Inventory control in a build-to-order environment

This dissertation addresses inventory control in a build-to-order environment. It consists of three independent sections: challenges of managing supply in the auto industry from a build-to-order (BTO) perspective and some solution approaches, a stochastic control problem dealing with managing supply, and exploring Lagrangian methods in stochastic models.; In the first part, focusing on the auto industry we look at the challenges and solution strategies of employing BTO with global supply. We consider some familiar tools for managing domestic supply and exploit them for managing international supply, and propose some alternative new methods. We study frequency of supply, a tool widely used in local supply, as a way to improve performance in global supply operations. We study the impact of forecast accuracy, and conclude that improvements there alone may not be sufficient to obtain desired savings. In fact, our analysis strongly suggests that reducing the level of demand detail communicated to distant suppliers can simultaneously improve their quality of service and reduce their cost in providing it. 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 stochastic control problem, which also provides theoretical evidence in support of the Ship-to-Average policies. 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. We consider an inventory whose content fluctuates as a Brownian motion in the absence of control. At any moment a controller can adjust the inventory level by any positive or negative quantity, but incurs both a fixed cost and a cost proportional to the magnitude of the adjustment. The inventory level must be nonnegative at all times and continuously incurs a linear holding cost. The objective is to minimize long-run average cost. We show that control band policies are optimal for the average cost Brownian control problem and explicitly calculate the parameters of the optimal control band policy. This form of policy is described by three parameters {lcub}q, Q, S{rcub}, 0 < q ≤ Q < S. When the inventory falls to 0 (rises to S), the controller expedites (curtails) shipments to return it to q ( Q). Employing apparently new techniques based on methods of 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. We also extend these results to the discounted cost problem.; The Brownian Control problem can be viewed as an idealization---without delivery delays, of the problem of supplying build-to-order operations. The conclusion that Control Band Policies are optimal in this idealized setting provides some theoretical explanation for the observed performance of Ship-to-Average policies. In fact, Ship-to-Average policies are a practical implementation of Control Band policies in the setting with delivery delays.; In the final part of the thesis we further study the Lagrangian approach developed in the second part. We explore the power and applicability in more details, demonstrate specific technical characteristics and describe additional applications. In this process, we look at several Brownian control problems with different forms of constraints. We solve these constrained Brownian control problems using Lagrange methods and note that the modelling aspect plays a critical role in the solution.