Optimal Sailing Speeds and Time Windows in Inland Water Transportation Operations Management: Mathematical Models and Applications

Haoqing Wang, Yuan Liu, Yong Jin, Shuaian Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review


Inland waterway transportation plays a pivotal role in advancing economic development and nurturing sustainable progress. It serves as a vital conduit linking communities, industries, and markets, thereby facilitating the seamless flow of essential commodities and fostering regional integration. However, in today’s era, marked by a resolute commitment to environmental responsibility and sustainability, inland shipping confronts formidable challenges, particularly pertaining to emission pollution and the escalating costs of fuel. These challenges represent significant impediments to the pursuit of environmentally conscious and sustainable growth by shipping companies. This research endeavor is geared towards the creation of a mathematical model that takes into account various factors, including the types of waterways, temporal constraints, and punctual arrival at the port of discharge. The primary objective is to empower shipping companies to make informed decisions about optimal sailing speeds and the most opportune time windows for entering one-way waterway segments. This, in turn, leads to reductions in fuel costs and waiting times for shipping companies, all while achieving cost minimization and mitigating emissions issues in inland waterway transportation. Ultimately, this research advances the cause of green and sustainable development in the inland waterway shipping sector. Specifically, this study focuses on routes that involve the dynamic transition between one-way and two-way segments. To accomplish this, an integer programming (IP) model is proposed to meticulously analyze the ideal sailing speed for each segment of the route and determine the optimal windows for accessing single-direction channels, thus representing a multistage decision-making process. Meanwhile, the model’s reliability is substantiated through a rigorous comparative assessment against three benchmark strategies (EAS, LAS, and MAS). In our experiments, the optimization model yielded a total cost for the entire inland waterway amounting to $80,626.20. This figure stands below the total costs of $87,118.14 under the EAS strategy and $83,494.70 under the MAS strategy (the LAS strategy failed to meet the port of discharge deadline), thereby conclusively validating its ability to guide vessels to their port of discharge within prescribed schedules, all while reducing overall operational costs and promoting sustainable and environmentally responsible practices.

Original languageEnglish
Article number4747
Issue number23
Publication statusPublished - Dec 2023


  • integer programming
  • shipping operations management
  • sustainability
  • vessel scheduling

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • General Mathematics
  • Engineering (miscellaneous)


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