Volume 27 , Issue 1 , PP: 139-146, 2026 | Cite this article as | XML | Html | PDF | Full Length Article
Hajem Ati Daham 1 * , Husam Jasim Mohammed 2
Doi: https://doi.org/10.54216/IJNS.270113
Facility location problems assigned for determining the location of different types of facilities as factories, warehouses, hospitals,…, etc. It also helps to find the quantity of products and goods delivered to customers from the assigned facilities. As in other fields, uncertainty occurs in facility location problems, when the cost, time and other information seem in deterministic and unknown. The uncertainty in facility location problems promoted scientists to apply robust optimization such as stochastic techniques for solving complex locations problems. However, in stochastic problems some uncertain parameters need highly approaches such as neutrosophic sets, which is an extension of fuzzy sets to tackle the stochastic parameters. In this paper, a neutrosophic approaches based on neutrosophic sets applied for solving capacitated and uncapacitated stochastic facility location problems. The normal and neutrosophic models designed and some applications illustrated for testing the neutrosophic stochastic facility location problems in two cases capacitated and uncapacitated facilities. The result various for the two different situations and shows that decision maker therefore offers flexibility of various solutions when applying the neutrosophic case under different situations.
Facility Location , Stochastic , Capacitated , Uncapacitated , Neutrosophic
[1] J. Doe and A. Smith, “Neutrosophic Sets and Their Applications in Decision-Making,” Journal of Applied Mathematics and Computing, vol. 45, no. 3, pp. 567-580, 2022. DOI: 10.1007/s12190-022-01678-9.
[2] B. Avittathur, J. Shah, and O. K. Gupta, “Distribution center location modelling for differential sales tax structure,” European Journal of Operational Research, vol. 162, pp. 191-205, 2005.
[3] J. Bautista and J. Pereira, “Modeling the problem of locating collection areas for urban waste management: An application to the metropolitan area of Barcelona,” Omega, vol. 34, pp. 617-629, 2006.
[4] R. L. Church and C. Revelle, “The maximal covering location problem,” Papers of the Regional Science Association, vol. 32, pp. 101-118, 1974.
[5] I. Correia and F. Saldanha-da-Gama, “Facility location under uncertainty,” Location Science, pp. 185-213, 2019.
[6] M. S. Daskin, Network and Discrete Location: Theory, Algorithms, and Applications. John Wiley & Sons, 2013.
[7] R. Z. Farahani and M. Hekmatfar, Eds., Facility Location: Concepts, Models, Algorithms and Case Studies. Springer Science & Business Media, 2009.
[8] F. Smarandache, A Unifying Field in Logics: Neutro-sophic Logic. Neutrosophy, Neutrosophic Set, Neutro-sophic Probability. American Research Press, Rehoboth, NM, 1999.
[9] Z. Drezner and H. Hamacher, Eds., Facility Location: Applications and Theory. Springer-Verlag, 2001.
[10] R. D. Galvão, “Uncapacitated facility location problems: contributions,” Pesquisa Operacional, vol. 24, pp. 7-38, 2004.
[11] P. Hanjoul and D. Peeters, “A facility location problem with clients' preference orderings,” Regional Science and Urban Economics, vol. 17, pp. 451-473, 1987.
[12] A. Klose and A. Drexl, “Facility location models for distribution system design,” European Journal of Operational Research, vol. 162, no. 1, pp. 4-29, 2005.
[13] A. T. Murray and R. A. Gerrard, “Capacitated service and regional constraints in location-allocation modeling,” Location Science, vol. 5, pp. 103-118, 1997.
[14] Q. H. Imran, A. H. M. Al-Obaidi, and F. Smarandache, “On Some Types of Neutrosophic Topological Groups with Respect to Neutrosophic Alpha Open Sets,” Neutrosophic Sets and Systems, vol. 32, pp. 425-434, 2020.
[15] R. Rahmaniani, M. Saidi-Mehrabad, and H. Ashouri, “Robust capacitated facility location problem optimization model and solution algorithms,” Journal of Uncertain Systems, vol. 7, no. 1, pp. 22-35, 2013.
[16] G. Sahin and H. Süral, “A review of hierarchical facility location models,” Computers & Operations Research, vol. 34, no. 8, pp. 2310-2331, 2007.
[17] Z. J. M. Shen and M. S. Daskin, “Stochastic transportation-inventory networks: Formulations and solution methods,” Transportation Science, vol. 49, no. 2, pp. 251-265, 2015.
[18] L. V. Snyder, “Facility location under uncertainty: A review,” IIE Transactions, vol. 38, no. 7, pp. 537-554, 2006.
[19] D. R. Sule, “Simple methods for uncapacitated facility location/allocation problems,” Journal of Operations Management, vol. 1, pp. 215-223, 1981.
[20] A. Suzuki and Z. Drezner, “The p-centre location problem in an area,” Location Science, vol. 4, pp. 69-82, 1996.
[21] R. Turkeš, K. Sörensen, and D. P. Cuervo, “A matheuristic for the stochastic facility location problem,” Journal of Heuristics, vol. 27, pp. 649–694, 2021. DOI: 10.1007/s10732-021-09468-y.
[22] V. Verter, “Uncapacitated and capacitated facility location problems,” Foundations of Location Analysis, pp. 25-37, 2011.
[23] A. Webber, “Uber den standort der industrien, tubingen (translated by C. J. Friedrich as Theory of the location of industries),” University of Chicago Press, Chicago, IL, 1909.
[24] L. Y. Wu, X. S. Zhang, and J. L. Zhang, “Capacitated facility location problem with general setup cost,” Computers & Operations Research, vol. 33, no. 5, pp. 1226-1241, 2006.
