Bunkering decisions for a shipping liner in an uncertain environment with service contract

As bunker fuel cost constitutes a major portion of the shipping liners’ operating cost, it is imperative for them to minimize the bunkering cost to remain competitive. Service contract with a fuel supplier is a strategy they venture on to reduce this cost. Typically, liner operators enter into a contract with fuel suppliers where the contract is specified by a fixed fuel price and amount, to mitigate the fluctuating spot prices and uncertain fuel consumption between the ports. In this paper, we study such bunkering service contracts with known parameters and determine the liner's optimal bunkering strategy. We propose to use bunker up to level policy for refueling, where the up to level is dynamic based on the observed spot price and determine the bunkering decisions (where to bunker and how much to bunker) at the ports. A dynamic programming model is formulated to minimize the total bunkering cost. Due to the inherent complexity in determining the gradient of the cost-to-go function, we estimate it by Monte Carlo simulation. Numerical experiments suggest that all the contract parameters must be considered together in determination of the optimal bunkering strategy. Contracting an amount lesser than the average consumption for the entire voyage, at a contract price lesser than the average spot price is found to be beneficial. The insights derived from this study can be helpful in designing these types of service contracts.