A new approach for solving Multi-commodity and bounded network transportation problem

Document Type : Original Paper


Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz-Iran


The purpose of this paper is to present a new method for solving multi-commodity and bounded transportation networks in optimization problems.

Multi-commodity and bounded transport networks with the aim of minimizing the total cost of transporting goods in the network, is an important and widely used issue in optimization problems.

Two very important and key features of multi-commodities and bounded are examined in different articles

and have provided algorithms to solve it.

We are ,based on the network simplex method, offer an innovative method without any complexity to obtain the solutions of multi-commodity and bounded transportation networks problems.

At the end, , the efficiency of this method is shown with some numerical examples.


Main Subjects

[1] دودانگه، مدل ریاضی حملونقل در سیستمهای لجستیک، فصلنامه مدیریت زنجیره تامین، شماره ۳۲ (1390).
[2] Archetti C. and Speranza M.G., A Tabu search algorithm for the split delivery VRP, Transportation Science, Vol.40, No.1, (2006), 64-73.
[3] Bazaraa M.S., Jarvis J.J. and Sherali H.D., linear programming and network flows, Wiley Publication, Fourth Edition 2010, (1990).
[4] Charnes A. and Klingman D, The Distribution Problem with Upper and Lower Bounds on the Node Requirements, Management Science, 16, (1970), 638-642.
[5] Crainic G. and Laporte G., Planning models for freight transportation, European Journal of Operational Research, (1997), 409-438.
[6] Dantzig G. and Ramser J., The truck dispatching problem, Management Science, V.6, (1959), 80-91.
[7] Gary M. and Johnson D., Computers and intractability: A guide to the theory of NP completeness, Freeman, San Francisco, (1979).
[8] Hakan Akyuz M., Öncan T. and Kuban Altınel İ., Branch and bound algorithms for solving the multicommodity capacitated multi-facility Weber problem, Annals of Operations Research, Vol. 279, (2019), 1-42
[9] Hitchcock F.L. and Frank L., The Distribution of a Product from Several Sources to Nulmerous Localities, Journalof Mathematical Physics, 20 , (1941), 224-230.
[10] Koopmans T.C., Optimum Utilization of the Transportation System, Econometrica, Supplement, 17, (1949), 136-146.
[11] Laporte G. and Dejax J., Dynamic Location-routing problem, Journal of Operation Research Society, V.40, No.5, (1989), 471-482.
[12] Laporte G. and Nobert Y., Exact algorithms for the VRP, Annals of Discrete Mathematics, 31, (1987), 147-184.
[13] Lenstra J. and Rinooy K.A., Complexity of vehicle routing and scheduling problems, Networks, V.11, N.2, (1981), 221-227.
[14] Olusina J., Solving Minimum Cost Multi-Commodity Network Flow Problem Using Lexicographic Goal Programming Approach, Journal of Applied Sciences and Environmental Management, Vol. 22 (3), (2018), 414–420
[15] Rodrigo N., Rjapaksha L., SMathematical Model and a Case Study for Multi-Commodity Transportation Problem, International Journal of Theoretical and Applied Mathematics Vol. 4, Issue 1, (2018), 1-7
[16] Stojčić M. Application of ANFIS model in road traffic and transportation: a literature review from 1993 to 2018, Operational Research in Engineering Sciences: Theory and Applications, Vol.1, Issue1, (2018), 40-61.
[17] Toth P. and Vigo D., The vehicle routing problem, Siam Monographs on Discrete Mathematics and Applications, Philadelphia, USA, (2002).
[18] Vaziri Sh., Etebari F. and Vahdani B., Development and optimization of a horizontal carrier collaboration vehicle routing model with multi-commodity request allocation, Journal of Cleaner Production, (2019).
[19] Yano C. and McGetting D., Vehicle rpoting at quality stores, Interfaces, V.17, N.2, (1987), 52-63.