Comparative Analysis of Optimization Methods for Grey Fuzzy Transportation Problems in Logistics

Karagül, Kenan

doi:https://doi.org/10.17093/alphanumeric.1503643

Comparative Analysis of Optimization Methods for Grey Fuzzy Transportation Problems in Logistics

Kenan Karagül, Ph.D.

Abstract

This study examines the Grey Fuzzy Transportation Problem, which represents decision-making processes under uncertainty in the transportation problem, a significant issue in the logistics sector and academic studies. The study provides comprehensive analysis and recommendations that contribute to the effective solution of the Grey Fuzzy Transportation Problem and better management of uncertain transportation problems. The research compares four different optimization methods, Closed Path Method, Interval Optimization, Robust Optimization, and Interval Optimization with Penalty Function, for the Grey Fuzzy Transportation Problem (GFTP). The analyses were conducted on a total of 40 test problems across four different problem sizes: small, medium, large, and extra-large. The results showed that the Interval Optimization and Robust Optimization methods demonstrated the best performance in terms of solution quality and computation time. Specifically, detailed analyses of the Interval Optimization with Penalty Function method confirmed that this method provides an effective and consistent solution approach for the GFTP.

Keywords: Grey Fuzzy Linear Programming, JuMP, Julia, SCIP, Transportation Problem

Jel Classification: C61, C63, C65

Suggested citation

Karagül, K. (2024). Comparative Analysis of Optimization Methods for Grey Fuzzy Transportation Problems in Logistics. Alphanumeric Journal, 12(3), 169-194. https://doi.org/10.17093/alphanumeric.1503643

bibtex

References

Aydemir, E. (2020). A New Approach for Interval Grey Numbers: n-th Order Degree of Greyness. The Journal of Grey System, 32(2), 89–103.
Aydemir, E., Sahin, Y., & Karagul, K. (2023). A Cost Level Analysis for the Components of the Smartphones Using Greyness Based Quality Function Deployment. In Emerging Studies and Applications of Grey Systems (pp.313–330). Springer Nature Singapore. https://doi.org/10.1007/978-981-19-3424-7\_12
Aydemir, E., Yılmaz, G., & Oruc, K. O. (2020). A grey production planning model on a ready-mixed concrete plant. Engineering Optimization, 52(5), 817–831. https://doi.org/10.1080/0305215x.2019.1698034
Bai, C., & Sarkis, J. (2010). Integrating sustainability into supplier selection with grey system and rough set methodologies. International Journal of Production Economics, 124(1), 252–264. https://doi.org/10.1016/j.ijpe.2009.11.023
Baidya, A. (2024). Application of grey number to solve multi-stage supply chain networking model. International Journal of Logistics Systems and Management, 47(4), 494–518. https://doi.org/10.1504/ijlsm.2024.138873
Ben-Tal, A., & Nemirovski, A. (1998). Robust Convex Optimization. Mathematics of Operations Research, 23(4), 769–805. https://doi.org/10.1287/moor.23.4.769
Ben-Tal, A., & Nemirovski, A. (2002). Robust optimization ? methodology and applications. Mathematical Programming, 92(3), 453–480. https://doi.org/10.1007/s101070100286
Bilişik, Ö. N., Duman, N. H., & Taş, E. (2024). A novel interval-valued intuitionistic fuzzy CRITIC-TOPSIS methodology: An application for transportation mode selection problem for a glass production company. Expert Systems with Applications, 235, 121134. https://doi.org/10.1016/j.eswa.2023.121134
Christopher, M. (1992). Logistics and supply chain management. Pitman Publishing.
Deng, J.-L. (1982). Control problems of grey systems. Systems & Control Letters, 1(5), 288–294. https://doi.org/10.1016/S0167-6911(82)80025-X
Fu, C., & Cao, L. (2019). An uncertain optimization method based on interval differential evolution and adaptive subinterval decomposition analysis. Advances in Engineering Software, 134, 1–9. https://doi.org/10.1016/j.advengsoft.2019.05.001
Fu, L., Sun, D., & Rilett, L. (2006). Heuristic shortest path algorithms for transportation applications: State of the art. Computers & Operations Research, 33(11), 3324–3343. https://doi.org/10.1016/j.cor.2005.03.027
Gass, S. I., & Assad, A. A. (2005). An Annotated Timeline of Operations Research. Kluwer Academic Publishers.
Ghosh, S., Küfer, K.-H., Roy, S. K., & Weber, G.-W. (2022). Type-2 zigzag uncertain multi-objective fixed-charge solid transportation problem: time window vs. preservation technology. Central European Journal of Operations Research, 31(1), 337–362. https://doi.org/10.1007/s10100-022-00811-7
Guerra, M. L., Sorini, L., & Stefanini, L. (2017). A new approach to linear programming with interval costs. 2017 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), 1–6. https://doi.org/10.1109/fuzz-ieee.2017.8015661
Hitchcock, F. L. (1941). The Distribution of a Product from Several Sources to Numerous Localities. Journal of Mathematics and Physics, 20(1–4), 224–230. https://doi.org/10.1002/sapm1941201224
Jayswal, A., Preeti, & Arana-Jiménez, M. (2022). Robust penalty function method for an uncertain multi-time control optimization problems. Journal of Mathematical Analysis and Applications, 505(1), 125453. https://doi.org/10.1016/j.jmaa.2021.125453
Kacher, Y., & Singh, P. (2023). A generalized parametric approach for solving different fuzzy parameter based multi-objective transportation problem. Soft Computing, 28(4), 3187–3206. https://doi.org/10.1007/s00500-023-09277-4
Karmakar, S., & Bhunia, A. K. (2014). Uncertain constrained optimization by interval-oriented algorithm. Journal of the Operational Research Society, 65(1), 73–87. https://doi.org/10.1057/jors.2012.151
Klir, G. J., & Yuan, B. (1995). Fuzzy sets and fuzzy logic: theory and applications. Prentice Hall.
Kumar, A., Singh, P., & Kacher, Y. (2023). Neutrosophic hyperbolic programming strategy for uncertain multi-objective transportation problem. Applied Soft Computing, 149, 110949. https://doi.org/10.1016/j.asoc.2023.110949
Li, F.-C., & Jin, C.-X. (2008). Study on fuzzy optimization methods based on principal operation and inequity degree. Computers & Mathematics with Applications, 56(6), 1545–1555. https://doi.org/10.1016/j.camwa.2008.02.042
Liu, S., & Lin, Y. (2006). Grey Information Theory and Practical Applications. Springer-Verlag. https://doi.org/10.1007/1-84628-342-6
Mardanya, D., & Roy, S. K. (2023). New approach to solve fuzzy multi-objective multi-item solid transportation problem. RAIRO - Operations Research, 57(1), 99–120. https://doi.org/10.1051/ro/2022211
Moore, R. E., Kearfott, R. B., & Cloud, M. J. (2009). Introduction to Interval Analysis. Society for Industrial, Applied Mathematics. https://doi.org/10.1137/1.9780898717716
Moslem, S., Saraji, M. K., Mardani, A., Alkharabsheh, A., Duleba, S., & Esztergar-Kiss, D. (2023b). A Systematic Review of Analytic Hierarchy Process Applications to Solve Transportation Problems: From 2003 to 2022. IEEE Access, 11, 11973–11990. https://doi.org/10.1109/access.2023.3234298
Moslem, S., Stević, Ž., Tanackov, I., & Pilla, F. (2023a). Sustainable development solutions of public transportation:An integrated IMF SWARA and Fuzzy Bonferroni operator. Sustainable Cities and Society, 93, 104530. https://doi.org/10.1016/j.scs.2023.104530
Nasseri, H., & Khabiri, B. a. (2019). A Grey Transportation Problem in Fuzzy Environment. Journal of Operational Research and Its Applications, 16(3). http://jamlu.liau.ac.ir/article-1-1371-en.html
Pourofoghi, F., Saffar Ardabili, J., & Darvishi Salokolaei, D. (2019). A New Approach for Finding an Optimal Solution for Grey Transportation Problem. International Journal of Nonlinear Analysis and Applications, 10(Special Issue (Nonlinear Analysis in Engineering and Sciences). https://doi.org/10.22075/ijnaa.2019.4399
Simon, H. A. (1960). The new science of management decision. Harper & Brothers. https://doi.org/10.1037/13978-000
Steuer, R. E. (1981). Algorithms for Linear Programming Problems with Interval Objective Function Coefficients. Mathematics of Operations Research, 6(3), 333–348. https://doi.org/10.1287/moor.6.3.333
Taylor, F. W. (1911). The Principles of Scientific Management. Harper & Brothers.
Teodorović, D. (1999). Fuzzy logic systems for transportation engineering: the state of the art. Transportation Research Part A: Policy and Practice, 33(5), 337–364. https://doi.org/10.1016/s0965-8564(98)00024-x
Tokat, S., Karagul, K., Sahin, Y., & Aydemir, E. (2022). Fuzzy c-means clustering-based key performance indicator design for warehouse loading operations. Journal of King Saud University - Computer and Information Sciences, 34(8), 6377–6384. https://doi.org/10.1016/j.jksuci.2021.08.003
Voskoglou, M. G. (2018). Solving Linear Programming Problems with Grey Data. Oriental Journal of Physical Sciences, 3(1), 17–23. https://doi.org/10.13005/OJPS03.01.04
Yu, Q., Yang, C., Dai, G., Peng, L., & Li, J. (2024). A novel penalty function-based interval constrained multi-objective optimization algorithm for uncertain problems. Swarm and Evolutionary Computation, 88, 101584. https://doi.org/10.1016/j.swevo.2024.101584
Zadeh, L. (1965). Fuzzy sets. Information and Control, 8(3), 338–353. https://doi.org/10.1016/s0019-9958(65)90241-x
Zhang, H., Huang, Q., Ma, L., & Zhang, Z. (2024). Sparrow search algorithm with adaptive t distribution for multi-objective low-carbon multimodal transportation planning problem with fuzzy demand and fuzzy time. Expert Systems with Applications, 238, 122042. https://doi.org/10.1016/j.eswa.2023.122042
Zimmermann, H.-J. (1996). Fuzzy Set Theory–and Its Applications. Springer Netherlands. https://doi.org/10.1007/978-94-015-8702-0
Çelikbilek, Y., Moslem, S., & Duleba, S. (2022). A combined grey multi criteria decision making model to evaluate public transportation systems. Evolving Systems, 14(1), 1–15. https://doi.org/10.1007/s12530-021-09414-0
Şahin, Y., & Karagül, K. (2023). Gri ilişkisel analiz tekniğiyle taşımacılık firması için treyler çekici araç seçimi. In S. Karaoğlan & T. Arar (Eds.), Yönetim, Pazarlama ve Finans Uygulamalarıyla Çok Kriterli Karar Verme (pp. 65–80). Nobel Akademik Yayıncılık.