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# A Fuzzy approach for the variable cost and size bin packing

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<subfield code="a">A Fuzzy approach for the variable cost and size bin packing</subfield>
<subfield code="c">Jorge Herrera-Franklin, Alejandro Rosete, Milton García-Borroto</subfield>
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<subfield code="a">The Variable Cost and Size Bin Packing Problem (VCSBPP) is a known NP-Hard problem that consists in minimizingthe cost of all bins used to pack a set of items. There are many real-life applications of the VCSBPP where the focus is to improve the efficiency of the solution method. In spite of the existence of fuzzy approaches to adapt other optimizationproblems to real life conditions, VCSBPP has not been extensively studied in terms of relaxations of the crisp conditions. In this sense, the fuzzy approaches for the VCSBPP varies from relaxing the capacity of the bins to the items weights. In this paper we address a non-explored side consisting inrelaxing the set of items to be packed. Therefore, our main contribution is a fuzzy version of VCSBPP that allows incomplete packing. The proposed fuzzy VCSBPP is solved by a parametric approach. Particularly, a fast heuristic algorithm is introduced that allows to obtain a set of solutions with interesting trade-offs between cost and relaxation of the original crisp conditions. An experimental study is presented to explore the proposed fuzzy VCSBPP and its solution.</subfield>
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<subfield code="a">Rosete, Alejandro</subfield>
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<subfield code="a">García-Borroto, Milton</subfield>
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<subfield code="t">Revista Iberoamericana de Inteligencia Artificial</subfield>
<subfield code="d">IBERAMIA, Sociedad Iberoamericana de Inteligencia Artificial , 2018-</subfield>
<subfield code="x">1988-3064</subfield>
<subfield code="g">15/02/2021 Volumen 24 Número 67 - febrero 2021 , p. 71-89</subfield>
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