Pricing and Assortment Optimization under an MNL Model with Default Specific Consideration

Sajjad Najafi (), Zhiyuan Sun and Stefanus Jasin
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Sajjad Najafi: HEC Paris
Zhiyuan Sun: University of California, Los Angeles (UCLA); University of Michigan at Ann Arbor
Stefanus Jasin: University of Michigan, Stephen M. Ross School of Business

No 1548, HEC Research Papers Series from HEC Paris

Abstract: Problem definition: Customers tend to consider products that are familiar and comfortable to choose. This phenomenon is commonly referred to as the default effect, recognized among the most robust phenomena in economics and cognitive psychology. In this paper, we consider the Multinomial Logit (MNL) model with the so-called "Default Specific Consideration'' (DSC), one of the most widely studied classes of choice models in economics that captures the default effect, which we will simply label as the DSC model for brevity. The DSC model can be viewed as a two-stage choice model where, in the first stage, the customer only considers her default option, and purchases it if its utility dominates that of the no-purchase option. Otherwise, the customer may move on to the second stage, where she chooses from all the available products. Moreover, the DSC model accounts for customer heterogeneity, as different individuals may have different default products. We consider both the pure pricing and pure assortment problems under the DSC model. Methodology/results: In the pure pricing setting, we find that the renowned same-price (or same-markup) policy is no longer optimal. Interestingly, however, we show that a variant of this policy continues to hold, where non-default products admit the same-price (or same-markup) policy whereas, for the default products, their prices can all be different from each other. Finding the optimal policy is still computationally expensive as the set of default products can potentially be large and the expected revenue function is not well-behaved. Thus, we develop a polynomial-time approximation algorithm that provides a (1-\epsilon)-optimal solution. In the pure assortment setting, we show that the so-called revenue-ordered property no longer holds. However, there exists an optimal policy where the non-default products continue to follow the revenue-ordered property, while the default products may deviate from this property. This introduces a more intricate structure, allowing default products to be included even if they do not conform to the revenue-ordered principle. We design a different polynomial-time approximation algorithm that ensures a (1 - \epsilon)-optimal solution. Managerial implications: Our analysis shows that disregarding the default effect can result in highly sub-optimal pricing and assortment policies, highlighting the profound impact of default effects on operational decisions in retail. Incorporating the default effect, we show numerically that our proposed algorithm can significantly improve a retailer's expected total revenues.

Keywords: MNL; Model (search for similar items in EconPapers)
JEL-codes: C10 (search for similar items in EconPapers)
Pages: 49 pages
Date: 2025-02-24
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Persistent link: https://EconPapers.repec.org/RePEc:ebg:heccah:1548

DOI: 10.2139/ssrn.5111398

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