Recent Developments in Transportation Problem and Solution Techniques

The transportation problem is a fundamental optimization model in operations research that plays a vital role in logistics, supply chain management, and distribution planning. Traditional transportation models focus on minimizing cost under deterministic assumptions; however, real-world transportation systems are often complex, uncertain, and multi-objective in nature. In recent years, significant developments have been made to address these limitations by introducing various transportation problem variants and advanced solution techniques. This paper presents a comprehensive review of recent developments in transportation problems, including unbalanced, capacitated, multi-objective, stochastic, fuzzy, time-dependent, and sustainable transportation models. The advantages and limitations of different solution techniques are discussed to highlight their suitability for various transportation scenarios. Finally, the paper identifies key research gaps and future directions, emphasizing the need for scalable, data-driven, and environmentally sustainable transportation optimization models. This review aims to serve as a useful reference for researchers and practitioners working in transportation optimization and related areas.

Transportation Problem, Operations Research, Optimization, Fuzzy and Stochastic Models, Sustainable Transportation

1. Hitchcock, F. L., “The Distribution of a Product from Several Sources to Numerous Localities,” Journal of Mathematical Physics, vol. 20, no. 1, pp. 224–230, 1941. [Google Scholar] [Crossref]

2. Kantorovich, L. V., “On the Translocation of Masses,” Management Science, vol. 5, no. 1, pp. 1–4, 1958. [Google Scholar] [Crossref]

3. Dantzig, G. B., Linear Programming and Extensions, Princeton University Press, Princeton, 1963. [Google Scholar] [Crossref]

4. Taha, H. A., Operations Research: An Introduction, 10th ed., Pearson Education, New Delhi, 2017. [Google Scholar] [Crossref]

5. Hillier, F. S., and Lieberman, G. J., Introduction to Operations Research, 10th ed., McGraw-Hill Education, New York, 2015. [Google Scholar] [Crossref]

6. Charnes, A., and Cooper, W. W., “The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation Problems,” Management Science, vol. 1, no. 1, pp. 49–69, 1954. [Google Scholar] [Crossref]

7. Sharma, J. K., Operations Research: Theory and Applications, 5th ed., Macmillan India Ltd., New Delhi, 2013. [Google Scholar] [Crossref]

8. Zimmermann, H. J., Fuzzy Set Theory and Its Applications, 4th ed., Springer, Berlin, 2001. [Google Scholar] [Crossref]

9. Gen, M., and Cheng, R., Genetic Algorithms and Engineering Optimization, Wiley-Interscience, New York, 2000. [Google Scholar] [Crossref]

10. Kaur, A., and Kumar, A., “Fuzzy Transportation Problems: A Review,” International Journal of Computer Applications, vol. 37, no. 11, pp. 42–47, 2012. [Google Scholar] [Crossref]

11. Rao, S. S., Engineering Optimization: Theory and Practice, 4th ed., Wiley, New Jersey, 2009. [Google Scholar] [Crossref]

12. Pattanayak, S. K., and Nayak, P. K., “A Comparative Study of Transportation Problem Solution Methods,” International Journal of Applied Engineering Research, vol. 10, no. 20, pp. 18045–18050, 2015. [Google Scholar] [Crossref]

13. Abdelaziz, F. B., “A Multi-objective Transportation Problem,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 433–442, 2006. [Google Scholar] [Crossref]

14. Li, X., and Liu, B., “A Stochastic Transportation Problem with Fuzzy Parameters,” Soft Computing, vol. 12, no. 3, pp. 293–298, 2008. [Google Scholar] [Crossref]

15. Singh, S. R., and Gupta, S., “Transportation Problems under Uncertainty: A Review,” International Journal of Mathematical Modelling and Numerical Optimisation, vol. 6, no. 3, pp. 219–238, 2015. [Google Scholar] [Crossref]

• Interplay of Students’ Emotional Intelligence and Attitude toward Mathematics on Performance in Grade 10 Algebra
• Numerical Simulation of Fitzhugh-Nagumo Dynamics Using a Finite Difference-Based Method of Lines
• Fixed Point Theorem in Controlled Metric Spaces
• Usage of Moving Average to Heart Rate, Blood Pressure and Blood Sugar
• Exploring Algebraic Topology and Homotopy Theory: Methods, Empirical Data, and Numerical Examples