Optimal Control of an Assembly System with Demand for the End-Product and Intermediate Components

We consider the production and admission control of a two-stage manufacturing system where intermediate components are produced to stock in the first stage and an end-product is assembled from these components through a second stage assembly operation which may allow backorders. The manufacturing firm faces two types of demand. The one directed at the end-product is satisfied immediately if there are available products in inventory, and the firm has the option to accept the order for later delivery or to reject the order if no inventory is available. The second type of demand is for any of the intermediate components and the firm again has the option to accept the order or reject it to keep the components available for assembly purposes. We provide structural results for the demand admission, component production and product assembly decisions. We also extend the model to take into account multiple customer classes based on revenue and a more general revenue collecting scheme where only an upfront partial payment for an item is received if a customer demand is accepted for future delivery with the remaining revenue received upon delivery. Since the optimal policy structure is rather complex and defined by switching surfaces in a multidimensional space, we also propose a simple heuristic policy for which the computational load grows linearly with the number of products and test its performance under a variety of example problems