Relevant Degree Programs
Graduate Student Supervision
Doctoral Student Supervision (Jan 2008 - April 2022)
This thesis comprises three studies. Within each study, we analyze a stochastic multi-period decision making problem in the area of service management. Throughout the dissertation, we incorporate dynamic programming techniques to develop the mathematical models and analyze the solution approaches for each of the discussed problems.In the first two studies, we consider a queueing system in which customers require some conditions to be met prior to receiving service. We investigate whether an individual arriving to this system should join the queue at that time, or wait to join at some future time. Chapters 2 and 3 discuss two variations of this problem. We formulate the problem as a Markov decision process and show how the structure of the optimal policy depends on various parameters of the model.Furthermore, in Chapter 3, we use the construct of “level-k” thinking from the behavioral and experimental economics literature to model the bounded rationality of customers, and also to characterize their equilibrium strategy. We present the structural results of the customers’ joining policies and show the threshold structure of customers’ decisions with different levels of rationality. We also analyze the socially optimal solution and compare it to the equilibrium policy. The optimal policies we derive allow for a better management of customers’ waiting time and also give information on their joining behavior to service providers.In the third study, we analyze another dynamic decision making problem in a different context than the previous two studies. Through tracking drivers’ behavior, Usage Based Insurance (UBI) allows insurance companies to connect insurers’ premiums more closely to their actual driving performance. Chapter 4 provides a theoretical model to capture the effects of UBI on the auto insurance market. We formulate the underlying problem as a dynamic principal-agent model with hidden information and hidden action. Developing a dynamic programming algorithm, we characterize the full history-dependent optimal contract. Our model results shed light on how to design the contract to manage a UBI program, the extent to which a UBI policy can outperform a traditional policy, and how the potential gains depend on the demographics of the target market.
This thesis comprises three independent essays in operations management. The first essay explores a specific issue encountered by mobile gaming companies. The remaining two essays address the contracting problem in a supply chain setting. In the first essay, we study the phenomena of game companies offering to pay users in "virtual" benefits to take actions in-game that earn the game company revenue from third parties. Examples of such "incentivized actions" include paying users in "gold coins" to watch video advertising and speeding in-game progression in exchange for filling out a survey etc. We develop a dynamic optimization model that looks at the costs and benefits of offering incentivized actions to users as they progress in their engagement with the game. We find sufficient conditions for the optimality of a threshold strategy of offering incentivized actions to low-engagement users and then removing incentivized action to encourage real-money purchases once a player is sufficiently engaged. Our model also provides insights into what types of games can most benefit from offering incentivized actions. In the second essay, we propose what we call a generalized price-only contract, which is a dynamic generalization of the simple wholesale price-only contract. We derive some interesting properties of this contract and relate them to well-known issues such as double marginalization, relative power in a supply chain due to Stackelberg leadership, contract structure and commitment issues. In the third essay, we consider a supplier selling to a retailer with private inventory information over multiple periods. We focus on dynamic short-term contracts, where contracting takes place in every period. At the beginning of each period, with inventory or backlog kept privately by the retailer, the supplier offers a one-period contract and the retailer decides his order quantity in anticipation of uncertain customer demand. We cast the problem as a dynamic adverse-selection problem with Markovian dynamics. We show that the optimal short-term contract has a threshold structure, with possibly multiple thresholds. In certain cost regimes, the optimal contract entails a base-stock policy yet induces partial participation.
This dissertation addresses two topics in the domain of operations management. First we study a single utility’s optimal policies under the Renewable Portfolio Standard, which requires it to supply a certain percentage of its energy from renewable resources. The utility demonstrates its compliance by holding a sufficient amount of Renewable Energy Certificates (RECs) at the end of each year. The utility’s problem is formulated as a stochastic dynamic program. The problem of determining the optimal purchasing policies under stochastic demand is examined when two energy options, renewable or regular, are available, with different prices. Meanwhile, the utility can buy or sell RECs in any period before the end of the horizon in an outside REC market. Both the electricity prices and REC prices are stochastic. We find that the optimal trading policy in the REC market is a target interval policy. Sufficient conditions are obtained to show when it is optimal to purchase only one kind of renewable energy and regular energy, and others to show when it is optimal to purchase both of them. Explicit formulas are derived for the optimal purchasing quantities in each case. In the second essay, we examine the interaction between a buyer (Original Equipment Manufacturer, OEM) and his supplier during new product development. A “white box” relationship is assumed: the OEM designs the specification of the product and outsources the production to his supplier. The supplier may suggest potential specification problems. Our research is motivated by the fact that the supplier may detect potential specification problems, and one cannot take for granted that the supplier would inform the OEM. We solve an optimization problem from the perspective of the OEM. We first prove that it is strictly better for the OEM to design the contract so that the supplier will inform the OEM should she detect any flaws. Then we characterize the optimal solutions for the OEM. We also perform some sensitivity analysis at the end.
There are three topics in operations management presented in this dissertation. Each topic deals with a specific issue encountered by managers from various organizations. In the context of non-profit operations, we study a two-customer sequential resource allocation problem whose objective function has a max-min form. For finite discrete demand distribution, we give a sufficient and necessary condition under which the optimal solution has monotonicity property. However, this property never holds with unbounded discrete distributions. Then, we look at a service system with two servers serving arriving single class jobs. Servers care about fairness, and they can endogenously choose capacities in response to the routing policy. We focus on four commonly seen policies and examine the two-server game where the servers' objective functions have a term that reflects fairness. Theoretical results concerning the existence and uniqueness of the Nash equilibrium are proved for some policies. Numerical studies also provide insights on servers' off-equilibrium behaviours and the system efficiency under different policies. Finally, suppose that a firm has heterogeneous servers who provide service with different quality levels, and that there exists a learning curve of the servers so that the quality can be improved by accumulating experience in serving customers. As customers decide their service procurement based on the quality and system congestion, what pricing scheme should the firm adopt to achieve optimal revenue in the long run? We compare a traditional pricing scheme with a proposed one, and theoretically establish the superiority of the proposed pricing scheme. Based on both theoretical and numerical evidence, we characterize the sensitivity of some parameters with respect to the comparison.
This thesis comprises three chapters with applications of the stochastic optimization models in healthcare as a central theme. The first chapter considers a patient screening problem. Patients on the kidney transplant waiting list are at higher risk for developing cardiovascular disease (CVD), which makes them ineligible for transplant. Therefore, transplant centers screen waiting patients to identify patients with severe CVD. We propose a model for finding screening strategies, with the objective of minimizing sum of the expected screening cost and the expected penalty cost associated with transplanting an organ to an ineligible patient. Our results suggest that current screening guidelines, which are only based on patients' risk for developing CVD, are significantly dominated by policies that also consider factors related to patients' waiting time.In the second chapter, we extend our results from the first chapter to the case of inspecting a vital component which is needed at a random future time when an emergency occurs. If the component is not operational at that time, the system incurs a large penalty, which we want to avoid through inspections and replacements. We propose a model and solution algorithm for finding an inspection policy that minimizes the infinite horizon discounted expected penalty, replacement, and inspection costs. We also discuss other structural properties of the solution, as well as insights based on numerical results. In the third chapter, we consider inventory decisions regarding issuing blood in a hospital. This research is motivated by recent findings in medicine that the age of transfused blood can affect health outcomes, with older blood contributing to more complications. Current practice at hospital blood banks is to issue blood in order from oldest to youngest inventory, so as to minimize shortage. However, the conflicting objective of reducing the age of blood transfused requires an issuing policy that also depends on the inventory of units of different ages. We propose a model that balances the trade-off between the average age of blood transfused and the shortage rate. Our numerical results suggest we can significantly reduce the age of transfused blood with a relatively small increase in the shortage rate.
Master's Student Supervision (2010 - 2021)
This research studies the delivery service assortment and product pricing problem in the context of online retailing where the seller selects a series of delivery options from a set of available alternatives for the customers to choose from and decides the price for the product and the listed surcharge for each delivery service. We aim to examine the impact of seller's pricing flexibility and customer rating on the optimal decisions and the optimal expected profit of the seller. By solving and comparing the results of four related problems, we find that usually it would be optimal for the seller to include all the available delivery options and charge a constant mark-up for all the options. But when the customer rating is aggregated, the seller would have to solve a combinatorial optimization problem to find out the optimal assortment when pricing is restricted to the product only and he should differentiate the mark-up for each option when he enjoys the pricing flexibility to re-price the quoted surcharges. We also show that two simple heuristic algorithms provide very good performance for the mentioned combinatorial optimization problem. We explain why the aggregated rating would only hurt the seller and how pricing flexibility could remove its negative effect while assortment adjustment can only weaken its impact. In addition, numerical studies present the comparison between the two main problems with aggregated customer rating and provide some observations of the impact on delivery service providers and the customers. The findings in this thesis yield useful managerial insights for the delivery service providers as well as the seller for making their strategic decisions.