Short-term liner shipping bunker procurement with swap contracts

The bunker price fluctuations in recent years have severely threatened the stability of liner shipping companies’ operations. As an efficient countermeasure, the swap contract is widely adopted throughout the liner shipping industry to hedge the procurement risk resulting from the bunker price fluctuation. This paper looks at the short-term liner shipping bunker procurement problem with swap contracts (BPPSC), aiming to optimally plan the amount of bunker purchased from the spot market and the amount hedged by the swap contract for several months ahead. This BPPSC is first formulated as a bunker procurement cost mean-variance minimization (MVM) model, and is subsequently solved using a tangible two-step approach developed in this study. In the first step, the movements of the swap contract price and the spot market price of the bunker are described using a calibrated multivariate generalized autoregressive conditional heteroskedasticity (mGARCH) time series model. In the second step, the MVM model is approximated and solved by a price scenario tree constructed from the mGARCH time series model. A numerical example shows that the risk hedging strategy obtained can simultaneously control the bunker procurement cost as well as the procurement risk from price fluctuations. This article is a revised and expanded version of the abridged eight-page paper entitled ‘Optimal hedging for liner bunker procurement’ presented at ‘2015 International Conference on Logistics and Maritime Systems (LOGMS 2015)’, Hong Kong, 27–29 August 2015.