This dissertation presents mathematical models and algorithms that draw from optimization and statistics and are motivated by practical problems in operations management. We discuss theoretical properties of the proposed models as well as their relevance to practice. In particular, we focus on the role these models can play in addressing challenges in healthcare operations and policy.

In Chapter 2, we address the problem of building models of agent behavior from observational data regarding the agent's decisions. Concretely, we consider the inverse optimization problem, which refers to the estimation of unknown model parameters of a convex optimization problem from observations of its optimal solutions. First, we provide a new formulation for inverse optimization, which takes the form of a bi-level program where the optimality conditions of the lower level program are expressed using strong duality. In contrast to existing methods, we show that the parameter estimates produced by our formulation are statistically consistent under appropriate conditions. Second, we propose two solution algorithms based on our duality-based formulation: an enumeration algorithm that is applicable to settings where the dimensionality of the parameter space is modest, and a semiparametric approach that combines nonparametric statistics with a modified version of our formulation. These numerical algorithms are shown to maintain the statistical consistency of the underlying formulation. Lastly, using both synthetic and real data, we demonstrate that our approach performs competitively when compared with existing heuristics.

In Chapter 3, we employ an inverse optimization approach to redesign a class of Medicare contracts. We formulate the existing contract between Medicare and a provider as a principal-agent model. We then propose an alternate contract, which we show to dominate the status quo contract under reasonable conditions by producing a strictly higher expected payoff for both Medicare and the provider. We then propose an estimator based on inverse optimization for estimating a model of provider behavior, using a dataset containing the financial performance of a group of Medicare providers that account for 7 million beneficiaries and over $70 billion in Medicare spending. We estimate a performance improvement -- in terms of savings accrued by Medicare -- of 40% under the alternate contract, which suggests significant room for improvement in the status quo.

In Chapter 4, we propose a data-driven modeling approach to facility location in a setting where the location of demand points is subject to uncertainty. The model is motivated by the problem of placing automated external defibrillators in public locations in anticipation of sudden cardiac arrest. We propose a distributionally robust optimization approach where the demand distribution is continuous in the plane and uncertain. We propose a solution technique based on row-and-column generation that exploits the structure of the uncertainty set and allows us to solve practical-sized instances of the defibrillator deployment problem. Using real cardiac arrest data, we conduct an extensive numerical study and find that hedging against cardiac arrest location uncertainty can produce defibrillator deployments that outperform a intuitive sample average approximation by 9 to 15%. Our findings suggest that accounting for cardiac arrest location uncertainty can lead to improved accessibility of defibrillators during cardiac arrest emergencies and the potential for improved survival outcomes.

In the recent decades, new modes of transportation have been developed due to urbanization, highly dense population, and technological advancement. As a result, design and operation of urban transportation have become increasingly important to better utilize the resources and efficiently meet demand. This dissertation was motivated by two problems on optimizing design and control of urban transportation. In the first one, we consider a problem of dynamically matching heterogeneous market parcitipants so as to maximize the total number of matching, which was motivated by practices of ride-sharing platforms. In the other problem, we study efficient design of elevator zoning system in high-rises with uncertainty in customer batching.

In Chapter 1, we consider a multiperiod stochastic optimization of a market that matches heterogeneous and impatient agents. The model was mainly motivated from carpooling products run by ride-sharing platforms such as Uber and Lyft, and kidney exchange market, where market participants are heterogeneous in terms of how likely they can be matched with others. In the case of a ride-sharing platform, one of the key operational decisions for carpooling is to efficiently match riders and clear the market in a timely manner. In doing so, the platform needs to take into account the heterogeneity of riders in terms of their trip types(e.g origin-destination pair) and different matching compatibility. For example, some customers may request rides within San Francisco, while others may request rides from San Francisco to outside the city. Since picking up and dropping off a customer within the city can be done within relatively short amount of time, those who want to travel within the city can be matched with any other riders for carpooling. However, the destinations of those who want to travel to outside the city may be very different, and in order to maintain customers' additional transit time due to carpooling, it is likely that they can be only matched with those who want to travel within the city. In the case of kidney exchange where market participants arrive in the form of patient-donor pair, pairs with donor who can donate her kidney to most of patients (for example, blood type O) and patient who can get kidney from most of donors (for example, blood type AB) can be easily matched to other pairs. The opposite case would be hard-to-match pair that is incompatible for matching with most of other pairs. Our model is an abstraction of these two motivating examples, and considers two types of agents: easy-to-match agents that can be matched with either type of agents, and hard-to-match agents that can be only matched with easy-to-match ones. We first formulate a dynamic program to solve for optimal matching decisions over infinite time horizon in a discrete time setting, and characterize structure of optimal stationary policies. Inspired by practices in kidney exchange where the market is cleared for every fixed time interval, we connect the discrete time model to a continuous time setting by investigating the effect of the length of matching intervals on the matching performance. Results from numerical experiments indicate certain patterns in the relationship between the length of matching intervals and the maximum number of matching achieved, and provides valuable insights for future direction of research.

In Chapter 2, we consider a zoning problem for elevator dispatching systems in high-rises. In practice, zoning is frequently used to improve efficiency of elevator systems. The idea of zoning is to prevent different elevators from stopping at common floors, which may result in long service times of elevators and thus long waiting times of customers. Our goal is to provide a mathematical framework that can help a system planner decide optimal zoning design with some performance guarantee. To this end, we focus on uppeak traffic situation during morning rush hour, which is in general the heaviest traffic during the day. The performance in the uppeak traffic situation can be considered as the system's capacity, because if the system can handle uppeak traffic well, it can also serve other types of traffic with good performance. Thus, the performance measure in the uppeak traffic situation can be used as a metric to choose the optimal zoning configuration. One of the components that complicate the problem is customer batching, on which the system may not have a control. In view of this, we formulate an adversarial optimization problem that can measure the system performance of different zoning decisions. By considering the heaviest traffic situation of the day and using the adversarial framework, we provide a model that can be used for capacity planning of elevator systems. We formulate mixed-integer linear program(MILP)s to find the optimal zoning configuration. To solve the MILPs, we show that we can use simple greedy algorithms and solve smaller linear programs. We also provide a few illustrative examples as well as numerical experiments to verify the theoretical results and obtain insights for further analysis.

Flexible system design has received increasingly more attention in the last a few decades. Flexibility can increase systems' ability to adjust against fast-changing environment, and thereby improves efficiency and reliability, and avoids huge cost from rare but severe disruptions, or loss due to congestions caused by system uncertainties. In this dissertation, we focus on the design and management of flexible systems. In particular, we study three types of flexibility: process flexibility, network flexibility, and payment flexibility. We present quantitative formulations for these problems, and develop different methodologies to solve them. We further conduct numerical studies to generate insights as guidelines for the design of flexible systems in practice. \

Flexible supply chains have been widely used by companies to deal with uncertainties. It is well known that chaining structure is very efficient in balanced supply chains. However, it is not clear whether it will work well when supply chains are unbalanced. We study the flexibility design problem of a general supply chain with unbalanced and nonhomogeneous structure. Both demand uncertainty and disruptions are considered in our model. We derive exact solutions for several special cases of the uncapacitated problem where the number of links is fixed, propose an efficient algorithm for solving the general uncapacitated problem, and use simulations to derive some managerial insights for the capacitated problem.\

A similar idea is applied to network design. Air transportation networks suffer a lot from disruptions caused by severe weather, natural disasters, power outage, etc. We propose a flexible hub-and-spoke structure in which airports are allowed to have up to $N$ hubs, and formulate the problem as a mixed-integer program that minimizes fixed cost, flexibility cost, and expected transportation cost and penalty cost. Benders decomposition algorithm is applied to solve this problem. Numerical studies show that the performance of the network can be improved substantially with flexible hub assignment, and a flexible structure with $N=2$ can achieve most of the benefit of those with greater $N$. We also demonstrate the impact of the correlation between airport disruptions and address the importance of considering it in stochastic air transportation models.\

Trade credit, as a form of flexible payment, is a major tool used by small businesses to obtain external finance. It benefits the buyer and the supplier in multiple ways, and brings risk to them at the same time. We investigate the impact of trade credit on growing small businesses and their suppliers. By looking at a one-supplier-one-retailer supply chain, we study the expansion and inventory policies of the retailer when trade credit is extended or not. It is shown that the retailer grows faster and orders more with trade credit. It is also shown by numerical study that the effect of trade credit depends on demand correlation. When demand is positively correlated, trade credit makes the retailer more likely to go bankrupt, and thereby lowers the supplier's long-term profit and may even cause the failure of the supplier.

This dissertation studies analytical and computational aspects of two types of problems in applied operations research. In the first part of the dissertation, we consider the reliable facility location models in which facilities are subject to unexpected failures. We propose a compact mixed integer programming formulation that is polynomial in size. To compute optimal facility locations that balance the trade-off between normal operation and failure costs, we develop two exact algorithms: one is based on Lagrangian Relaxation, and the other is a hybrid of neighborhood search and cutting plane procedures. To obtain more managerial insights, we further investigate a Continuum Approximation (CA) model that predicts the total system cost without details about facility locations and customer assignments. The CA model is a valuable tool for sensitivity analysis, as well as a fast heuristic for large problem instances.

The second part of the dissertation is dedicated to theoretical and applied mechanism design, which consists of two chapters. In the first chapter, we study a problem of allocating limited capacity of a queueing system to serve several segments of customers, who differ in their willingness to pay and their sensitivity to delays, both of which are their private information. We show that probabilistic admission control, randomized priority rule, and strategic idleness can emerge as optimal solutions in a revenue maximizing mechanism.

In the second chapter of part two, we revisit the optimal auction design problem and propose a robust formulation based on an uncertainty set that characterizes the conservativeness of the bidders' beliefs, with two special cases being the Bayesian and Ex post formulations. Using the network approach, we identify the necessary and sufficient conditions under which the expected revenues achieved by different formulations are identical. Furthermore, we show that in a multiple-object auction, the auctioneer's expected revenue may strictly decrease as the bidders' beliefs become more uncertain.

Traditional supply chain management models typically require complete model information, including structural relationships (e.g., how pricing decisions affect customer demand), probabilistic distributions, and parameters. However, in practice, the model information may be uncertain. My dissertation research seeks to address model uncertainty in supply chain management problems using data-driven and robust methods. Incomplete information typically comes in two forms, namely, historical data and partial information. When historical data are available, data-driven methods can be used to obtain decisions directly from data, instead of estimating the model information and then using these estimates to find the optimal solution. When partial information is available, robust methods consider all possible scenarios and make decisions to hedge against the worst-case scenario effectively, instead of making simplified assumptions that could lead to significant loss.

Chapter 1 provides an overview of model uncertainty in supply chain management, and discusses the limitations of the traditional methods. The main part of the dissertation is on the application of data-driven and robust methods to three widely-studied supply chain management problems with model uncertainty.

Chapter 2 studies the reliable facility location problem where the joint-distribution of facility disruptions is uncertain. For this problem, usually, only partial information in the form of marginal facility disruption probabilities is available. Most existing models require the assumption that the disruptions at different locations are independent of each other. However, in practice, correlated disruptions are widely observed. We present a model that allows disruptions to be correlated with an uncertain joint distribution, and apply distributionally-robust optimization to minimize the expected cost under the worst-case distribution with the given marginal disruption probabilities. The worst-case distribution has a practical interpretation, and its sparse structure allows us to solve the problem efficiently. We find that ignoring disruption correlation could lead to significant loss. The robust method can significantly reduce the regret from model misspecification. It outperforms the traditional approach even under very mild correlation. Most of the benefit of the robust model can be captured at a relatively small cost, which makes it easy to implement in practice.

Chapter 3 studies the pricing newsvendor problem where the structural relationship between pricing decisions and customer demand is unknown. Traditional methods for this problem require the selection of a parametric demand model and fitting the model using historical data, while model selection is usually a hard problem in itself. Furthermore, most of the existing literature on pricing requires certain conditions on the demand model, which may not be satisfied by the estimates from data. We present a data-driven approach based only on the historical observations and the basic domain knowledge. The conditional demand distribution is estimated using non-parametric quantile regression with shape constraints. The optimal pricing and inventory decisions are determined numerically using the estimated quantiles. Smoothing and kernelization methods are used to achieve regularization and enhance the performance of the approach. Additional domain knowledge, such as concavity of demand with respect to price, can also be easily incorporated into the approach. Numerical results show that the data-driven approach is able to find close-to-optimal solutions. Smoothing, kernelization, and the incorporation of additional domain knowledge can significantly improve the performance of the approach.

Chapter 4 studies inventory management for perishable products where a parameter of the demand distribution is unknown. The traditional separated estimation-optimization approach for this problem has been shown to be suboptimal. To address this issue, an integrated approach called operational statistics has been proposed. We study several important properties of operational statistics. We find that the operational statistics approach is consistent and guaranteed to outperform the traditional approach. We also show that the benefit of using operational statistics is larger when the demand variability is higher. We then generalize the operational statistics approach to the risk-averse newsvendor problem under the conditional value-at-risk (CVaR) criterion. Previous results in operational statistics can be generalized to maximize the expectation of conditional CVaR. In order to model risk-aversion to both the uncertainty in demand sampling and the uncertainty in future demand, we introduce a new criterion called the total CVaR, and find the optimal operational statistic for this new criterion.

The past decade has seen tremendous growth in the availability of voluminous high-quality data in many modern decision systems such as supply chain management. Big data provides new opportunities to tackle one of the main difficulties in decision-making systems – uncertain behavior driven by some unknown ground truth probability distribution. My dissertation mainly focuses on answering the following question: How do we use (non-perfect) data samples generated from the unknown distribution to make more automatic and reliable decisions, especially for supply chain management and retail operations?

In Chapter 2, this dissertation study a practical multi-period inventory management problem faced by online retailers and propose a practical, data-driven, end-to-end (E2E) framework for multi-period inventory management that leverages the power of deep learning. Instead of adopting the two-step approach that first forecasts demand and vendor lead-time (VLT) separately and then, based on the predictions, solves for a solution that minimizes inventory costs, we directly learn the underlying mapping from features to the optimal solution by adopting a supervised learning approach.

In Chapter 3, we propose an integrated conditional estimation-optimization (ICEO) framework that uses statistical learning theory to estimate the underlying conditional distribution while considering the structure of the optimization problem. This method provides a generic learning framework and applies to a broad class of convex contextual stochastic optimization problems with uncertainty in the objective. We provide statistical performance guarantees and address the computational challenges that arise in performing this framework.

In Chapter 4, we focus on data-driven distributionally robust optimization (DRO) methods. We examine the conditional quantile prediction problem, which is equivalent to the contextual newsvendor problem, and propose a DRO framework. In contrast to the traditional setting where the design points are considered as random and i.i.d., we consider a fixed-design setting, which is more suitable for cases when features are pre-designed, such as through a series of controlled experiments.

Chapter 5 continues our study on the contextual newsvendor problem and considers inter-temporal correlations and moderate non-stationarities in the contextual demand process. Under these comparatively more realistic assumptions, we provide performance guarantees in the form of out-of-sample generalization bounds.

This thesis presents models and algorithms that leverage data analytics and optimization approaches to address the challenges in traditional manufacturing systems as well as emerging smart city contexts. The increasing availability of data sources and computing power has created the need for smarter data-driven decision making models, which motivates us to explore various ways of integrating statistics and optimization tools. In particular, we focus on analyzing practical operational problems with real-world data sets. Chapter 2 is devoted to improving yield prediction accuracy in integrated circuit manufacturing using the wafer map data. We propose an innovative yield prediction model, called adjacency-clustering, to capture the neighborhood effect that is often present in the wafer map. The adjacency-clustering model can be solved efficiently and deliver superior prediction performance than the state-of-the-art methods. Chapter 3 studies the order assignment problem in urban last-mile delivery services. We propose a framework to integrate travel time predictors with assignment optimization models to capture the drivers' practical routing behaviors. The proposed framework yields tractable formulations compatible with the existing stochastic and robust optimization tools. We further develop a branch-and-price algorithm to facilitate its real-time application. The real-world case study demonstrates the substantial benefits of applying our framework. Chapter 4 addresses the urban bike lane planning problem based on the real-world GPS trajectory data. We present a flexible optimization model based on the cyclists' utility functions. We analyze the problem structure and propose efficient algorithms to solve the bike lane planning model. We perform extensive numerical experiments on a real-world trajectory data set to validate the performance of our models and algorithms. The numerical study also generates managerial insights to help the city managers improve their bike lane planning decisions.

This dissertation is concerned with service operations systems with considerations of incentives, information asymmetries and bounded rationalities. Chapter 1 provides an overview of the dissertation.

In Chapter 2, motivated by the information service operations for the agricultural sectors in the developing economies, we propose a Cournot quantity competition model with price uncertainty, wherein the marketing boards of farmers' cooperatives have the options to obtain costly private information, and form information sharing coalitions. We study the social value of market information and the incentives for information sharing among farmers.

In Chapter 3, we offer a behavioral (bounded rationality) theory to explain product/technology adoption puzzle: Why superior investment goods are not widely purchased by consumers? We show that present-bias encourages procrastination, but discourages strategic consumer behavior. Advance selling is beneficial not only to the consumers as a commitment device, but also to the seller as a price discrimination instrument.

In Chapter 4, motivated by the fresh-product delivery industry, we propose a model of service operations systems in which customers are heterogeneous both in terms of their private delay sensitivity and taste preference. The service provider maximizes revenue through jointly optimal pricing strategies, steady-state scheduling rules, and probabilistic routing policies under information asymmetry. Our results guide service mechanism design using substitution strategies.

In Chapter 5, motivated by the puzzle of excessively long queue for low quality service in tourism and healthcare industries, we study the customers’ learning behaviors in the service operations systems, when they hold incorrect beliefs about the population distribution. We highlight a simple behavioral explanation for the blind ``buying frenzy'' in service systems with low quality: The customers under-estimate others' patience and are trapped in a false optimism about the service quality.

Chapter 6 concludes the dissertation with a summary of the main results and policy recommendations.

In recent years, autonomous driving technologies are developing so fast that we can expect in the near future, fleets of autonomous vehicles will be driving on public roads and providing services to passengers. And the introduction of autonomous vehicles would bring us numerous opportunities to improve the operations of transportation systems, since we can have better real-time control of these vehicles. This dissertation focuses on two representative operational problems for the transportation systems with autonomous vehicles: how to build more effective real-time routing services for these vehicles, and how to better manage the fleet of autonomous vehicles for taxi services.

Most previous works in addressing these two problems are focusing on developing parametric models to reflect the network dynamics and designing efficient algorithms to solve these models. Although there are some clear advantages of these parametric models, there are some major limitations when applying them to real networks. First, in order to allow for efficient solutions, strong assumptions or approximations have to be made in most of the parametric models. However, many of the assumptions can not be validated in reality. Second, some of the proposed parametric models still suffer from the curse of dimensionality, i.e. they can be applied to small networks but can not be incorporated into larger networks. With these considerations, the aim of this dissertation is to explore the use of non-parametric model-free methods for these two problems in transportation networks. More specifically, we incorporate the framework of Reinforcement Learning (RL), which is primarily concerned with how to obtain the optimal policy when the model of the Markov decision process (MDP) is not available.

We first study the problem of adaptive routing in stochastic and time-dependent networks. The problem is formulated as a MDP first, and we present the idea of Q learning to solve it in discrete state space, which is also compared with traditional stochastic dynamic programming method. Our case study on a mid-size network shows that Q learning outperforms the traditional dynamic programming method in most cases, especially during peak demand periods. Then in order to resolve the curse of dimensionality, we introduce an offline tree-based batch mode reinforcement learning method called fitted Q iteration (FQI), which can work in continuous state space and incorporate any regression algorithm as an approximation for the value function. The case study shows that it can further improve the routing policy and deliver a more flexible strategy during peak hours. Furthermore, the computational study shows that FQI can make more sufficient use of data at hand, since if there are more data fed into the training process of FQI, the resulting routing performance could be improved consistently.

Then we present a deep reinforcement learning approach for the problem of dispatching autonomous vehicles for tax services. We formulate the problem first and present our basic assumptions on the problem. Then we propose an actor-critic framework with neural networks as approximations for both the actor and critic functions, and with adaptations to the output action function. Furthermore, we provide a benchmark by formulating the problem as an integer program in order to maximize the total rewards. From our case study based on the New York yellow taxi data, we find that no matter the system dynamics are deterministic or stochastic, the RL method can always converge to some value close to the true optimal. Furthermore, when we choose to consider user priority and first serve those impatient passengers, we notice that the average waiting time of all passengers would sacrifice, but we add more fairness to the system by making sure there are less extreme long waiting times.

As e-commerce expands, warehouse systems face new challenges, leading to the development of robotic warehouses. These warehouses typically employ part-to-picker systems, where mobile robots and stationary human workers collaborate. To improve the performance of these systems, we proposed new performance evaluation models and operational strategies. We also proposed innovative designs aimed at fully robotic warehouses in the foreseeable future.

Performance prediction and evaluation are crucial in designing and operating robotic warehouses, especially given the highly stochastic and complex nature of robot traffic congestion. We introduced a new evaluation model that accounts for robot congestion by initially modeling the system as a closed queueing network (CQN) with blocking. Simulation observations led us to propose a congestion mechanism and simplify the system to a CQN without blocking. Demonstrating the asymptotic Poisson properties of robot arrivals enabled us to further approximate the simplified CQN as a transportation network. This approach allowed us to estimate congestion delays as closed-form functions of traffic flow. We integrated these estimated delays with the CQN model and developed an iterative algorithm to estimate the system throughput. Our numerical experiments confirmed that this method could accurately predict throughput under transportation congestion when the system was stable.

Effective real-time robotic warehouse operation requires strategic decisions regarding workstation assignments and collision-free robot path planning. To improve system efficiency, we developed an integrated method for task assignment and path planning, implemented in both offline and online phases. In the offline phase, based on our evaluation model, we estimated an approximated optimal steady-state traffic assignment, while the online phase guided robots according to offline traffic patterns using a decentralized and computationally efficient algorithm. The simulation results indicated that our method achieved 5-10% higher throughput and required much less computational time compared to current industrial implementations.

The advent of robotic arms has made fully robotic warehouses feasible. We proposed a new layout design that positions workstations, called internal workstations, equipped with robotic arms within the storage area to minimize transportation costs. We introduced a batching pool mechanism using special pods to collect and transport assembled totes in batches from internal to external workstations. This system was evaluated using an open queueing network (OQN), which led to a closed-form queue delay approximation. We found an upper bound for the relative error in the sojourn time estimation using this approximation and showed that our approximation is accurate. Using this approximation, we developed a location-allocation-queuing model, which can be transformed into mixed integer second-order conic programming (MISOCP) for efficient solving, to find the optimal workstation locations and pod-to-workstation allocation plans. This model demonstrated a significant reduction in transportation costs and an improvement in the robot machine time of 10-20% for large or deep systems in our simulations.