## Managing Uncertainty in Capacity Investment, Revenue Management, and Supply Chain Coordination

##### Abstract

"Uncertainty" is used broadly to refer to things that are unknown or incompletely understood. In operations management, basic sources of uncertainty may include decision uncertainty, model uncertainty, analytical uncertainty, data uncertainty, and so on. Although uncertainty is unavoidable in decision making, different mechanisms can be designed to mitigate the impact of uncertainty. One commonly used strategy is "decision postponement," wherein the decision maker purposefully delays some of the decisions to a time when uncertainty is reduced or resolved. This type of a recourse action provides the decision maker with increased ability to match supply with demand. In this dissertation, we study the value of decision postponement in the context of different settings, including capacity investment, revenue management, and supply chain coordination. These problems share one characteristic in common: decision postponement, and as such, are all modeled as two-stage stochastic programming problems. In the first stage, a set of decisions are made under uncertainty so as to maximize the expected profit or utility. Then in the second stage, all uncertainty is resolved and a deterministic optimization problem is solved to determine the postponed decisions, constrained by the first stage decisions.

In capacity investment, we study the capacity, pricing, and production decisions of a monopolist producing substitutable products with flexible or dedicated resources. While the capacity decision needs to be made ex-ante, under demand uncertainty, pricing and production decisions can be postponed until after uncertainty is resolved. We show how key demand parameters (the nature of uncertainty, market size, market risk, and risk attitude) impact the optimal capacity decision under the linear demand function. In particular, we show that if the demand shock is multiplicative, then in terms of the "invest or not" decision, the firm will be immune to forecast errors in parameters of the underlying demand shock distribution. Furthermore, incorrectly modeling the demand shock as additive, when, in fact, it is multiplicative, may lead to overinvestment. On the other hand, while the concept of a growth in market size leads to similar conclusions under both additive and multiplicative demand shocks, how market risk affects the optimal capacity decision depends critically on the form of the demand shock. In addition, the decision-makerâ s attitude toward risk significantly affects the optimal capacity level, and its impact highly depends on the structure of the resource network. Our analysis provides insights and principles on the optimal capacity investment decision under various settings.

In airline revenue management, a well-studied problem is the optimal allocation of seat inventory among different fare-classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this dissertation, we study the seat inventory control problem considering the aircraft swapping option. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed-capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal seat allocation under the swapping possibility. We also perform a numerical study, which indicates that the revenue impact of using the "true" optimal booking limits under the swapping possibility can be significant.

In supply chain coordination, we consider the influenza vaccine supply chain, which, due to the biological complexity of the production process, has a unique characteristic in that production yield is highly uncertain. Given the market demand and price, a monopolist supplier must decide how much raw material to input into production in the first stage. However, since the yield is unknown and production is costly, it is not necessarily in the supplierâ s best interest to ensure that all market demand is met. The supplierâ s input quantity depends on the trade-off between the costs of overproduction and undersupply. This, in fact, is one of the reasons why the influenza vaccine manufacturers in the United States lack motivation to produce sufficient amounts of vaccine to meet all demand [Williams (2005), Chick et al. (2008)]. In operations management, it is a well-known result that decentralized supply chains, where each player is only interested in optimizing her own objective, often lead to poor overall performance for the supply chain. However, a higher efficiency is achievable through contracting on a set of transfer payments [Cachon (2004)]. A "coordinating" contract is referred to as one in which each playerâ s objective is in accordance with the supply chainâ s objective. Given the fact that influenza vaccine plays an important role in health care industry, it is important to study how different contracts impact the influenza vaccine supply chain, where the uncertainty is on the supply side. We study a game in which the supplier and the retailer are engaged in certain type of contracts that specify how risk is shared between the players. We study both the pre-ordering and the post-ordering settings, which respectively refer to the cases where the retailer orders the vaccine before or after the vaccine production is completed. We show that pre-ordering wholesale price contracts dominate post-ordering wholesale price contracts in terms of the resulting supply chain efficiency, but neither of them are able to fully coordinate the supply chain. We also find that cost-sharing contracts are able to coordinate the supply chain, while payback and advance-ordering wholesale price contracts fail to do so. Finally, we prove that if the unsold vaccine can be salvaged with some positive value, then the supply chain can be easily coordinated with wholesale price contracts.

In studying this type of stochastic programming problems, it is not only important to characterize the optimal solution, but also important to gain an understanding of how the optimal solution will be affected by environmental parameters. Since the most inaccurate part in stochastic programming often lies in the parameters of the distribution functions, it is both interesting and meaningful to investigate how the optimal solution varies with the intrinsic nature of the random variables. Consequently, we make use of stochastic order relationships to study the behavior of the optimal solutions when the underlying random variables become either "larger" or "more risky."

##### Collections

- Doctoral Dissertations [12579]