Optimising containership speed and fleet size under a carbon tax and an emission trading scheme

This paper addresses the problem of determining the ship speed, fleet size, and chartered ship number subject to environmental regulations consisting of a carbon tax and an emission trading scheme. The objective of the problem is to minimise bunker consumption cost, ship operating cost, ship charterage and either the carbon tax or the revenue/cost of selling/purchasing CO2 emissions permits. We formulate the problems as non-linear programmes by considering the two regulations independently. This study also suggests Lagrangian heuristics to solve the problems. A case study is performed to evaluate the applicability of the heuristics.