A Decomposition Algorithm for Solving A Class of Bi-Criteria Multistage Transportation Problem With Case Study
ISSN ONLINE(2319-8753)PRINT(2347-6710)

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## A Decomposition Algorithm for Solving A Class of Bi-Criteria Multistage Transportation Problem With Case Study

 Dr. Jasem M.S. Al-Rajhi, Dr. Hilal A. Abdelwali, Dr. Elsayed E.M. Ellaimony, Dr. Swilem A.M. Swilem* Assistant Professor, Department of Automotive and Marine, College of Technological Studies, PAAET, Kuwait. Corresponding Author: Dr. Swilem A.M. Swilem, Related article at Pubmed, Scholar Google

### Abstract

In transportation problems with one or multistages, single criterion of minimizing the total cost is usually considered. But in certain practical situations two or more objectives are relevant. For example, the objectives may be minimizations of the total cost, consumption of certain scarce resources such as energy, total deterioration of goods during transportation, etc. Clearly, this problem can be solved using any of the multiobjectives linear programming techniques, but the computational efforts needed would be prohibitive in many cases. The computational complexity in these techniques arises from the fact that each of the methods finds the set of efficient extreme points in the decision space where such extreme points are, generally, many. Therefore, this paper develops a method of finding the nondominated extreme points in the criteria space, for a certain model of multistage transportation problems. This paper presents the mathematical formulation of different bi-criteria multistage transportation problem, and an algorithm for solving a class of them. This class can be solved using the decomposition technique of linear programming utilizing the special nature of the transportation problem and the method of finding the no-dominated extreme points in the criteria space. A case study is included in this paper to find the efficient distribution of wheat and flour in Middle Egypt mill-stones company.

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