Title: Fuzzy facility location problem with point and rectangular destinations

Authors: Nemat Allah Taghi-Nezhad; Sadjad Moradi; Gholamreza Karamali

Addresses: Department of Mathematics, Faculty of Basic Science, Gonbad Kavous University, Gonbad Kavous, Iran ' Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran ' Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran

Abstract: Facility location problem with point and area destinations is a special kinds of location problems in which, some demand centres considered as areas. Based on our knowledge, this issue has not been addressed in fuzzy literature and we have tried to investigate this issue in fuzzy environment. For this purpose, all customer demands are considered as fuzzy numbers, and the distances between points and destinations are calculated by L₁ norm. To solve this fuzzy problem, three fuzzy theorems are proved which show that the objective function is separable, convex and piecewise continuous. Then, by using these fuzzy theorems, two fuzzy algorithms named fuzzy critical point algorithm and fuzzy weighting average algorithm are presented to obtain the best place for locating the facility centre. These two algorithms are based on piecewise differentiability of objective function and weighted average property, respectively. Finally, the applicability of our two presented algorithms is demonstrated by solving some numerical examples.

Keywords: fuzzy number; location problem; continues location problem; rectangular destinations; fuzzy weights.

DOI: 10.1504/IJMOR.2021.112288

International Journal of Mathematics in Operational Research, 2021 Vol.18 No.1, pp.21 - 44

Received: 08 May 2019
Accepted: 25 Jul 2019
Published online: 06 Jan 2021 *

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