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This paper studies the order-fulfillment process of a supplier producing customized capital goods. It is critical for firms in capital goods industries to determine the optimal time to start the order-fulfillment process. On one hand, their customers expect them to be responsive and the time that they are prepared to wait for the product is much shorter than the time needed to produce and deliver it. On the other hand, it is risky for the firms to start production before customers confirm their orders due to inventory holding costs and the possibility of order cancellation. In this study, we extend the existing literature to consider two different products, which share the same capacity and are ordered by different customers. The supplier can only work on one product at any time due to capacity constraints. The capacity constraints complicate the timing issue significantly because the supplier needs to determine not only the optimal time to start the order fulfillment, but also the right sequence. Apart from late initiation of the process, production scheduling difficulties alone could cause late delivery. We formulate this problem as a discrete time Markov decision programming. For the problem where the order for one product has been confirmed, but that of the other has not and its arrival time is random, under a set of intuitive conditions, the optimal time to start as well as the optimal sequence follow a threshold-type structure and can be fully characterized. However, for the more general problem in which the arrival times of the orders for both products are uncertain, the optimal policy does not have a simple structure. Three heuristics are proposed and their performance tested.
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