Selected Journal Publications


Buying and Selling: The Effects of Product Substitution

Production and Operations Management, Vol. 25, No. 6, June 2016, pp.1088–1105
XU, He | YAO, David D. | ZHENG, Shaohui
Optimal Policies for a Two-Product Inventory System under a Flexible Substitution Scheme

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.

The author’s more generalised model used a two-product inventory that allows for substitution with a one-time replenishment opportunity at the beginning of the season.

“Our work here treats offering different discount prices as a part of the substitution decision while assuming the nominal prices as given, and considers a more general substitution scheme”, the authors explain.

Overall, using a two-substitutable system, the authors were able to show that “the objective function is concave and submodular in the inventory levels”. They were also able to help identify threshold policies for the optimal solution / pricing decision. While their findings do not extend to multiple products, the authors are encouraged that heuristic policies can be developed based on their structural results.


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