Process flexibility in homogeneous production–inventory systems with a single-period demand

Most studies of process flexibility have considered a make-to-order setting, whereas in practice, production systems usually have a make-to-stock environment. In this article, we investigate the process flexibility in homogeneous production–inventory systems with a single-period demand. We formulate the capacitated multi-product production–inventory system as a convex optimization model with an implicit objective function, which is then transformed into a network flow problem. We develop optimality conditions for the production decision problem based on concepts such as the flow position and the influencing set of each product node in the associated network for any given flexibility design. We further characterize the optimal production decision with an analytical approach for dedicated and completely flexible systems and two numerical algorithms for production systems with general flexibility designs. We then investigate the popular long chain design in homogeneous production–inventory systems with a comprehensive numerical study, showing that its performance is more sensitive to the asymmetry in initial product inventory than the system cost structure. However, the long chain design is still capable of achieving most of the benefits gained from a completely flexible design in a make-to-stock environment unless the asymmetry in product initial inventory is too high.