A general iterative solver for unbalanced inconsistent transportation problems

Doina Carp; Constantin Popa; Cristina Serban

doi:10.5604/08669546.1203199

Authors

Doina Carp University Constanta Maritime University, Constanta, Romania Author
Constantin Popa Ovidius University of Constanta, Faculty of Mathematics and Computer Science, Constanta, Romania Author
Cristina Serban Ovidius University of Constanta, Faculty of Civil Engineering, Constanta, Romania Author

DOI:

https://doi.org/10.5604/08669546.1203199

Keywords:

inconsistent linear inequalities, east squares solutions, projection-type algorithm, Kaczmarz Extended, transportation problem, simplex algorithm, Han’s algorithm

Abstract

The transportation problem, as a particular case of a linear programme, has probably the highest relative frequency with which appears in applications. At least in its classical formulation, it involves demands and supplies. When, for practical reasons, the total demand cannot satisfy the total supply, the problem becomes unbalanced and inconsistent, and must be reformulated as e.g. finding a least squares solution of an inconsistent system of linear inequalities. A general iterative solver for this class of problems has been proposed by S. P. Han in his 1980 original paper. The drawback of Han’s algorithm consists in the fact that it uses in each iteration the computation of the Moore-Penrose pseudoinverse numerical solution of a subsystem of the initial one, which for bigger dimensions can cause serious computational troubles. In order to overcome these difficulties we propose in this paper a general projection-based minimal norm solution approximant to be used within Han-type algorithms for approximating least squares solutions of inconsistent systems of linear inequalities. Numerical experiments and comparisons on some inconsistent transport model problems are presented.

References

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