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On two speed optimization problems for ships that sail in and out of emission control areas
Institution:1. Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway;2. Norwegian Marine Technology Research Institute (MARINTEK), Trondheim, Norway;3. Department of Transport, Technical University of Denmark, Lyngby, Denmark;1. Norwegian University of Science and Technology, Department of Industrial Economics and Technology Management, Trondheim, Norway;2. Norwegian Marine Technology Research Institute (MARINTEK), Trondheim, Norway;1. Department of Technology and Innovation, University of Southern Denmark, Niels Bohrs Alle 1, 5230 Odense M, Denmark;2. Department of Environmental and Business Economics, University of Southern Denmark, Niels Bohrs Vej 9, DK-6700 Esbjerg, Denmark;1. Department of Mathematical Science, Xi’an Jiaotong-Liverpool University, 111 Ren Ai Road, Suzhou, Jiangsu 215123, China;2. Department of Management Engineering, Technical University of Denmark, 2800 Kgs. Lyngby, Denmark;3. Department of Maritime and Mechanical Engineering, Liverpool John Moores University, L3 3AF Liverpool, United Kingdom
Abstract:This paper deals with two speed optimization problems for ships that sail in and out of Emission Control Areas (ECAs) with strict limits on sulfur emissions. For ships crossing in and out of ECAs, such as deep-sea vessels, one of the common options for complying with these limits is to burn heavy fuel oil (HFO) outside the ECA and switch to low-sulfur fuel such as marine gas oil (MGO) inside the ECA. As the prices of these two fuels are generally very different, so may be the speeds that the ship will sail at outside and inside the ECA. The first optimization problem examined by the paper considers an extension of the model of Ronen (1982) in which ship speeds both inside and outside the ECA are optimized. The second problem is called the ECA refraction problem, due to its conceptual similarity with the refraction problem when light travels across two different media, and also involves optimizing the point at which the ship crosses the ECA boundary. In both cases the objective of the problem is to maximize daily profit. In addition to mathematical formulations, examples and sensitivity analyses are presented for both problems.
Keywords:Maritime transportation  Speed optimization  Emission control areas
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