Capacitated Assortment Optimization with Pricing under the Paired Combinatorial Logit Model

TL;DR

This paper addresses the complex problem of optimizing product assortments and pricing under capacity constraints using a paired combinatorial logit model, proposing novel algorithms and heuristics for better solutions.

Contribution

It introduces a new formulation for the assortment and pricing problem under the paired combinatorial logit model and develops algorithms to efficiently find high-quality solutions.

Findings

The proposed methods effectively solve the non-linear mixed integer program.

Heuristic algorithms balance solution quality and computational efficiency.

Numerical experiments demonstrate the approaches' effectiveness.

Abstract

In this paper, we investigate the capacitated assortment optimization problem with pricing under the paired combinatorial logit model, whose goal is to identify the revenue-maximizing subset of products as well as their selling prices subject to a known capacity limit. We model customers' purchase behavior using the paired combinatorial logit model, which allows for covariance among any pair of products. We formulate this problem as a non-linear mixed integer program. Then, we propose a two-step approach to obtain the optimal solution based on solving a mixed integer program and Lambert-W function. To further improve its performance, we design a greedy heuristic algorithm and a greedy randomized adaptive search procedure to obtain high-quality solutions so as to balance the tradeoff between accuracy and computational efficiency. A series of numerical experiments are conducted to gauge the efficiency and quality of our proposed approaches.