The thesis starts with a brief description outlining the main features, in general terms, of the models to be studied. The second chapter reviews the existing literature on ordering policies for perishable inventories. Chapter 3 studies an (s,S) continuous review model for inventory with a fixed lifetime. In this model we assume that the demand is a general renewal process and the lead-time is zero. In Chapter 4, we study a similar perishable inventory model in which the demand follows a Poisson process with batch arrivals. By finding some regenerative points, we study these two models with the Markov renewal technique. After solving the Markov renewal equations, the stationary probability distribution for the inventory level can be obtained. We then construct closed form expressions fo...[ Read more ]

The thesis starts with a brief description outlining the main features, in general terms, of the models to be studied. The second chapter reviews the existing literature on ordering policies for perishable inventories. Chapter 3 studies an (s,S) continuous review model for inventory with a fixed lifetime. In this model we assume that the demand is a general renewal process and the lead-time is zero. In Chapter 4, we study a similar perishable inventory model in which the demand follows a Poisson process with batch arrivals. By finding some regenerative points, we study these two models with the Markov renewal technique. After solving the Markov renewal equations, the stationary probability distribution for the inventory level can be obtained. We then construct closed form expressions for the expected cost functions. The optimal s* and S* are obtained numerically. We analyze the properties of s*, S* and the corresponding cost functions for different parameters.

Recently, there is a noticeable increase in research interest in discrete-time queues, motivated mainly by the applications of discrete-time queues to some engineering systems where time is slotted. In Chapter 5, we describe the study of a discrete-time model for perishable inventory systems subject to stochastic demands. By constructing a multi-dimensional Markov chain with a finite state space, we obtain the closed form solution for the steady state probability distribution of the inventory level and for other system performance measures; then a closed form expected cost function is constructed. Based on the optimal (s,S) policies for zero lead-time, in Chapter 6, we derive the optimal policy for a positive lead-time case by combining a heuristic approach and simulation method.

Perishable inventory theory is an important part of the general inventory theory. It is often more difficult to analyze. The main objective of this thesis is to provide both analytical and numerical solutions to a number of difficult models. We hope to gain enough managerial and system insights so that the challenging problems of positive replenishment lead- times in complex perishable inventory systems can be addressed with a combination of exact analytical methods and numerical approximation methods.