Optimal Pooling of Inventories with Substitution: A Literature Review

In many inventory management systems, some kind of substitution flexibility exists, meaning that a substitute or more flexible item can be used (at an additional cost) when the preferred product stocks out. Through the use of substitution flexibility, we can take advantage of the risk pooling effect on the flexible item. Since risk pooling reduces total inventory holding costs, a trade-off between inventory holding costs and flexibility costs will determine the optimal inventory control parameters for the different items. In this research paper, we focus on different types of inventory management systems with substitution flexibility, and discuss three methods suggested in the literature (i.e., newsvendor models, Monte Carlo simulation and continuoustime Markov chains) in order to optimally exploit substitution flexibility.