Optimal policies for multi-echelon production-inventory systems with random demands

This thesis consists of three parts. The first part deals with a multi-stage production-inventory systems in series with unit demands and inter-arrival times with increasing failure rates (IFR) under continuous review. A release policy involving stage specific delays is shown to be optimal. An item released to the system is labeled with a target demand. The label drops by one every time a demand arrives. Each stage has a stage specific threshold. If the label is above the threshold, the item waits until the next demand and its label drops by one. If the label is below the threshold the item is released immediately. Finally, if the label is equal to the threshold, a stage specific delay is induced. The item is released at the end of the delay or when a new demand arrives, whichever occurs first. An efficient heuristic is proposed to compute stage specific thresholds and delays. The numerical study shows that heuristic is near-optimal and performs significantly better than traditional base stock policies. A general assembly production-inventory system is proved to be equivalent to a serial system. The second part studies serial production-inventory systems under periodic review. Decomposing the problem into a series of problems with single item-customer pair, again an release policy involving stage specific delays is shown to be optimal. The last part focuses on the flexibility of supply chains. A firm receives orders that will be required at an uncertain time given by an Erlang distribution. The firm, in turn, places orders at a linear cost from a supplier with fixed lead time l and has the option of converting (expediting) each order, at a cost, over a certain time interval after the order is originally placed. A converted order arrives le < l units of time after it is converted. A threshold policy is shown to be optimal. Under such a policy the firm places an order after a certain number of exponential events have been observed. An order is converted the first time, if any, when the residual lead time exceeds a time threshold related to the number of exponential events realized since the order was placed.