Schedule design for liner services under vessel speed reduction incentive programs

Dan Zhuge, Shuaian Wang, Lu Zhen, Gilbert Laporte

Research output: Contribution to journalArticlepeer-review

13 Citations (SciVal)
24 Downloads (Pure)


Gas and particulate emissions from ship transportation have been increasing in recent years. In order to mitigate ship emissions near coastal areas, voluntary vessel speed reduction incentive programs (VSRIPs) were put in place by a number of ports. This paper studies a schedule design problem faced by liner shipping companies under VSRIPs. It proposes a mixed-integer nonlinear mathematical model for the minimization of the total cost, consisting of fuel cost, as well as operating cost, minus dockage refunds. The model balances three determinants, that is, the compliance of VSRIPs, the speed limit (the maximum physical speed of ships and the upper speed limit imposed by VSRIPs), and the limited number of ships. An enumerative algorithm and a piecewise-linear approximation algorithm are developed, based on some properties of the nonlinear model. The efficiency of the proposed algorithms is validated through extensive computational experiments.

Original languageEnglish
Pages (from-to)45-62
Number of pages18
JournalNaval Research Logistics
Issue number1
Publication statusPublished - 1 Feb 2020


  • enumerative algorithm
  • liner shipping
  • piecewise-linear approximation
  • schedule design
  • speed limit
  • Sustainability
  • Green transportation

ASJC Scopus subject areas

  • Modelling and Simulation
  • Ocean Engineering
  • Management Science and Operations Research


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