Neutrosophic Discrete Facility Location Problems

Hajem Ati Daham

Department of Mathematics, College of Education for Pure Science, Al-Muthanna University, Iraq

Email: hajem.daham@mu.edu.iq

ORCID ID: https://orcid.org/0000-0001-9673-7100

Abstract

Discrete facility location problems are classified as types of facility location problems, wherein decisions on choosing facilities in specific locations are made to serve the demand points of customers, thus minimizing the total cost. The covering- and median-based problems are the common classified types of discrete facility location problems, which both comprise different classes of discrete problems as reviewed in this research. However, the discrete facility location problems shown in deterministic and known information and data under uncertain, vague, and ambiguous environments have usually been solved using intuitionistic fuzzy approaches. Neutrosophic is recently applied to tackle the uncertainty and ambiguity of information and data. This paper considered solving the discrete facility location problems under the neutrosophic environment, wherein the information of the locations, distances, times, and costs is uncertain. The mathematical models for the main types of neutrosophic discrete facility location problems, which remain unclear till now despite previous related works, are formulated in this study. Numerical examples demonstrated testing of the neutrosophic discrete models and comparison with the optimization solutions obtained from the normal situations. 

Keywords: Discrete Facility Problems; Neutrosophic Facility Problems; Neutrosophic Theory; Set Covering Facility Location Problems; Median Based Facility Location Problems