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Berth scheduling with variable cost functions

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Maritime Economics & Logistics Aims and scope

Abstract

This article presents a new mathematical formulation for the berth scheduling problem. The objective is to simultaneously minimize the total costs from vessels’ late departure and waiting time, and maximize the total premiums from vessels’ early departures. It is assumed that different vessels have different variable penalty/premium cost functions (PPCFs) that are based on contractual agreements between the liner shipping company and the terminal operator. A genetic algorithms-based heuristic is proposed to solve the resulting problem. A number of computational examples are presented to: (a) assess four different berth scheduling policies that are based on three different contractual agreements and (b) evaluate the effect of non-linear PPCFs. Computational results show that: (a) penalty/premium cost distribution among vessels display distinctive variations between the four berth scheduling policies, and (b) contractual agreements with constant (within a time window), followed by hourly (outside the time window) penalties/premiums should be favored during contractual agreement negotiations between terminal operators and liner shipping companies.

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Notes

  1. The term berth allocation problem is also found in the literature and refers to the same problem.

  2. The introduction of technical restrictions to existing berth scheduling models is rather straightforward and is therefore not attempted here. We refer to Bierwirth and Meisel (2010) for a classification and discussion on the different berth scheduling models found in the published literature.

  3. The term cost function in this article refers only to the tardy penalties and early premiums of departures and should not be confused with a vessel's total cost function or that of the terminal operator (Haralambides, 2002).

  4. The interested reader is referred to Bierwirth and Meisel (2010) and Theofanis et al (2009) for a detailed and critical literature review.

  5. http://www.americanshipper.com/NewWeb/news_page_SNW2.asp?news=179286.

  6. In the objective function, the constant penalties/premiums (that is, second term) are raised to the same power as the rest of the components to avoid a diminishing influence (of this term) to the objective function (and thus vessel-to-berth assignment) as the degree (α) increases.

  7. See Steenken et al (2004) and Theofanis et al (2009) for a discussion on the operational, tactical and planning levels at container terminals.

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Acknowledgements

This research has been partially supported by the Intermodal Freight Transportation Institute (IFTI), University of Memphis and the Kathikas Institute of Research and Technology (KIRT). Any opinions, findings, conclusions or recommendations expressed in this article are those of the authors and do not necessarily reflect the views of IFTI or KIRT. The authors are grateful to two anonymous referees for their constructive comments and suggestions.

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Golias, M., Haralambides, H. Berth scheduling with variable cost functions. Marit Econ Logist 13, 174–189 (2011). https://doi.org/10.1057/mel.2011.4

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