Annals of An Effective Modification to Solve Transportation Problems: A Cost Minimization Approach

Mollah Mesbahuddin, Ahmed, Abu Sadat, Muhammad Tanvir, Shirin Sultana, Sultan Mahmud, Md Uddin
2014 Annals of Pure and Applied Mathematics   unpublished
It is well-known that Linear Programming Problem (LPP) is one of the most potential mathematical tools for efficient allocation of operational resources. Many problems in real situation can be formulated as LPP. When a situation can be entirely modeled as a network, very efficient algorithms exist for the solution of the optimization problem which is many times more efficient than the solution methods of LPP. Transportation problems (TP), as is known, are a basic network problem which can be
more » ... mulated as a LPP. The main objective of TP is to minimize the transportation cost of distributing a product from a number of sources (e.g. factories) to a number of destinations (e.g. ware houses). It is to be mentioned that Balanced TP and Unbalanced TP are the types of TP. If the sum of the supplies of all the sources is equal to the sum of the demands of all the destinations, the problem is termed as a balanced transportation problem. Again, if the sum of the supplies of all the sources is not equal to the sum of the demand of all the destinations, the problem is termed as unbalanced transportation problem. Here we have developed a new method of finding an Initial Basic Feasible Solution (IBFS) for both the Balanced TP and Unbalanced TP.
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