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A key challenge in supply chain management is to match supply and demand of various products. In dealing with this challenge, substitution is a useful option of recourse for managing product inventories: when the demand for a certain type of product exceeds its supply, use another product type, often one of a higher grade in terms of quality or functionality, as a substitute to supply the demand, at the demanded product’s price. For instance, semiconductor manufacturers may use higher-performance integrated circuits to satisfy the demand for lower-end circuits if the latter are out of stock, and hotels may upgrade a customer’s booking from a standard room to a luxury room. This type of substitution is usually referred to as “firm-driven”. 

Conversely, “customer-driven” substitution occurs when the customer is unable to purchase a desired product, but instead chooses an alternative product (at a nominal price) as a substitute, which might be of higher, lower, or similar value. For instance, a customer may purchase a business class ticket at a higher price if all other seats are unavailable when booking.

Previous studies have examined either supplier-driven substitution or customer-driven substitution. The study by He Xu, David D. Yao, and Shaohui Zheng explains that substitution can include both of the aforementioned schemes simultaneously. For example, if a product is out of stock, a salesperson may offer a discount on a different product, in the purpose of inducing the customer to accept a substitution. This may or may not be accepted by the customer, based on the size of the discount.

To address this interactive form of substitution, the researchers looked at how substitution is tied together with pricing decisions, and how much of a discount (if any) should be offered. More specifically, they explained “when a higher-grade product is offered as a substitute, it may very well be offered at a discount, but not necessarily at the same price as the lower-grade product”. In essence, there is a probability of a customer accepting a substitution along with a discount, which is a decreasing function of the price offered.