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Article

Facilities Delocation in the Retail Sector: A Mixed 0-1 Nonlinear Optimization Model and Its Linear Reformulation

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Departamento de Ciencias de la Computación, Arquitectura de Computadores, Lenguajes y Sistemas Informáticos y Estadística e Investigación Operativa, Universidad Rey Juan Carlos, 28933 Madrid, Spain
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Departamento de Estadística e Investigación Operativa, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain
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Independent Researcher, 28935 Madrid, Spain
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Author to whom correspondence should be addressed.
Mathematics 2020, 8(11), 1986; https://doi.org/10.3390/math8111986
Received: 1 October 2020 / Revised: 30 October 2020 / Accepted: 2 November 2020 / Published: 7 November 2020
(This article belongs to the Section Mathematics and Computer Science)
The problem concerning facilities delocation in the retail sector is addressed in this paper by proposing a novel mixed 0-1 linear optimization model. For this purpose, the aim of the problem is to decide whether to close existing stores or consider an alternative type of store management policy aimed at optimizing the profit of the entire retail network. Each management policy has a different repercussion on the final profit of the stores due to the different margins obtained from the customers. Furthermore, closing stores can cause customers to leave the whole retail network according to their behavior. This behavior is brought about through their tendency to abandon this network. There are capacity constraints imposed depending on the number of stores that should stay open and cease operation costs, customer behavior and final prices. These constraints depend on the type of management policy implemented by the store. Due to the commercial requirements concerning customer behavior, a set of non-linear constraints appears in the definition of the model. Classical Fortet inequalities are used in order to linearize the constraints and, therefore, obtain a mixed 0-1 linear optimization model. As a result of the size of the network, border constraints have been imposed to obtain results in a reasonable computing time. The model implementation is done by introducing smart sets of indices to reduce the number of constraints and variables. Finally, the computational results are presented using data from a real-world case study and, additionally, a set of computational experiments using data randomly generated as shown. View Full-Text
Keywords: facilities delocation; retail network restructuring; mixed 0-1 nonlinear optimization; mixed 0-1 linear optimization; linearization facilities delocation; retail network restructuring; mixed 0-1 nonlinear optimization; mixed 0-1 linear optimization; linearization
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MDPI and ACS Style

Sierra-Paradinas, M.; Alonso-Ayuso, A.; Martín-Campo, F.J.; Rodríguez-Calo, F.; Lasso, E. Facilities Delocation in the Retail Sector: A Mixed 0-1 Nonlinear Optimization Model and Its Linear Reformulation. Mathematics 2020, 8, 1986. https://doi.org/10.3390/math8111986

AMA Style

Sierra-Paradinas M, Alonso-Ayuso A, Martín-Campo FJ, Rodríguez-Calo F, Lasso E. Facilities Delocation in the Retail Sector: A Mixed 0-1 Nonlinear Optimization Model and Its Linear Reformulation. Mathematics. 2020; 8(11):1986. https://doi.org/10.3390/math8111986

Chicago/Turabian Style

Sierra-Paradinas, María, Antonio Alonso-Ayuso, Francisco Javier Martín-Campo, Francisco Rodríguez-Calo, and Enrique Lasso. 2020. "Facilities Delocation in the Retail Sector: A Mixed 0-1 Nonlinear Optimization Model and Its Linear Reformulation" Mathematics 8, no. 11: 1986. https://doi.org/10.3390/math8111986

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