International Journal of Neutrosophic Science

Journal DOI

https://doi.org/10.54216/IJNS

2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 19 , Issue 1 , PP: 29-47, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Neutrosophic Discrete Facility Location Problems

Hajem Ati Daham 1 *

• 1 Department of Mathematics, College of Education for Pure Science, Al-Muthanna University, Iraq - (hajem.daham@mu.edu.iq)
• Doi: https://doi.org/10.54216/IJNS.190102

Received: March 02, 2022 Accepted: August 18, 2022
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

References

[1] A. Salama and F.Smarandache. Neutrosophic Crisp Set Theory, 2015, Education Publishing, Columbus.

[2] Abedallah Zaid Abualkishik , Ali A. Alwan, Multi-objective Chaotic Butterfly Optimization with Deep Neural Network based Sustainable Healthcare Management Systems, American Journal of Business and Operations Research, Vol. 4 , No. 2 , (2021) : 39-48

[3] Avittathur, B., Shah, J. & Gupta, O. K. Distribution center location modeling for differential sales tax structure. European Journal of Operational Research, 162, 191-205, 2005.

[4] Bautista, J. & Pereira, J. Modeling the problem of locating collection areas for urban waste management. An application to the metropolitan area of Barcelona. Omega, 34, 617-629, 2006.

[5] Bhattacharya, U., Rao, J., And Tiwari, R. Fuzzy multi-criteria facility location problem. Fuzzy Sets and Systems 51, 3, 277–287. 1992.

[6] Bhattacharya, U., Rao, J., And Tiwari, R. Bi-criteria multi-facility location problem in fuzzy environment. Fuzzy Sets and Systems 56, 2, 145–153, 1993.

[7] Church, R. L. & Revelle, C.. The maximal covering location problem. Papers of the Regional Science Association, 32 101-118. CHYR, F., MING LIN, T. & HO, C. 1990. An extension of the EOQ production model based on damage costs. Emerald Backfiles, 71-76, 1974.

[8] Daskin, M.S., Snyder, L.V. and Berger, R.T.. Facility location in supply chain design. In Logistics systems: Design and optimization (pp. 39-65). Springer, Boston, MA. , 2005

[9] Daskin, M. S. What you should know about location modeling. Naval Research Logistics, 55, 283-294, 2008.

[10] Florentin Smarandache , Said Broumi, Neutro-Intelligent Set is a particular case of the Refined Neutrosophic Set, Journal of Neutrosophic and Fuzzy Systems 1, 1: 34-36, 2021 (Doi:  https://doi.org/10.54216/JNFS.010103)

[11] Katy D. Ahmad , Mikail Bal , Arwa A. Hajjari , Rozina Ali, Novel Applications Of Neutrosophic AH-Isometries To The Group Of Units Problem In Neutrosophic Rings and Refined Neutrosophic Rings, Journal of Neutrosophic and Fuzzy Systems, 1, 2: 89-98, 2021 (Doi   :  https://doi.org/10.54216/JNFS.010205)

[12] Farahani, R.Z. and Hekmatfar, M. eds., 2009. Facility location: concepts, models, algorithms, and case studies. Springer Science & Business Media.

[13] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. American Research Press, Reho-both, NM, (1999).

[14] F.Smarandache(T, I, F)-Neutrosophic Structures, University of New Mexico, 705 Gurley Ave., Gallup, NM 87301, USA.

[15] Facility Location: Applications and Theory. Edited by Z. Drezner and Hamacher, 2001 Springer-Verlag, ISBN 3-540-42172-6.

[16] Florentin Smarandache, An introduction to the Neutrosophy probability applied in Quantum Physics, International Conference on introduction Neutro-soph Physics, Neutrosophic Logic, Set, Probability, and Statistics, University of New Mexico, Gallup, NM 87301, USA2-4 December (2011).

[17] Hanjoul, P. & Peeters, D. A facility location problem with client's preference orderings. Regional Science and Urban Economics, 17, 451-473, 1987.

[18] I. Hanafy, A.A. Salama and K. Mahfouz, Correlation of neutrosophic Data, International Refereed Journal of Engineering and Science (IRJES), Vol. (1), Issue 2, (2012), pp. 39-43.

[19] International Journal of Applied Operational Research Vol. 9, No. 1, pp. 1-9, Winter 2019 Journal homepage: ijorlu.liau.ac.ir.

[20] Jia, H., Ordóñez, F. & Dessouky, M. M. Solution approach for facility location of medical supplies for large-scale emergencies. Computers & Industrial Engineering, 52, 257-276, 2007.

[21] Kawther F. Alhasan , A.A. Salama , Florentin Smarandache, Introduction to Neutrosophic Reliability Theory, International Journal of Neutrosophic Science, 15, 1: 52-61, 2021(Doi   :  https://doi.org/10.54216/IJNS.150105)

[22] M. Rezaei, M. H. F. Zarandi, Facility location via fuzzy modeling and simulation, Appl. Soft Comput., 11,2011, https://doi.org/10.1016/j.asoc.2011.05.026

[23] M. Wen, K. Iwamura, Facility location-allocation problem in random fuzzy environment: Using(α, β) -cost minimization model under the Hurewicz criterion, Comput. Math. Appl., 55, 704–713, 2008. https://doi.org/10.1016/j.camwa.2007.03.026

[24] Murray, A. T. & Gerrard, R. A. Capacitated service and regional constraints in location-allocation modeling. Location Science, 5, 103-118, 1997.

[25] Mai Mohamed, Abdel Nasser H Zaied and Florentin Smarandache , Neutrosophic Integer Programming Problem Neutrosophic Sets and Systems, Vol. 15, 2017.

[26] Sundus Naji AL-Aziz , Reem Atassi , Abd Al-Aziz Hosni El-Bagoury, Hybridization of Neutrosophic Logic with Quasi-Oppositional Chimp Optimization based Data Classification Model, International Journal of Neutrosophic Science, Vol. 18 , No. 3: 125-134, 2022 (Doi   :  https://doi.org/10.54216/IJNS.1803011)

[27] Nivetha Martin , Florentin Smarandache , broumi said, COVID-19 Decision-Making Model using Extended Plithogenic Hypersoft Sets with Dual Dominant Attributes, International Journal of Neutrosophic Science, Vol. 13 , No.2: 75-86, 2021 (Doi   :  https://doi.org/10.54216/IJNS.130204)

[28] Florentin Smarandache, Surapati Pramanik (Editors), New Trends in Neutrosophic Theory, Pons Editions Brussels, Belgium, EU, 2016

[29] Irina V. Pustokhina, Blockchain technology in the international supply chains, International Journal of Wireless and Ad Hoc Communication, Vol. 1, No. 1: 16-25, 2020

[30] Shen, Z. J. A profit-maximizing supply chain network design model with demand choice flexibility. Operations Research Letters, 34, 673-673-682, 2006.

[31] Shen, Z. J., Coullard, C. & DASKIN, M. S. 2003. Joint location inventory model. Transportation Science.

[32] Smarandache, F, (2014). Introduction to neutrosophic statistics. Infinite Study.

[33] Sourirajan, K., Ozsen, L. & Uzsoy, R. A single product network design model with lead time and safety stock considerations. IIE Transactions, 39, 411-424, 2007.

[34] Sule, D. R. Simple methods for uncapacitated facility location/allocation problems. Journal of Operations Management, 1, 215-223, 1981.

[35] Suzuki, A. & Drezner, Z. The p-center location problem in an area. Location Science, 4, 69-82, 1996.

[36] S. M. Wang, J. Watada, W. Pedrycz, Value-at-risk based two-stage fuzzy facility location problems, IEEE T. Ind. Inform., 5, 465–482, 2009. https://doi.org/10.1109/TII.2009.2022542

[37] S. Y. Choua, Y. H. Changa, C. Y. Shen, A fuzzy simple additive weighting system under group decision-making for facility location selection with objective/subjective attributes, European Journal of Operational Research, 189, 132–145, 2008,. https://doi.org/10.1016/j.ejor.2007.05.006

[38] Mustafa El-Taie , Aaras Y.Kraidi, Optimized Resource Allocation Algorithm for Crowd-Creation Space Computing Based on Cloud Computing Environment, Journal of Intelligent Systems and Internet of Things, Vol. 4, No. 1: 08-25, 2021

[39] WEBBER, A. 1909. Uber den standort der industrien, tubingen (translated by CJ, Friedrich as Theory of the location of industries), Chicago, IL, University of Chicago Press.

[40] Z. M. Liu, S. J. Qu, Z. Wu, Y. Ji, Two-stage fuzzy mixed integer optimization model for three-level location-allocation problems under uncertain environment, J. Intell. Fuzzy Syst., 39, 6741–6756, 2020. https://doi.org/10.3233/JIFS-191453