To prevent loss of lives during seasonal disasters, relief agencies distribute critical supplies and provide lifesaving services to the affected populations. Despite agencies' efforts, frequently occuring disasters increase the cost of relief operations. The purpose of our study is to minimize the cost of relief operations, considering that such disasters cause random demand. To achieve this, we have formulated a series of models, which are distinct from the current studies in three ways. First, to the best of our knowledge, we are the first ones to capture both perishable and durable products together. Second, we have aggregated multiple products in a different way than current studies do. This unique aggregation requires less data than that of other types of aggregation. Finally, our models are compatible with the practical data generated by FEMA. Our models offer insights on the impacts of various parameters on optimum cost and order size. The analyses of correlation of demand and quality of information offer interesting insights; for instance, under certain cases, the quality of information does not influence cost. Our study has considered both risk averse and risk neutral approaches and provided insights. The insights obtained from our models are expected to help agencies reduce the cost of operations by choosing cost effective suppliers.

This dissertation consists of three independent sections: In the first part, focusing on the auto industry we look at the challenges and solution strategies of employing build-to-order (BTO) with global supply. We consider some familiar tools for managing domestic supply and exploit them for managing international supply, and propose new methods. We study frequency of supply as a way to improve performance. We study the impact of forecast accuracy, and conclude that improvements there alone may not be sufficient to obtain desired savings. Within this perspective we look at a new shipping policy, 'Ship-to-Average", which prescribes sending a fixed quantity, based on the long term average forecast, with each shipment and making adjustments only if the inventory strays outside a prescribed range. In the second part we look at a Brownian control problem. When a manufacturer places repeated orders with a supplier to meet changing production requirements, he faces the challenge of finding the right balance between holding costs and the operational costs involved in adjusting the shipment sizes. Consider a storage system whose content fluctuates as a Brownian motion in the absence of control. A linear holding cost is incurred continuously. Inventory level can be adjusted by any quantity at a fixed plus proportional cost. We show control band policies are optimal for the average cost problem and calculate the optimal policy parameters. This form of policy is described by three parameters q, Q, S. When the inventory falls to 0 (rises to S), the controller expedites (curtails) shipments to return it to q (Q). Developing techniques based on Lagrangian relaxation we show that this type of policy is optimal even with constraints on the size of adjustments and on the maximum inventory level. The Brownian Control problem can be viewed as an idealization --without delivery delays, of the problem of supplying BTO operations, and provides some theoretical explanation for the Ship-to-Average policies. In fact, Ship-to-Average policies are a practical implementation of Control Band policies in the setting with delivery delays. Finally, we explore the power and applicability of the Lagrangian approach developed in the second part.

In this study, we focus on a real life problem that involves a single item which is used in military operations. The items in use fail according to a Poisson process and lead times are deterministic. Four alternative inventory control models are developed. Among these models, a two-echelon system consisting of a depot in the upper and several bases in the lower echelon is operated currently. This system is compared to a single-echelon system that consists of several bases. The comparison reveals the importance of the holding cost incurred for the items intransit between the depot and the base which is ignored in most of the studies in literature. Both the two and single-echelon models are also extended to have repair ability. A continuous-review base-stock policy is used for all models. Exact models are formulated. The results are obtained under various lead time, unit costs and demand parameters. Results of four different settings are compared and the findings are reported.