**TITLE**

An Algorithm for Cost-Minimizing in Transportation via Road Networks Problem

**PDF**

**ABSTRACT**

This paper presents an algorithm for solving transportation via road network problem to distribute goods from a number of sources to a number of destinations. The objective is to minimize transportation cost. Since the trucks travel over the roads that are suitable for the cargo weight, then the cargo weight and the transportation distance become both independent variables in the standalone transportation and network problems. Therefore, the transportation cost and the network distance matrices will not be available for a prior, and the solution requires a merging of the transportation and network models in one framework. Herein, the solutions of the linear programming transportation model and the road network problem are simultaneously attained using the proposed iterative algorithm. Meanwhile, the computation of the transportation cost is obtained in the same framework. Based on the transportation prices of domestic agencies, a simulation of a numerical example is used to explain the proposed algorithm.

**KEYWORDS**

Transportation problem, Network problems, Linear programming, Floyd’s algorithm, Cost Minimization.

**REFERENCES**

[1] Abdulla Fouad Alrouby ‘Multi-Objective Stochastic Transportation via road network of Materials and Wastes to and from Infrastructure Projects’, Master thesis, Isra University, May 2014

[2] Adlakha V, Kowalski K, and Lev B (2006) ‘Solving transportation Problem with mixed constraints’ International Journal of Management Science and Engineering Management, Vol. 1, pp. 47-52

[3] Alexander Schrijver (2010) ‘On the history of the shortest path problem’, Mathematics Subject Classification, Documenta Mathematica. Extra Volume ISMP (2012), pp. 155–167

[4] Alfred Asase (2011) ‘The Transportation Problem: Case study (Guiness Ghana Limited), Master thesis, Faculty of Physical Science and Technology-Department of Mathematics KNUST

[5] Badra M. N. (2007) ’Sensitivity Analysis of Transportation Problem’, Journal of Applied Sciences Research 668-657

[6] Doustdagholi S, Als D. A, and Abasgholipour V (2009) ‘A sensitivity analysis of Right Hand-Side parameter in Transportation Problem’ Applied Mathematical Science, Vol. 3, No. 30, 1501-1511

[7] Dykstra, D. P, (1984) ‘Mathematical Programming for Natural Resource Management’, New York: McGraw-Hill, Inc.

[8] Hamdy A. Taha (2010) ‘Introduction to operation research’, 9th Edition, Prentice Hall.

[9] Hitchcock, F. (1941) ‘The distribution of a product from several sources to numerous localities’, Journal of Mathematics and Physics, 20, pp. 224-230.

[10] K. Antony Arokia, and Chandrasekharan Rajendran (2009) ‘Fast heuristic algorithm to solve a single-stage fixed charge transportation problem’, International Journal of operational Research Vol. 6, No. 3, pp. 304-329.

[11] Mark Berwick, Mohammad Farooq (2003) ‘Truck Costing Model for Transportation Managers’, Upper Great Plains Transportation Institute North Dakota State University, August 2003.

[12] Nana B. B. Kudjo (2013) ‘The transportation Problem: Case Study of Coca Cola Bottling Company Ghana’ Master thesis, Kwame Nkrumah University of Science and Technology, April 2013.

[13] Reem Z. Al-Douri (2014) ‘Solution of Uncertain Resource Allocation Problem in Activity Networks for Project Management’, Master thesis, Isra University, August 2014.

[14] R. Panneerselvam (2003) ‘Operations Research’, Prentice- Hall of India, New Delhi.

[15] Sigrun Dewess, (2014) ‘A Pivot generation Approach for the Classical Hitchcock transportation Problem’, International Journal of operational Research Vol. 19, No. 3, pp. 302- 314.

[16] Sven B. Erlander (2010) ‘Cost-Minimizing Choice Behavior in Transportation Planning: A theoretical framework for logic Modules’ Spriger 2010.

[17] Tanveer Hussain (2010) ‘Transportation of raw material optimization of production system and reliability’, Master thesis, Dalarna University Röda vägen 3 S-781 88 Borlänge, Sweden.

[18] W. Ho, P. Ji (2005) ‘A genetic algorithm for the generlised transportation problem’, International Journal of computer Applications Vol. 22, No. 4, pp. 190-197.

[19] Weisstein, Eric (2009) ‘Floyd-Warshall Algorithm’, Wolfram MathWorld, Retrieved 13 November 2009.

[20] Zhi-Feng Hao, Han Huang, Xiao-Wei Yang (2006) ‘A Noval Particle Swarm Optimization Algorithm for Solving Transportation Problem’, IEEE Machine Learning and Cybernetics 2006 International Conference on, 13-16 Aug, pages 2178-2183, Dalian, China.

**Cite this paper**

Rami A. Maher, Abdulla Fouad Alrouby. (2017) An Algorithm for Cost-Minimizing in Transportation via Road Networks Problem. *International Journal of Mathematical and Computational Methods, ***2**, 292-299

Copyright © 2017 Author(s) retain the copyright of this article.

This article is published under the terms of the Creative Commons Attribution License 4.0