Models and Algorithms for the Product Pricing with Single-Minded Customers Requesting Bundles

Víctor Bucarey (1, 2) , Sourour Elloumi (3, 4, 5) , Martine Labbé (1) , Fränk Plein (2)

1 GOM - Graphes et Optimisation Mathématique [Bruxelles]
2 INOCS - Integrated Optimization with Complex Structure
3 CEDRIC - Centre d'études et de recherche en informatique et communications
4 CEDRIC - OC - CEDRIC. Optimisation Combinatoire
5 OC - Optimisation et commande

We analyze a product pricing problem with single-minded customers, each interested in buying a bundle of products. The objective is to maximize the total revenue and we assume that supply is unlimited for all products. We contribute to a missing piece of literature by giving some mathematical formulations for this single-minded bundle pricing problem. We first present a mixed-integer nonlinear program with bilinear terms in the objective function and the constraints. By applying classical linearization techniques, we obtain two different mixed-integer linear programs. We then study the polyhedral structure of the linear formulations and obtain valid inequalities based on an RLT-like framework. We develop a Benders decomposition to project strong cuts from the tightest model onto the lighter models. We conclude this work with extensive numerical experiments to assess the quality of the mixed-integer linear formulations, as well as the performance of the cutting plane algorithms and the impact of the preprocessing on computation times.

Mots clés: Pricing Problems; Integer Programming Formulations; Benders Decomposition

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]

Víctor Bucarey, Sourour Elloumi, Martine Labbé, Fränk Plein. Models and Algorithms for the Product Pricing with Single-Minded Customers Requesting Bundles. Computers and Operations Research, 2020, ⟨10.1016/j.cor.2020.105139⟩. ⟨hal-02056763⟩