The “DUKC Optimiser” Ship Scheduling System

We present an automated ship scheduling system – DUKC R © Optimiser – which selects sailing times for a set of cargo ships at a port, so as to maximise total cargo throughput while meeting port operational and safety guidelines, as well as producing schedules that are fair to all companies using the port. The system has been developed by maritime engineering company OMC International, incorporating elements of the author’s PhD research at the Australian National University and NICTA. A prototype of the system has undergone user testing in late 2010, and is planned to undergo further development in order to include additional functionality and incorporate results into a web-based ship management system. DUKC R © Optimiser is the first ship scheduling system that accounts for environmentally-dependent constraints on the times when ships can enter or leave a port. The system uses OMC’s existing Dynamic Under-Keel Clearance (DUKC R ©) software to calculate sailing windows for each ship. The results of the DUKC R © calculations are then converted into a Mixed-Integer Programming model, formulated in the MiniZinc modelling language, and solved using the G12 constraint optimisation solver. Ship Scheduling Background Ship scheduling deals with assigning sailing times to a fleet of ships, as well as optionally the amount and type of cargo that each ship carries. Ship scheduling is a problem with significant real-world impact, as the majority of the world’s international trade is transported by sea, so even a small improvement in schedule efficiency can have significant benefits to industry (Christiansen, Fagerholt, and Ronen 2004). One consideration in ship scheduling is that most ports have restrictions on the draft of ships that are able to safely enter the port. Draft is the distance between the waterline and the ship’s keel, and is a function of the amount of cargo loaded onto the ship. Ships with a deep draft risk running aground when entering or leaving the port, therefore most ports restrict the draft of ships allowed to transit through the port. Copyright c © 2011, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. In existing ship scheduling algorithms, draft constraints have only been considered in trivial ways, for example, assuming that a given port will always allow ships with a draft of 13 metres or less, and never allow ships with deeper drafts to enter (Fisher and Rosenwein 1989). Other ship scheduling algorithms leave draft constraints entirely up to human schedulers (Fagerholt 2004). In practice, most ports restrict ship sailing drafts using safety rules that estimate the under-keel clearance (UKC) – the depth of water under a ship’s keel. In recent years, OMC International has developed algorithms to accurately calculate under-keel clearance using real-time environmental conditions. OMC’s Dynamic Under-Keel Clearance (DUKC R ©) software allows significantly more cargo to be loaded safely onto each vessel compared to the static UKC rules previously used by most ports, which don’t take real-time environmental data into account (OMC 2011). However, ship scheduling has not been able to take advantage of these recent improvements in UKC estimation, due to not considering complex time-varying draft constraints. In this presentation, we demonstrate the DUKC R © Optimiser software, which is the first ship scheduling system that can take environmentally-dependent time-varying draft constraints into account. Dynamic Under-Keel Clearance Figure 1 illustrates all aspects of ship motion taken into account by the Dynamic Under-Keel Clearance (DUKC R ©) software in calculating under-keel clearance. Components of ship motion taken into account by the DUKC R © software include: Draft: the distance from the waterline to the bottom of the ship’s keel. Squat: a phenomenon caused by the Bernoulli effect which causes a ship travelling fast through shallow water to sink deeper into the water than a ship travelling slowly. Heel: the effect of a ship leaning towards one side, caused by the centripetal force of turning, or the force of wind on the side of the ship. Figure 1: Dynamic Under-Keel Clearance Components Wave Response: the motion resulting from the action of waves on the ship. Only the vertical component of this motion affects under-keel clearance. Under-keel clearance is computed as follows: UKC = Tide + Depth Draft Squat Heel Wave Response The Bottom Clearance and Manoueverability Margin shown in Figure 1 are safety factors that ensure the ship has sufficient distance from the highest points on the channel bottom (Bottom Clearance) and that there is sufficient water around the ship to maintain good manoeuverability (Manoueverability Margin). If the under-keel clearance is below either the Bottom Clearance or Manoueverability Margin safety limits, then the DUKC R © software will advise the operator not to sail. However, the DUKC R © software only provides navigational advice; the final decision always rests with the ship’s pilot or captain. For a more detailed analysis of Dynamic Under-Keel Clearance methodology, see (O’Brien 2002).