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A general iterative solver for unbalanced inconsistent transportation problems

Carp D., Popa C., Serban C.

Archives of Transport

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2016

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Vol. 37, iss. 1

7--13

EN

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.

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Regularized Han-type Algorithms for Inconsistent Maritime Container Transportation Problems

Carp D., Popa C., Şerban C.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2014

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Vol. 8 no. 4

579--583

EN

In this paper we analyse several ways to compute the weights from the Regularized Han (RH) algorithm, the regularized version of Han’s algorithm for approximating the least squares solutions of inconsistent (incompatible) systems of linear inequalities. We tested our approaches on a classical transportation problem, aiming to provide a cost optimized solution to real world transportation problems, which often are unbalanced and inconsistent.

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Project “e-Marine”, a new approach for port and maritime activities

Carp D.

TransNav : International Journal on Marine Navigation and Safety of Sea Transportation

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2007

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Vol. 1, no. 2

223--225

EN

An important problem our days is to recognize the knowledge, the skills and the competencies wherever it might be acquired. Most European countries are currently developing and implementing methods, institutions and systems for the validation of non-formal and informal learning.