A revised weighted fuzzy c-means and Nelder-Mead algorithm for probabilistic demand and customer positions

Bayturk E., Esnaf S., KÜÇÜKDENİZ T.

JOURNAL OF INTELLIGENT & FUZZY SYSTEMS, vol.42, no.1, pp.465-475, 2022 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 1
  • Publication Date: 2022
  • Doi Number: 10.3233/jifs-219204
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Applied Science & Technology Source, Business Source Elite, Business Source Premier, Communication Abstracts, Compendex, Computer & Applied Sciences, INSPEC, Metadex, zbMATH, Civil Engineering Abstracts
  • Page Numbers: pp.465-475
  • Keywords: Multi-facility location problem, Nelder-Mead, probabilistic fuzzy c-means, probabilistic demand and position, LOCATION-ALLOCATION PROBLEM, SIMPLEX-METHOD, WEBER PROBLEM, FACILITY
  • Istanbul University Affiliated: Yes


Facility location selection is a vital decision for companies that affects both cost and delivery time over the years. However, determination of the facility location is a NP-hard problem. A hybrid algorithm that combines revised weighted fuzzy c-means with Nelder Mead (RWFCM-NM) performs well when compared with well-known algorithms for the facility location problem (FLP) with deterministic customer demands and positions. The motivation of the study is both analyzing performance of the RWFCM-NM algorithm with probabilistic customer demands and positions and proposing a new approach for this problem. This paper develops two new algorithms for FLP when customer demands and positions are probabilistic. The proposed algorithms are a probabilistic fuzzy c-means algorithm and Nelder-Mead (Probabilistic FCM-NM), a probabilistic revised weighted fuzzy c-means algorithm and Nelder Mead (Probabilistic RWFCM-NM) for the un-capacitated planar multi-facility location problem when customer positions and customer demands are probabilistic with predetermined service level. Proposed algorithms performances were tested with 13 data sets and comparisons were made with four well known algorithms. According to the experimental results, probabilistic RWFCM-NM algorithm demonstrates superiority on compared algorithms in terms of total transportation costs.