Mathematical modeling and optimization of vessel route selection and refueling decisions

Abstract

Maritime transportation is a volatile and growing sector. In order to survive in this competitive sector, maritime companies have to continuously strive for lower costs in performing vessel operations. Today, fuel (bunker) comprises about 50-60 percent of a vessel’s voyage expenses. This study aims the mathematical modeling and optimization of refueling policy and routing decisions. Refueling policy consists of the refueling ports and amounts of a vessel. The selection of refueling port affects the route of the vessel. Two mathematical models are developed in this study. One of them is the Single Voyage Bunkering Model, which is a mixed integer programming model and defines the refueling ports and amounts of a vessel whose a few number of loading/discharging ports are certain in a short term. The second model, the Long Term Bunkering Model, is developed as an infinite stage stochastic dynamic programming model. This model seeks to determine the refueling amount of a vessel at a port according to the arrival fuel amount of the vessel and the expected future destination from that port. Single Voyage Bunkering Model is applied to a real problem by the CPLEX solver within GAMS v23.3.3 software. The Long Term Bunkering Model is also solved by using real data and by different dynamic programming algorithms that are programmed in Visual Studio 2005 with C#. Apart from classic dynamic programming solution procedures, two new heuristic algorithms are also developed. At the end of the study, the results obtained are compared and discussed.