Inventory Control In A Build-To-Order Environment

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.