Bunkering policies for a fuel bunker management problem for liner shipping networks

This paper investigates the problem of bunker fuel management for liner shipping networks under different fuel pricing scenarios and taking into consideration different fuel bunkering policies. The fuel consumption of a vessel on a sailing leg may fluctuate as the real vessel speed deviates from the planned vessel speed. Furthermore, fluctuation of fuel prices at various ports increases the complexity of bunkering decisions related to the selection of the bunkering ports and the estimation of bunkered fuel cost. We have developed a mixed integer non-linear programming model to minimize the total expected cost consisting of inventory cost related to container transportation, operating cost associated with ship hiring, as well as bunkering cost and fuel consumption cost at the port. The novelty of our research lies in its consideration of stochastic fuel consumption for different sailing legs, stochastic fuel prices at each port and different fuel bunkering policies to determine optimal bunker fuel management strategies for the selection of bunkering ports and for the estimation of the amount of bunkered fuel required. We have proposed a novel approximate algorithm based on mathematical formulation and the fuel bunkering policies to calculate the total expected cost; the fuel inventory while arriving at and departing from the port; the number of vessels hired for weekly service; the arrival and departure time of the ship; and the amount of fuel bunkered at a port. We have performed extensive computational experiments on the practical routes to demonstrate the applicability, efficacy and robustness of the proposed novel methodology.