspective, it is desirable if resources are shared among all agents and they are distributed according to the production plan with the maximum profit. However, achieving this optimal distribution of resources can be challenging in practical settings since resource sharing is typically carried out in a decentralized way, i.e., each agent, independent of, or even oblivious to, other agents' decisions, determines her resource exchange quantity. In this thesis, we study how to coordinate the resource exchange decisions among decentralized agents through resource pricing approaches. Motivated by the operations of practical resource sharing alliances (e.g., capacity sharing in transportation alliances, equipment sharing in medical networks), we consider a framework where the central planner determines the prices at which the agents exchange resources, collects and fulfills agents' resource exchange requests. We assume the existence of a spot market where imbalance between resource supply and demand within the alliance can be addressed.The objective of the agents is to maximize their own profit which is formulated as a function of the resource price, as well as production and exchange variables. Hence, the choice of resource prices influence how much resource each agent is willing to sell/buy and accordingly the overall distribution of the resources in the decentralized problem. We measure the profitability of the decentralized resource exchange system through an efficiency ratio, which is defined as the worst case ratio between the aggregate profit in the decentralized system and its centralized counterpart. An efficiency ratio of one indicates that the total profit from the centralized and decentralized problems match, and the centrally optimal distribution of resources can be attained in the decentralized system. The problem of finding the resource prices under which the efficiency ratio is maximized is called the coordination problem. Coordinating decentralized resource exchanges via pricing approaches has been studied in the literature, which largely focuses on linear pricing, i.e., a constant unit price is applied for each resource. Our work first shows that linear pricing does not guarantee an efficiency ratio of one. Nonlinear price functions studied in the literature can potentially achieve an efficiency ratio of one,, but they suffer from two drawbacks: price discrimination (i.e., different agents pay according to different pricing schemes) and the need to subsidize the exchange transactions by the central planner. In this thesis, we study whether an efficiency ratio of one can be achieved under nonlinear pricing functions that apply the same unit price to all agents and that requires no subsidization from the central planner. We focus on a quadratic pricing function, and show that under certain conditions, (i.e., a constant term plus the product of another constant term and the exchange quantity) it achieves an efficiency ratio of one without discriminating among agents and with minimal subsidy. We finally extend our analysis to stochastic cases where the agents' revenue information is not fully-known when the resources pricing scheme is determined. We show that uncertainty undermines the effectiveness of the quadratic pricing scheme we proposed in the deterministic case in that it does not guarantee an efficiency ratio of one even under the conditions previously proposed. Nevertheless, we can numerically identify the quadratic pricing function that maximizes the efficiency ratio in the stochastic case, and we show the usefulness of our approach based on extensive numerical results.

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This item is under embargo until September 27, 2023.