The rank pricing problem: Models and branch-and-cut algorithms

Calvete, H.I. (Universidad de Zaragoza) ; Domínguez, C. ; Galé, C. (Universidad de Zaragoza) ; Labbé, M. ; Marín, A.

Resumen: 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.

Idioma: Inglés

DOI: 10.1016/j.cor.2018.12.011

Año: 2019

Publicado en: Computers and Operations Research 105 (2019), 12-31
ISSN: 0305-0548

Factor impacto JCR: 3.424 (2019)

Categ. JCR: OPERATIONS RESEARCH & MANAGEMENT SCIENCE rank: 21 / 83 = 0.253 (2019) - Q2 - T1
Categ. JCR: COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS rank: 34 / 109 = 0.312 (2019) - Q2 - T1
Categ. JCR: ENGINEERING, INDUSTRIAL rank: 14 / 48 = 0.292 (2019) - Q2 - T1

Factor impacto SCIMAGO: 1.663 - Computer Science (miscellaneous) (Q1) - Modeling and Simulation (Q1) - Management Science and Operations Research (Q1)

Financiación: info:eu-repo/grantAgreement/ES/MINECO/ECO2016-76567-C4-3-R

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)