S : optimum speed in miles per day
R : voyage freight rate
p : price of fuel
k : ship’s fuel constant
d : distance
In addition to freight rates, the optimum speed depends on the price of fuel, the efficiency of the ship and the length of the voyage
a fleet of ships
10 VLCCs
age distribution of the fleet ranges from 2 to 20 years in intervals of 2 years
Ship 1 (the newest ship) : low daily operating costs => lay-up point is $155 per million ton miles
Ship 10 (the oldest): high operating costs = lay-up point is $165 per million ton miles
The fleet supply function works by moving ships in and out of service in response to freight rates
supply responds to movements in freight rates
Over a longer period, the supply can be increased by building new more efficient ships and reduced by scrapping old ones.