Tramp ship routing and scheduling with speed optimization
01 Aug 2011-Transportation Research Part C-emerging Technologies (Pergamon)-Vol. 19, Iss: 5, pp 853-865
TL;DR: In this paper, the authors present a multi-start local search heuristic to solve the problem of ship routing and scheduling with speed optimization, where speed on each sailing leg is introduced as a decision variable.
Abstract: Tramp shipping companies are committed to transport a set of contracted cargoes and try to derive additional revenue from carrying optional spot cargoes. Traditionally, models for ship routing and scheduling problems are based on fixed speed and a given fuel consumption rate for each ship. However, in real life a ship’s speed is variable within an interval, and fuel consumption per time unit can be approximated by a cubic function of speed. Here we present the tramp ship routing and scheduling problem with speed optimization, where speed on each sailing leg is introduced as a decision variable. We present a multi-start local search heuristic to solve this problem. To evaluate each move in the local search we have to determine the optimal speed for each sailing leg of a given ship route. To do this we propose two different algorithms. Extensive computational results show that the solution method solves problems of realistic size and that taking speed into consideration in tramp ship routing and scheduling significantly improves the solutions.
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References
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TL;DR: This work proposes an alternative solution methodology, in which the arrival times are discretized and the problem is solved as a shortest path problem on a directed acyclic graph, and extensive computational results confirm the superiority of the shortest path approach and the potential for fuel savings on shipping routes.
Abstract: Fuel consumption and emissions on a shipping route are typically a cubic function of speed. Given a shipping route consisting of a sequence of ports with a time window for the start of service, substantial savings can be achieved by optimizing the speed of each leg. This problem is cast as a non-linear continuous program, which can be solved by a non-linear programming solver. We propose an alternative solution methodology, in which the arrival times are discretized and the problem is solved as a shortest path problem on a directed acyclic graph. Extensive computational results confirm the superiority of the shortest path approach and the potential for fuel savings on shipping routes.
321 citations
TL;DR: A cost model is constructed that is used to analyse the trade-off between speed reduction and adding vessels to a container line route, and a simple procedure is devised to identify the sailing speed and number of vessels that minimize the annual operating cost of the route.
Abstract: The changing prices of bunker fuel open the door for substantial cost savings by adjusting the sailing speed of ships. A large ship may be burning up to 100 000 USD of bunker fuel per day, which may constitute more than 75% of its operating costs. Reducing the cruising speed by 20% reduces daily bunker consumption by 50%. However, in order to maintain liner service frequency and capacity, reducing the cruising speed may require additional ships to operate a route. We construct a cost model that we use to analyse the trade-off between speed reduction and adding vessels to a container line route, and devise a simple procedure to identify the sailing speed and number of vessels that minimize the annual operating cost of the route. Using published data, we demonstrate the potential for large-cost savings when one operates close to the minimal-cost speed. The presented methodology and procedure are applicable for any bunker fuel price.
278 citations
TL;DR: The tradeoff between fuel savings through slow steaming and the loss of revenues due to the resulting voyage extension is analyzed in this article, and three models for the expli....
Abstract: The tradeoff between fuel savings through slow steaming on the one hand, and the loss of revenues due to the resulting voyage extension on the other hand is analyzed, and three models for the expli...
238 citations
TL;DR: This paper considers a real ship scheduling problem that can be considered as a multi-ship pickup and delivery problem with soft time windows (m-PDPSTW) and proposes an optimisation based approach based on a set partitioning formulation to solve the problem.
195 citations