An EOQ model for multiple products with varying degrees of substitutability

In this paper, the authors present an EOQ model with substitutions between products and a dynamic inventory replenishment policy. The key assumption is that many products in the market are substitutable at different levels, and that, in most cases, a customer who discovers that a desired product is unavailable will choose to consume a product with similar attributes or functionality, rather than not purchase at all. Therefore, given a firm that stocks multiple substitutable products, the authors assume that a stock out of one product has a direct impact on other products' demand. The main purpose of the model is to enable inventory managers to develop ordering policies that ensures that, in the event that a specific product runs out and cannot be replenished due to unforeseen circumstances, the consequent increase in demand for related products will not cause further stock out incidents. To this end, the authors introduce a dependency factor, a variable that indicates the level of dependency, or correlation, between one product and another. The dependencies among the various products offered by the firm are embedded into the EOQ formula and assumptions, enabling managers to update their ordering schedules as needed. This approach has the potential to generate more practical and realistic purchasing and inventory optimization policies.