Budgeting fuel consumption of container ship over round-trip voyage through robust optimization

A proposed practical fuel budget problem aims to determine a group of bunker fuel budget values for a liner container ship over a round-trip voyage under uncertainties caused by severe weather conditions. According to research collaboration with a global container shipping line in Singapore, the proposed problem holds a kernel position in the ship fuel efficiency management programs advocated by container shipping lines because of the downward pressure of soaring bunker prices. The synergetic influence of sailing speed and weather conditions on ship fuel consumption rate was considered when the bunker fuel budget of a ship over a round-trip voyage was estimated. To address the adverse random perturbation of fuel consumption rate under severe weather conditions, state-of-the-art robust optimization techniques were employed, and a robust optimization model for the fuel budget problem was developed. The developed model can be dualized into a mixed-integer linear programming model that may be solved by commercial optimization solvers. However, algorithmic findings in the field of robust optimization provided a polynomial time solution algorithm, and it was retrofitted to accommodate the proposed ship fuel budget problem. The case study of an Asia–Europe service demonstrates the computational performance of the proposed solution algorithm and the competence of the proposed robust optimization model to produce fuel budget values at different levels of conservatism possessed by the fuel efficiency specialists in container shipping lines.