Essays on Operations Management Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Operations Management and Manufacturing

Dissertation Abstract This dissertation focuses on the perishable inventory theory with health-care applications, the multi-variate input modeling for stochastic simulations, and temporal and bivariate dependence modeling for interarrival and service times of the queueing systems. This disser-tation contributes to the perishable inventory theory by introducing the critical level policy for the first time with application from the blood platelet inventory management. Moreover, this dissertation introduces the Vector-Auto-Regressive-to-Anything (VARTA) method as an advanced simulation input modeling to analyze the impact of temporal and bivariate dependent interarrival and service times in the queueing systems. A synopsis of the three chapters of the dissertation follows. Chapter 1: " Blood Platelet Inventory Management with Protection Levels and Substitution " We consider a discrete-time inventory system for a perishable product that has distinct demand streams for product of different ages; an example of such a system is blood platelets. In addition to inventory holding, outdating and shortage costs, our model includes substitution costs when a demand for a certain-aged item is satisfied by a different-aged item. Our objective is to minimize the expected cost over an infinite time horizon. We introduce the critical level policy to the perishable inventory literature, protecting the newest items against excessive Downward substitution, borrowing an approach from the spare parts literature. This reserves these newest items for future demand for procedures needing younger items (i.e. fresher blood platelets). We model the problem as a Markov Decision Process (MDP) and evaluate the costs of a common heuristic replenishment policy (with and without a protection level) against extant " near optimal " policies in the literature. We show that the protection level policy may outperform other policies, particularly if supplies are capacitated. Chapter 2: " Failure Probability of VARTA in Higher Dimensions " Vector-Autoregressive-To-Anything (VARTA) is a highly flexible model for driving large-scale stochastic simulations by generating samples of stationary multivariate time series with arbitrary marginal distributions. The construction of this model relies on a stable ii vector autoregressive process with a positive definite autocorrelation matrix. We show that there exists multivariate time-series input processes for which the conditions of stability and positive definiteness are violated. We investigate the likelihood of this event with increasing number of component time-series processes and order of dependence by extending the onion method, which is used for sampling positive definite correlation matrices for random vectors, to sample positive definite autocorrelation matrices for multivariate time series. We …