Optimal control of an assembly system with demand for the end-product and intermediate components

Abstract

This article considers the production and admission control decisions for 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. The firm faces two types of demand. The demand for the end-product is satisfied immediately if there are available products in inventory while the firm has the option to accept the order for later delivery or to reject it when no inventory is available. Demand for intermediate components may be accepted or rejected to keep components available for assembly purposes. The structure of demand admission, component production and product assembly decisions are characterized. The proposed model is extended to take into account multiple customer classes and a more general revenue collecting scheme where only an upfront partial payment is collected 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, a simple heuristic policy is proposed for which the computational load grows linearly with the number of products and its performance is tested under a variety of example problems.

Keywords:

• Production and inventory control
• multistage assembly systems
• inventory rationing
• demand management
• Markov decision processes
• dynamic programming
• optimal control