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

Víctor Bucarey 1, 2 Sourour Elloumi 3, 4 Martine Labbé 1 Fränk Plein 2
2 INOCS - Integrated Optimization with Complex Structure
ULB - Université Libre de Bruxelles [Bruxelles], Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : 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.
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Víctor Bucarey, Sourour Elloumi, Martine Labbé, Fränk Plein. Models and Algorithms for the Product Pricing with Single-Minded Customers Requesting Bundles. 2019. ⟨hal-02056763⟩

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