Consider an example when a retailer offers substitutable product, the customer is likely to choose and consume an alternative product with similar attributes or functionality, if such a product is available, rather than not purchase at all. This scenario occurs frequently in pharmaceutical markets: If a patient wishes to purchase a specific brand of medication that is not available, he or she might choose a different brand (or generic form) of the same type of medication, or select a different type of medication with a similar effect. The firm incurs substitution cost, when a customer is forced to suffice with a substitute for a desired product. Such costs can arise from the need to rework an item to make it substitutable for another, and from the loss of a customer's goodwill due to substitution, etc.
Notably, despite its clear practical importance, the influence of product substitution relationships on inventory management decisions has received little attention in the operations literature (see McGillivray and Silver 1978, Parlar and Goyal 1984, Noonan 1995, Parlar 1988, Wang and Parlar 1994, Rajaram and Tang 2001, Ernst and Kouvelis 1999). Herein, we seek to bridge this gap and propose a model of inventory management that takes these relationships into account, in terms of their effects on products' actual demand rate. This model incorporates a dependency factor, a variable that indicates the dependency between pairs of multiple substitutable products, and uses it to compute the products' future demand rate in the event that a specific related product should stock out. More specifically, the model, which is based on EOQ principles, comprises a five-step process in which, after identifying products that are substitutable for one another, the decision maker (probabilistically) computes the dependency factor for each pair of products. Then, our model uses this information to compute future demand and to generate a dynamic reorder point in the case of an unexpected stock out of a particular product.
The purchasing model we propose aims to assist inventory managers in dealing with the reality in which, even if the demand rate is purely constant—such that a standard EOQ model could presumably be easily applied—the supply side is highly complex and characterized by many uncertainties such as order delays, force majeure, disasters, quality issues, regulation and many others. In the presence of such circumstances, the use of a dynamic reorder point rather than a static one can enable the inventory manager to adapt to unforeseen circumstances and to replenish stock as needed and not even a day too late, regardless of the original ordering schedule—thereby decreasing the probability that a stock out of a given item will be followed by stock outs among substitutable items.
