Optimal production and inventory policies in capacitated supply chains under various ownership structures.

Abstract

One of the most significant challenges facing operations managers is to determine how to optimally produce and manage inventory within supply chains with capacity limitations. In the first model, we consider a centrally managed two-echelon system with the installation closer to the customer being more capacity constrained. We determine that a modified echelon base-stock policy is optimal for both finite horizons and infinite horizons under the discounted-cost and average-cost criteria. In the second model, we relax the assumption of central ownership and control of the system and consider a decentralized version of the first model. Using a Markov Equilibrium solution concept we find the sustainable equilibrium policy is a version of the modified echelon base-stock policy. When his penalty cost is too low, however, we find the supplier stocks no goods and the retailer orders to the newsboy level. In numerical experiments we find the relative total costs are robust to a variety of values of the total unit penalty cost and the penalty division between players. This latter result is highly desirable since it implies that good solutions may be achieved through normal operation for a broad range of the penalty cost divisions, reducing the need for coordinating contracts, which may be unenforceable. We also find that a more constrained system can force the players to cooperate more, resulting in a solution closer to the first-best solution. In the third model, we consider the effect a flexible capacity resource possessed by a multi-market incumbent has upon the possibility of single-market entry deterrence. We find that in contrast to conventional Industrial Organization wisdom, possessing the flexible resource does not weaken the incumbent's credibility, but rather it may permit him to invest in less total capacity but still deter entry and act as a monopolist in both markets.