We consider the optimal production and inventory control of an assemble-to-order system with m components, one end-product, and n customer classes. A control policy specifies when to produce each component and, whenever an order is placed, whether or not to satisfy it from on-hand inventory. We formulate the problem as a Markov decision process and characterize the structure of an optimal policy. We show that a base-stock production policy is optimal, but the base-stock level for each component is dynamic and depends on the inventory level of all other components (more specifically, it is nondecreasing). We show that the optimal inventory allocation for each component is a rationing policy with different rationing levels for different demand classes. The rationing levels for each component are dynamic and also nondecreasing in the inventory level of all other components. We compare the performance of the optimal policy to heuristic policies, including the commonly used base-stock policy with fixed base-stock levels, and find them to perform surprisingly well, especially for systems with lost sales.assemble-to-order (ATO) systems, production and inventory control, Markov decision processes, make-to-stock queues

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We consider the problem of allocating demand arising from multiple products to multiple production facilities with finite capacity and load-dependent lead times. Production facilities can choose to manufacture items either to stock or to order. Products vary in their demand rates, holding and backordering costs, and service-level requirements. We develop models and solution procedures to determine the optimal allocation of demand to facilities and the optimal inventory level for products at each facility. We consider two types of demand allocation, one in which we allow the demand for a product to be split among multiple facilities and the other in which demand from each product must be entirely satisfied by a single facility. We also consider two forms of inventory warehousing, one in which inventory locations are factory based and one in which they are centralized. For each case, we offer a solution procedure to obtain optimal demand allocations and optimal inventory base-stock levels. For systems with multiple customer classes, we also determine optimal inventory rationing levels for each class for each product. We use the models to characterize analytically several properties of the optimal solution. In particular, we highlight eight principles that relate the effects of cost, congestion, inventory pooling, multiple sourcing, customer segmentation, inventory rationing, and process and demand variability.production/inventory systems, queueing systems, generalized assignment problem, multi-item/multifacility systems