Tim Huh

This dissertation comprises two studies. In the first two chapters, we study individualized patient monitoring in hospitals under explicit consideration of alarm fatigue. Hospitals are rife with alarms, many of which are false. This leads to alarm fatigue, in which clinicians become desensitized and may inadvertently ignore real threats. We develop a partially observable Markov decision process (POMDP) model for recommending dynamic, patient-specific alarms in which we incorporate a cry-wolf feedback-loop of repeated false alarms. Our model takes into account patient heterogeneity in safety limits for vital signs and learns a patient’s safety limits by performing Bayesian updates during a patient’s hospital stay. In Chapter 2, we develop structural results of the optimal policy, and in Chapter 3 we perform a numerical case study based on clinical data from an intensive care unit (ICU). We find that compared to current approaches of setting patients’ alarms, our dynamic patient-centered model significantly reduces the risk of patient harm. In Chapter 4, we study elevator queue management during a pandemic. The social distancing requirement during COVID-19 reduced the elevator capacity in high-rise buildings by up to 70 %, which resulted in elevator queue build-up and increased the elevator wait time, thereby increasing the chance of the spread of the disease. We considered a real-life large clinic facility of the Vancouver general hospital (Diamond clinic) and studied the impact of rescheduling the clinic’s starttime on patients’ average wait time as well as on the queue length in the lobby during busy periods. Our results showed that by rescheduling the clinics (that are originally scheduled at busy times) by a maximum of 30 minutes, the average wait time can decrease by up to 85%, and the maximum queue length in the lobby can decrease by up to 95%.

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Decision making under uncertainty and limited information has been a critical challenge in operations. This thesis studies three applications and sheds light on how to make sequential decisions as data for learning are collected over time. In the first chapter, we consider the data-driven newsvendor problem where a manager makes inventory decisions sequentially and learns the unknown demand distribution based on observed samples of continuous demand (no truncation). We show that the widely-used sample average approximation approach is near-optimal. Moreover, we characterize how the best achievable performance depends on not only the time horizon but also the local flatness of the demand distribution.The second chapter considers a dynamic pricing and learning problem where a seller prices multiple products and learns from sales data about unknown demand. To avoid the classical problem of incomplete learning, we propose dithering policies under which prices are probabilistically selected in a neighborhood surrounding the myopic optimal price. We show that dithering policies achieve asymptotically optimal performance in three typical settings and their extensions with demand correlation, which demonstrates dithering as a unified approach to balance exploration and exploitation.The third chapter considers a sequential search over a group of similar alternatives to select the best one. The individual value of an alternative contains two components: an observable utility and an idiosyncratic value. Once an alternative is searched, the utility can be fully revealed, but the idiosyncratic value is unobservable and needs to be learned gradually by sampling. The utilities share an unknown population distribution, which captures the similarity across the alternatives and allows for knowledge transfer within the group. A novel feature of this problem is the combination of the individual and population levels of learning. We formulate the problem as a Bayesian dynamic program and show that the optimal policy can be found by comparing the mean estimates of the current alternative and the population. We also derive other structural properties to provide managerial insights and shed light on the two levels of learning.

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This dissertation addresses the implications of the satisficing decision making in retail and revenue management. In the first essay, we incorporate the satisficing behavior of customers in an assortment optimization problem. While different approaches to modelling customer choice have been adopted in assortment planning, all assume customers are utility maximizers. Our work bridges the research streams of assortment planning and bounded rationality, particularly satisficing behavior. Furthermore, by defining a limit for the search budget of customers, based on which customers leave without purchase after examining a certain number of items, we bring a new perspective to the assortment planning literature. We formulate this optimization problem and prove that the firm's problem of finding the optimal assortment is NP-hard. We also establish certain structural properties of the optimal decision to reformulate the problem as a mixed integer program. We show the size of the optimal assortment cannot exceed the maximum search budget of all customers. The second essay investigates the consequences of ignoring the satisficing behavior of customers. We identify analytically a tight upper bound on the firm's percentage loss of expected profit for small instances when it assumes incorrectly that its customers are utility maximizers. In this regard, we take the multinomial logit choice model as the representative of a utility maximizing model. For larger instances, we take a numerical approach to characterize the loss. Our results indicate that when the firm is dealing with satisficers, it may face considerable profit loss by ignoring this type of behavior.In the third essay, we propose a price optimization model for a firm offering two substitutable items to satisficing customers. We define acceptability probability functions for each item and formulate the demand of each product based on the assumption that customers examine the items one-by-one until they find an acceptable alternative. We prove unimodality of the revenue function when the acceptability probabilities follow certain structures. We then provide insights into price dispersion of a utility maximizing pricing model and our satisficing model, as well as the revenue loss of a firm adopting an incorrect choice model.

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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.

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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.

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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.

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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.

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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.

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