# APPLICATION OF TRANSPORTATION MODEL TO SOLVE TANKERS’ – ROUTING PROBLEM

• S. A. Ogumeyo
• C. E. O. Omole
Keywords: Petroleum products, Transportation, Tankers’-routing, Linear programming, Refinery

### Abstract

The problem of selecting minimum cost routes for tankers in distributing petroleum products and satisfying customers’ requirement without scarcity in Nigeria remains a huge challenge to major marketers in the oil industries. The cost of transporting petroleum products from sources to destinations matters a lot to oil marketers because of the direct impact it has on their profits. The means of distributing petroleum products from refineries to depots or filling stations are tankers’ routing and pipelines. In this research, we extended some existing tankers’-routing models in literature which use a discrete integer programming approach to determine efficient and effective distribution of petroleum products. Consequently, we developed a new transportation linear programming algorithm to determine minimum cost routes in the delivery of petroleum product from their supply centers (refinery) to demand centers (filling stations). The significance of the application we adopted in this research lies in the modified distribution approach to tackle the complexity involved when transportation problems are formulated as linear programming problem having several variables and constraints. In this research, we formulate a new version of transportation model of tankers’ routing with the aim of reducing the cost of petroleum products delivery. The proposed transportation linear programming model was applied to a numerical example alongside other existing transportation algorithms. It is observed that, the new algorithm produced approximately the same total cost obtained by using other existing algorithms

### References

Agra, A., Anderson, H. Christiansen, M. and Wolsey, L. (2013). Mixed Integer Formulations for a Short Sea Fuel Oil Distribution Problem. Transportation Science, 47 (1) 108-124. DOI: https://doi.org/10.1287/trsc.1120.0416

Agureev, I.E. and Akhromeshin, A.V. (2021). Mathematical Model of Transport Behavior Based on Transport Macro System Theory. World of Transport and Transportation, 19 (6) 141-146. DOI: https://doi.org/10.30932/1992-3252-2021-19-6-2

Awariefe, C. and Ogumeyo, S. A. (2023). Prediction Accuracy of Nigeria Military Expenditure: MLR, ARIMAX, and ANN Model in Statistical and Machine Learning Frameworks. FUDMA Journal of Sciences (FJS) 7 (6) 149-156. DOI: https://doi.org/10.33003/fjs-2023-0706-2180

Dantzi, G.B. and Koopman, T.C. (1951). Application of Simplex Method to Transportation Problem: Activity Analysis of Production and Allocation. John Wiley and Sons, New York.

Dantzi, G.B.and Fulkerson, D.R.(1954). Minimizing the Number of Tankers to Meet a Fixed Schedule. Naval Research Logistics Quart. (1) 217-222. DOI: https://doi.org/10.1002/nav.3800010309

Diz, G. Dos S. Santos O. and Hamacher, S. (2017). Improving Maritime Inventory Routing: Application to a Brazilian Petroleum Case. Maritime Policy and Management. 44 (1) 42-61. DOI: https://doi.org/10.1080/03088839.2016.1216622

Ekoko, P.O. (2011). Operations Research for Sciences and Social Sciences. Third Edition. Mindex Publishing Company Limited, Benin City.

Gupta P.K. and Hira D.S, (2005). Operations Research: Principles and Solutions. S. Chend and Co. Ltd New Delhi, Chapter 4.

Hitchcock, F.L. (1941). The Distribution of Products from Several sources to Numerous Localities: Journal of Mathematics and Physics (20) 224 -230. DOI: https://doi.org/10.1002/sapm1941201224

Kazemi, Y. and Szmerekovsky (2015). Modeling Downstream Petroleum Supply Chain: The Importance of Multi-mode Transportation to Strategic Planning. Transportation Research Part E. Logistics and Transportation Review 83: 111-125. DOI: https://doi.org/10.1016/j.tre.2015.09.004

Koopman, T.C. (1947). Optimum Utilization of Transportation system. Proc. International Conference Washington D.C.

Nagurney, A. (2004). Spatial Equilibrium in Transport Network, Handbook of Transport Geography and Spatial System, Netherlands 583 – 608, DOI: https://doi.org/10.1108/9781615832538-033

Noble, H. (2023). Transportation Problem in Operations Research. Available online at www. Linkedin. Com.

Ogumeyo, S.A and Panya, A.L (2024). Transportation Model to Determine Minimum Cost Routes Using a Dynamic Programming Approach. The Journal of the Nigeria Institution of Production Engineers.(28) 1-14.

Quan, L. Jiancheng W., Zhou W and Baez, S. (2018). Individual Travel Behaviour Modeling of Public Transport Passenger based on graph construction. Hindawi Journal of Advanced Transportation. Available online at DOI: http://doi.org/10.1155. DOI: https://doi.org/10.1155/2018/3859830

Rodrigues, V.P., Morabito, R. Yamashita, D., Da Silva, D.J.V., and Ribas, P.C. (2016). Ship Routing with Pickup and Delivery for a Maritime Oil Transportation. System: MIP Model Heuristics. Systems 4(3) 31. DOI: https://doi.org/10.3390/systems4030031

Salami, A.O (2014). Application of Transportation Linear Programming Alogrithm to Cost Production in Nigeria Soft Drinks Industry. International Journal of Economics and Management Engineering. 8 (2) 416 - 422.

Sharma S.D (1996). Operations Research. India: MC Kinsey Company Inc.

Shvetsov, V. I. (2021). Mathematical Modeling of Transport flows. Available online at http://www.mathnet.ru/php/getFT.ph.

Stanzani, A., Vitoria, D.L., Pureza, R.M. Virginio Da, B.J. Yamashita, D. and Cesar Ribas (2018). Optimizing Multi-ship Routing and Scheduling Constraints on Inventory Levels in a Brazilian Oil Company. International Transactions in Operational Research 25 (4) 1163-1198. DOI: https://doi.org/10.1111/itor.12478

Published
2024-04-30
How to Cite
OgumeyoS. A., & OmoleC. E. O. (2024). APPLICATION OF TRANSPORTATION MODEL TO SOLVE TANKERS’ – ROUTING PROBLEM. FUDMA JOURNAL OF SCIENCES, 8(2), 259 - 266. https://doi.org/10.33003/fjs-2024-0802-2352
Section
Research Articles