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

Year 2024, , 169 - 194, 31.12.2024

Kenan Karagül

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

Abstract

This study aims to explore the Grey Fuzzy Transportation Problem, which describes the decision-making processes under uncertainty in the transportation problem, which is an especially important study problem for the logistics sector and academic studies. Comprehensive analyses and suggestions are made to contribute to the effective solution of the Grey Fuzzy Transportation Problem and better control of transportation problems which contain uncertainty. In the research, four different optimization methods for the Grey Fuzzy Transportation Problem (GFTP), the Closed Path Method, Interval Optimization, Robust Optimization and Interval Optimization with Penalty Function, are comparatively analyzed. The analyses are done on a total of 40 test problems with four different problem sizes, small, medium, large and extra-large. The results revealed that Interval Optimization and Robust Optimization performed the best in terms of solution quality and computation time. In particular, extensive analyses on the Interval Optimization with Penalty Function method verified that this is an effective and consistent solution approach for GFTP.

Keywords

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

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.