Contract assembly: Dealing with combined supply lead time and demand quantity uncertainty

We consider a problem faced by a contract assembler that both assembles finished goods and procures the associated component parts for one of its major customers. Because of rapid changes in technology and ongoing engineering changes, all parts subject to obsolescence are purchased only for the current customer order. The procurement lead times of the components are random. Moreover, although the order for the finished product has a defined due date, the contract allows the customer to change the order quantity. Consequently, the assembler also faces a random demand. The assembler must determine how much to order and when to order each component part. The objective is to minimize the total expected cost, including the cost of holding components prior to their assembly, penalties for tardiness vis-à-vis the assembly due date, and overage and underage costs in satisfying the demand quantity. We present some structural results and discuss insights regarding optimal policies. We also present several simple heuristic policies and compare them to optimal policies. Computational results indicate that ignoring lead time variability can be costly, but relatively simple heuristics that consider lead time variability perform quite well.