Pricing Problems

Problem Description

Pricing problems refers to a class of combinatorial problems focused on the pricing of products from a certain company or institution. The pricing strategy is directly affected by the preferences and budgets from each customer.

These problems are mostly are NP-complete which requires the use of advanced heuristic or metaheuristic strategies to tackle real-world instances efficiently.

Industrial Context

Pricing is a crucial aspect for any institution which aims to maximize their own benefit. Optimal pricing can lead to huge improvement on products demand.

New pricing strategies could be meaningful for every company, but those based on multiple product versions business model could benefit the most.

Common Challenges

Within this family of problems, there are multiple variants:

• Rank Pricing Problems: The pricing strategy should take into account each customer’s preference list and budget, assuming an unlimited quantity of each product, with each customer purchasing at most one.
• Capacited Rank Pricing Problems: In this variant there is limited number of units for each product which affects the pricing strategy.
• Rank Pricing Problems with Ties: The preference list from each customer can have two different products on the same level, affecting the pricing strategy.

Solution Approaches

Given the computational complexity, various techniques are used to solve these problems:

• Exact Methods: Integer linear programming to solve small-sized instances.
• Heuristics and Metaheuristics: Most common methods. They include: Variable Neighborhood Search (VNS), population-based algorithms like genetic algorithms and Greedy Randomized Adaptive Search Procedure (GRASP).

References

1. Calvete, H.I., Domínguez, C., Galé, C, Labbé, M. & Marín, A. (2019). The rank pricing problem: Models and branch-and-cut algorithms. Computers & operations research.
2. Calvete, H.I., Galé, C., Hernández, A., Iranzo, J.A. (2024). An evolutionary algorithm for the rank pricing problemMetaheuristics International Conference.
3. Jiménez-Cordero, A., Pineda, S., Morales, J.M. (2025). An enhanced heuristic framework for solving the rank pricing problem. Expert Systems with Applications
4. Fauste-Jiménez, R., Salazar, S., Lozano-Osorio, I., & Sánchez-Oro, J. (2025). GRASP para el problema de fijación de precios basado en preferencias. XVI Congreso Español de Metaheurísticas, Algoritmos Evolutivos y Bioinspirados.

Acknowledgments

This summary was prepared by the RedHEUR4.0 network as part of its contribution to the digital transformation of the transportation and logistics sectors, supported by the Spanish Ministry of Science and Innovation.