Modified (Q, r) Inventory Control Policy for an Assemble-to-Order Environment

The traditional (Q,r) inventory control model assumes that the date at which the order is entered is the same as the date at which it is requested or expected to be delivered. Hence, the penalty cost is incurred when the customer places the order if inventory is unavailable. This is a reasonable assumption for retail systems and most distribution centers (DC), but not for an assemble-to-order (ATO) environment. In this scenario, there is a delivery time which is usually pre-negotiated and in addition to considering the manufacturing process time and in some cases the outbound transportation time, it also has some safety time built-in. This safety time is defined by the manufacturer and represents information related to when the penalty is incurred. The main objective of this research is to develop a modified (Q,r) policy that incorporates the safety time, and to evaluate this policy in terms of expected inventory cost and expected penalty cost / late orders. The problem is addressed following the heuristic approach discussed by Hadley and Whitin (1963). Two main models are developed based on the following assumptions: 1) early shipments are allowed by the customer, and 2) no early shipments are allowed. The behavior of both models is analyzed mathematically and by means of numerical examples. It is shown that from a manufacturer perspective, the first model is preferred over the traditional (Q,r) model. However, it poses a threat for the long term business relationship with the customer because the service level deteriorates, and for the implications that early shipments have on the customer inventory. The behavior of the second model is strictly related to the problem being addressed. Its merits with respect to the traditional and the "early shipment" model are discussed. This discussion is centered on the coefficient of variation of the lead-time demand, the ratio (IC/pi), and the location of the supplier. A final model which is a hybrid of the previous two shipping policies is developed. The models developed in the course of this research are generalizations of the traditional (Q,r) model.