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Fully Fuzzy Linear Programming Model for the Berth Allocation Problem with Two Quays

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Uncertainty Management with Fuzzy and Rough Sets

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 377))

Abstract

In this work, we study the berth allocation problem (BAP), considering the cases continuous and dynamic for two quays; also, we assume that the arrival time of vessels is imprecise, meaning that vessels can be late or early up to a allowed threshold. Triangular fuzzy numbers represent the imprecision of the arrivals. We present two models for this problem: The first model is a fuzzy MILP (Mixed Integer Lineal Programming) and allows us to obtain berthing plans with different degrees of precision; the second one is a model of Fully Fuzzy Linear Programming (FFLP) and allows us to obtain a fuzzy berthing plan adaptable to possible incidences in the vessel arrivals. The models proposed have been implemented in CPLEX and evaluated in a benchmark developed to this end. For both models, with a timeout of 60 min, CPLEX find the optimum solution for instances up to 10 vessels; for instances between 10 and 65 vessels it finds a non-optimum solution and for bigger instants no solution is founded. Finally we suggest the steps to be taken to implement the model for the FFLP BAP in a maritime terminal of containers.

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Acknowledgements

This work was supported by INNOVATE-PERU, Project N PIBA-2-P-069-14.

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Authors and Affiliations

  1. Department of Mathematics, National University of Piura, Piura, Peru

    Flabio Gutierrez

  2. Department of Informatics, National University of Trujillo, Trujillo, Peru

    Edwar Lujan

  3. Department of Mathematics, National University of Trujillo, Trujillo, Peru

    Rafael Asmat & Edmundo Vergara

Authors
  1. Flabio Gutierrez
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  2. Edwar Lujan
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  3. Rafael Asmat
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  4. Edmundo Vergara
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Corresponding authors

Correspondence to Flabio Gutierrez , Edwar Lujan , Rafael Asmat or Edmundo Vergara .

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Editors and Affiliations

  1. Department of Computer Science, Universidad Central "Marta Abreu" de Las Villas, Santa Clara, Villa Clara, Cuba

    Rafael Bello

  2. School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, ON, Canada

    Rafael Falcon

  3. Department of Computer Science and Artificial Intelligence, Technical School of Informatics and Telecommunications Engineering, University of Granada, Granada, Spain

    José Luis Verdegay

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Gutierrez, F., Lujan, E., Asmat, R., Vergara, E. (2019). Fully Fuzzy Linear Programming Model for the Berth Allocation Problem with Two Quays. In: Bello, R., Falcon, R., Verdegay, J. (eds) Uncertainty Management with Fuzzy and Rough Sets. Studies in Fuzziness and Soft Computing, vol 377. Springer, Cham. https://doi.org/10.1007/978-3-030-10463-4_5

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