The Rank Pricing Problem: models and branch-and-cut algorithms - Archive ouverte HAL Access content directly
Journal Articles Computers and Operations Research Year : 2019

The Rank Pricing Problem: models and branch-and-cut algorithms


One of the main concerns in management and economic planning is to sell the right product to the right customer for the right price. Companies in retail and manufacturing employ pricing strategies to maximize their revenues. The Rank Pricing Problem considers a unit-demand model with unlimited supply and uniform budgets in which customers have a rank-buying behavior. Under these assumptions, the problem is first analyzed from the perspective of bilevel pricing models and formulated as a non linear bilevel program with multiple independent followers. We also present a direct non linear single level formulation bearing in mind the aim of the problem. Two different linearizations of the models are carried out and two families of valid inequalities are obtained which, embedded in the formulations by implementing a branch-and-cut algorithm, allow us to tighten the upper bound given by the linear relaxation of the models. We also study the polyhedral structure of the models, taking advantage of the fact that a subset of their constraints constitutes a special case of the Set Packing Problem, and characterize all the clique facets. Besides, we develop a preprocessing procedure to reduce the size of the instances. Finally, we show the efficiency of the formulations, the branch-and-cut algorithms and the preprocessing through extensive computational experiments.
Fichier principal
Vignette du fichier
RPP_dic_2018.pdf (555.34 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-01782958 , version 1 (02-05-2018)
hal-01782958 , version 2 (27-06-2018)
hal-01782958 , version 3 (03-12-2018)



Herminia Calvete, Concepción Domínguez, Carmen Galé, Martine Labbé, Alfredo Marín. The Rank Pricing Problem: models and branch-and-cut algorithms. Computers and Operations Research, 2019, 105, pp.12-31. ⟨10.1016/j.cor.2018.12.011⟩. ⟨hal-01782958v3⟩
328 View
222 Download



Gmail Facebook X LinkedIn More