An approach for the network flow problem with multiple objectives
Computers and Operations Research
An algorithm for the biobjective integer minimum cost flow problem
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Information Sciences—Informatics and Computer Science: An International Journal
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Computers and Industrial Engineering
Ranking function-based solutions of fully fuzzified minimal cost flow problem
Information Sciences: an International Journal
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Information Sciences: an International Journal
Fuzzy Linear Programming Approach for Solving Fuzzy Transportation Problems with Transshipment
Journal of Mathematical Modelling and Algorithms
Fuzzy optimal solution of fuzzy transportation problems with transshipments
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Some concepts of the fuzzy multicommodity flow problem and their application in fuzzy network design
Mathematical and Computer Modelling: An International Journal
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This paper studies the minimal cost flow problem (MCFP) with fuzzy link costs, say fuzzy MCFP, to understand the effect of uncertain factors in applied shipment problems. With respect to the most possible case, the worst case and the best case, the fuzzy MCFP can be converted into a 3-objective MCFP. Applying a lexicographical ordering on the objective functions of derived problem, two efficient algorithms are provided to find the preemptive priority-based solution(s), namely p-successive shortest path algorithm and p-network simplex algorithm. In both of them, lexicographical comparison is used which is a natural ordering in many real problems especially in hazardous material transportation where transporting through some links jeopardizes people's lives. The presented schemes maintain the network structure of problem and so, they are efficiently implementable. A sample network is also given to illustrate the procedure and to compare the computational experiences with those of previously established works. Finally, the presented approach is applied to find an appropriate plan to transit hazardous materials in Khorasan roads network using annual data of accidents.