Product commonality in multiple-period, make-to-stock systems

It is well known that replacing several products by a single common product can reduce required safety stock levels due to the benefits of risk pooling. Recent research utilizing single-period models has investigated the cost savings (or losses) from doing so. This paper uses a very general multiple-period model, with general demand distributions, any number of products, and the objective of minimizing production, holding, and shortage costs. Two scenarios are considered – one that utilizes a common product and one that does not. Prior results utilizing single-period models indicate that even if the common product is more expensive than the products it replaces, there are many circumstances under which it is still worthwhile to employ. Surprisingly, this paper will show that this is almost never the case in a multiple-period model.