On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization

19 Pages Posted: 8 Jun 2016 Last revised: 8 Jul 2016

See all articles by Hakjin Chung

Hakjin Chung

College of Business, Korea Advanced Institute of Science and Technology (KAIST)

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business

Stefanus Jasin

University of Michigan, Stephen M. Ross School of Business

Date Written: June 6, 2016

Abstract

Motivated by the classic exogenous demand model and the recently developed Markov chain model, we propose a new approximation to the general customer choice model based on random utility called multi-attempt model, in which a customer may consider several substitutes before finally deciding to not purchase anything. We show that the approximation error of multi-attempt model decreases exponentially in the number of attempts. However, despite its strong theoretical performance, the empirical performance of multi-attempt model is not satisfactory. This motivates us to construct a modification of multi-attempt model called re-scaled multi-attempt model. We show that re-scaled 2-attempt model is exact when the underlying true choice model is Multinomial Logit (MNL); if, however, the underlying true choice model is not MNL, we show numerically that the approximation quality of re-scaled 2-attempt model is very close to that of Markov chain model. The key feature of our proposed approach is that the resulting approximate choice probability can be explicitly written. From a practical perspective, this allows the decision maker to use off-the-shelf solvers, or borrow existing algorithms from literature, to solve a general assortment optimization problem with a variety of real-world constraints.

Suggested Citation

Chung, Hakjin and Ahn, Hyun-Soo and Jasin, Stefanus, On (Re-Scaled) Multi-Attempt Approximation of Customer Choice Model and its Application to Assortment Optimization (June 6, 2016). Ross School of Business Paper No. 1322, Available at SSRN: https://ssrn.com/abstract=2791127 or http://dx.doi.org/10.2139/ssrn.2791127

Hakjin Chung

College of Business, Korea Advanced Institute of Science and Technology (KAIST) ( email )

85 Hoegiro Dongdaemun-Gu
Seoul 02455
Korea, Republic of (South Korea)

Hyun-Soo Ahn

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan St
R5456
Ann Arbor, MI 48109-1234
United States

Stefanus Jasin (Contact Author)

University of Michigan, Stephen M. Ross School of Business ( email )

701 Tappan Street
Ann Arbor, MI MI 48109
United States

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
91
Abstract Views
549
rank
316,608
PlumX Metrics