Solving biobjective network flow problem associated with minimum cost-time loading

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Baghani O.; Ghafoori S.

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Journal Paper

Paper Information

Journal: IRANIAN JOURNAL OF NUMERICAL ANALYSIS AND OPTIMIZATION Year:2020 | Volume:10 | Issue:2 Page(s): 33-48

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Information Journal Paper

Title

Solving biobjective network flow problem associated with minimum cost-time loading

Author(s)

Baghani O. | Ghafoori S. | Issue Writer Certificate

Keywords

Biobjective network flow

Minimum cost-time

Primal-dual algorithm

Fixed time

Abstract

We apply a primal-dual simplex algorithm for solving the biobjective min imum cost-time network flow problem such that the total shipping cost and the total shipping Fixed time are considered as the first and second objective functions, respectively. To convert the proposed model into a single-objective parametric one, the weighted sum scalarization technique is commonly used. This problem is a mixed-integer programming, which the decision variables are directly dependent together. Generally, the previous works have consid ered the linear biobjective problem with the traditional network flow con straints, while in this paper, corresponding to each flow variable, a binary variable is defined. These zero-one variables are utilized to describe a fixed shipping time for positive flows. The proposed method is successful in finding all supported efficient solutions of a real numerical example.

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