An Algorithm for Assortment Optimization Under Parametric Discrete Choice Models

37 Pages Posted: 8 May 2019

See all articles by Tien Mai

Tien Mai

Singapore-MIT Alliance for Research and Technology

Andrea Lodi

Polytechnic School of Montreal

Date Written: April 12, 2019

Abstract

This work concerns the assortment optimization problem that refers to selecting a subset of items that maximizes the expected revenue in the presence of the substitution behavior of consumers specified by a parametric choice model. The key challenge lies in the computational difficulty of finding the best subset solution, which often requires exhaustive search. The literature on constrained assortment optimization lacks a practically efficient method which that is general to deal with different types of parametric choice models (e.g., the multinomial logit, mixed logit or general multivariate extreme value models). In this paper, we propose a new approach that allows to address this issue. The idea is that, under a general parametric choice model, we formulate the problem into a binary nonlinear programming model, and use an iterative algorithm to find a binary solution. At each iteration, we propose a way to approximate the objective (expected revenue) by a linear function, and a polynomial-time algorithm to find a candidate solution using this approximate function. We also develop a greedy local search algorithm to further improve the solutions. We test our algorithm on instances of different sizes under various parametric choice model structures and show that our algorithm dominates existing exact and heuristic approaches in the literature, in terms of solution quality and computing cost.

Keywords: parametric choice model, multinomial logit, mixed multinomial logit, multivariate extreme value, assortment optimization, binary trust region, greedy local search

Suggested Citation

Mai, Tien and Lodi, Andrea, An Algorithm for Assortment Optimization Under Parametric Discrete Choice Models (April 12, 2019). Available at SSRN: https://ssrn.com/abstract=3370776 or http://dx.doi.org/10.2139/ssrn.3370776

Tien Mai (Contact Author)

Singapore-MIT Alliance for Research and Technology ( email )

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Singapore
Singapore

Andrea Lodi

Polytechnic School of Montreal ( email )

P.O. Box 6079, Downtown Station
Montreal H3C 3A7, Quebec
United States

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