Robust Ship Scheduling with Multiple Time Windows Marielle Christiansen, 1 Kjetil Fagerholt 2 1 Section of Operations Research, Norwegian University of Science and Technology, Trondheim, Norway 2 MARINTEK and Department of Marine Systems Design, Norwegian University of Science and Technology, Trondheim, Norway Received 19 September 2000; revised 5 February 2002; accepted 7 February 2002 Abstract: We present a ship scheduling problem concerned with the pickup and delivery of bulk cargoes within given time windows. As the ports are closed for service at night and during weekends, the wide time windows can be regarded as multiple time windows. Another issue is that the loading/discharging times of cargoes may take several days. This means that a ship will stay idle much of the time in port, and the total time at port will depend on the ship’s arrival time. Ship scheduling is associated with uncertainty due to bad weather at sea and unpredictable service times in ports. Our objective is to make robust schedules that are less likely to result in ships staying idle in ports during the weekend, and impose penalty costs for arrivals at risky times (i.e., close to weekends). A set partitioning approach is proposed to solve the problem. The columns correspond to feasible ship schedules that are found a priori. They are generated taking the uncertainty and multiple time windows into account. The computational results show that we can increase the robustness of the schedules at the sacrifice of increased transportation costs. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 611– 625, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/nav.10033 1. INTRODUCTION Ocean shipping is already the major transportation mode for international trade, and the trend goes towards an increase in the use of ships. Often, the shipping industry is divided into deep sea and short sea shipping, where deep sea is shipping between continents and short sea shipping takes place within a continent. The shipping industry has a monopoly regarding transportation between continents for large volumes. This activity will probably increase in the future with the continuous growth in the world population, combined with product specialization and depletion of local resources. With an increase in deep sea activities we need feeder systems for short sea shipping, so that the latter is expected to increase as well. In addition, we will probably see an increase in the area of short sea shipping, due to heavily congested road networks and air corridors. In this growth period, the shipping industry will meet new challenges. Efficient operation of the whole supply chain from the supplier to the end customer will be emphasized both in time Correspondence to: M. Christiansen. © 2002 Wiley Periodicals, Inc.