Title :

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

Author(s) :

Calvete, Herminia [Auteur]
Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
Domínguez, Concepción [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Université libre de Bruxelles [ULB]
Universidad de Murcia
Galé, Carmen [Auteur]
Universidad de Zaragoza = University of Zaragoza [Saragossa University] = Université de Saragosse
Labbé, Martine [Auteur]
Integrated Optimization with Complex Structure [INOCS]
Graphes et Optimisation Mathématique [Bruxelles] [GOM]
Marín, Alfredo [Auteur]
Departamento de Estadística e Investigación Operativa, Facultad de Matematicas

Journal title :

Computers and Operations Research

Pages :

12-31

Publisher :

Elsevier

Publication date :

2019-05-01

ISSN :

0305-0548

English keyword(s) :

Bilevel Programming
Rank Pricing Problem
Integer Programming
Set Packing
Pricing Problems

HAL domain(s) :

Mathématiques [math]/Combinatoire [math.CO]
Computer Science [cs]/Operations Research [math.OC]

English abstract : [en]

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. ...
Show more >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.Show less >

Language :

Anglais

Popular science :

Non

Collections :

• Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189

Source :

Harvested from HAL