Mahesh Nagarajan

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 dissertation addresses three topics in the domain of operations management.First we study the problem of profit allocation in a supply chain using a bargainingapproach. We present a novel framework for the analysis of this problem.The application of our framework results in a prescription for the required profitallocations. We prove that in a setting where all supply chain agents can communicate,possibly coordinating their actions, the allocation prescribed by our bargainingframework coincides with the Shapley value of a cooperative game associatedwith the setting. Next, we study revenue management in the presence of strategicconsumers, who face some uncertainty regarding the product valuation. We show,contradictory to the main stream of the literature regarding strategic consumers,that under certain circumstances, the retailer may prefer facing strategic consumersrather than myopic ones. Finally, we study the issue of cross-dock operations managementat a shift-level. We target the main gap identified in the literature for thisissue, and present a holistic framework for the allocation of cross-dock resourcesto processing of containers and freight. We show, using simulated data that ourapproach outperforms current practices.

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