Offering Free Upgrades Even before Stocks Run Out: The Value of Proactive Upgrades

Abstract

Problem Definition: When selling multiple products with different feature combinations over a short selling season, a seller often adopts a reactive'' policy by offering a free to the next-price-level product only after'' a customer's preferred product is out of stock. However, when customer preference is heterogeneous for different feature combinations, some unyielding customers may reject free upgrades. In this paper, we consider a new proactive'' policy under which the seller may offer free upgrades ``even before'' a product is out of stock. Academic/Practical Relevance: The proactive policy enables the seller to strategically keep some units of a product in reserve to secure future sales of this product for those unyielding customers. However, the value of proactive policy over the traditional reactive policy remains unclear. Methodology: We use the Multinomial Logistic Model to determine the upgrade acceptance probability'' of each arriving customer, so that we can formulate the proactive policy problem as a finite horizon dynamic program with an embedded Markov Decision Process, and we determine the optimal proactive policy. Results: By exploiting the underlying mathematical structure, we prove that the optimal value function possesses the anti-multimodularity'' property so that the optimal strategy under the proactive policy is governed by two state-dependent thresholds: one threshold dictates when to offer proactive upgrades, and the other threshold dictates when to offer reactive upgrades. We also show that the proactive policy can create significant value over the reactive policy when the next-price-level product has similar consumer utility or when the price sensitivity is intermediate. Managerial Implications: We identify the conditions under which the proactive policy provides significant value over the traditional reactive policy. These results can be useful for sellers who sell variants of similar products with different feature combinations to customers with heterogeneous feature preference.