An enhanced heuristic framework for solving the Rank Pricing Problem

TL;DR

This paper introduces a novel heuristic framework combining Variable Neighborhood Search, genetic algorithms, and local searches to efficiently solve the complex Rank Pricing Problem, outperforming traditional exact methods in solution quality and computational efficiency.

Contribution

The paper presents a new heuristic approach for RPP that leverages problem structure and combines multiple algorithms for improved solutions without optimality guarantees.

Findings

Outperforms mixed integer programming in solution quality

Reduces computational burden compared to exact methods

Effective in obtaining high-quality solutions for RPP

Abstract

The Rank Pricing Problem (RPP) is a challenging bilevel optimization problem with binary variables whose objective is to determine the optimal pricing strategy for a set of products to maximize the total benefit, given that customer preferences influence the price for each product. Traditional methods for solving RPP are based on exact approaches which may be computationally expensive. In contrast, this paper presents a novel heuristic approach that takes advantage of the structure of the problem to obtain good solutions. The proposed approach consists of two phases. Firstly, a standard heuristic is applied to get a pricing strategy. In our case, we choose to use the Variable Neighborhood Search (VNS), and the genetic algorithm. Both methodologies are very popular for their effectiveness in solving combinatorial optimization problems. The solution obtained after running these algorithms is improved in a second phase, where four different local searches are applied. Such local searches use the information of the RPP to get better solutions, that is, there is no need to solve new optimization problems. Even though our methodology does not have optimality guarantees, our computational experiments show that it outperforms Mixed Integer Program solvers regarding solution quality and computational burden.