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

Author

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  • María Sierra-Paradinas

    (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)

  • Antonio Alonso-Ayuso

    (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)

  • Francisco Javier Martín-Campo

    (Departamento de Estadística e Investigación Operativa, Instituto de Matemática Interdisciplinar, Universidad Complutense de Madrid, 28040 Madrid, Spain)

  • Francisco Rodríguez-Calo

    (Independent Researcher, 28935 Madrid, Spain)

  • Enrique Lasso

    (Independent Researcher, 28935 Madrid, Spain)

Abstract

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.

Suggested Citation

  • María Sierra-Paradinas & Antonio Alonso-Ayuso & Francisco Javier Martín-Campo & Francisco Rodríguez-Calo & Enrique Lasso, 2020. "Facilities Delocation in the Retail Sector: A Mixed 0-1 Nonlinear Optimization Model and Its Linear Reformulation," Mathematics, MDPI, vol. 8(11), pages 1-19, November.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:11:p:1986-:d:441405
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    References listed on IDEAS

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