This dissertation consists of three essays that analyze stochastic dynamic optimization models and game models in operations management.
Markov decision processes (MDPs) and sequential games are good models of many real sequential decision processes. However, in diverse applications in operations research and economics, the state of the MDP is a vector and the curse of dimensionality obstructs analysis and computations. Several veins of research seek to exorcise this curse. One vein, the domain of the first essay, identifies MDPs with myopic optima, namely sequential decision processes that can be solved via a temporal sequence of static problems. The first essay identifies new classes of MDPs with myopic optima and sequential games with myopic equilibrium points.
Seasonal fashion goods and seats on specific airline fights exemplify a job lot whose sale as time passes should be managed closely as a deadline approaches. The second essay analyzes a dynamic revenue management model in which firms set prices and hold back inventory for sale later in the season. We concentrate on a model with demand functions that are stochastic, nonstationary, and iso-elastic. If there is only a single firm, the resulting Markov decision process has a myopic optimum that can
be specified nearly explicitly and is easily computed. If there are multiple firms, there is a myopic Markov-perfect equilibrium point that can be computed easily and facilitates the analysis of comparative dynamics.
A pricing schedule is nonlinear if the resulting revenue is not a linear function of quantity. The third essay presents a dynamic nonlinear pricing model with stochastic demand. We start with a two-segment model for illustrative purposes and derive properties of the model and its optimum which include the existence of a myopic optimum that can be specified nearly explicitly and is easily computed. Furthermore, the optimal policy is a linear decision rule. The essay ends by extending the two- segment model to an arbitrary number of segments and uses numerical examples to compare models with two and three segments.