IDEAS home Printed from
   My bibliography  Save this article

Berth scheduling with variable cost functions


  • Mihalis M Golias

    () (Department of Civil Engineering, University of Memphis, Memphis, 3815 Central Ave, Memphis, Tennesse 38152, USA.)

  • Hercules E Haralambides

    () (Center for Maritime Economics and Logistics (MEL), Erasmus University Rotterdam, PO Box 1738, Rotterdam, DR 3000, the Netherlands.)


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.

Suggested Citation

  • Mihalis M Golias & Hercules E Haralambides, 2011. "Berth scheduling with variable cost functions," Maritime Economics & Logistics, Palgrave Macmillan;International Association of Maritime Economists (IAME), vol. 13(2), pages 174-189, June.
  • Handle: RePEc:pal:marecl:v:13:y:2011:i:2:p:174-189

    Download full text from publisher

    File URL:
    File Function: Link to full text PDF
    Download Restriction: Access to full text is restricted to subscribers.

    File URL:
    File Function: Link to full text HTML
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Bierwirth, Christian & Meisel, Frank, 2015. "A follow-up survey of berth allocation and quay crane scheduling problems in container terminals," European Journal of Operational Research, Elsevier, vol. 244(3), pages 675-689.

    More about this item


    Access and download statistics


    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pal:marecl:v:13:y:2011:i:2:p:174-189. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla) or (Rebekah McClure). General contact details of provider: .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.