Liner service string design
How a weekly container string is sized: round-voyage time divided by seven, the integer step function in ship count, and what a speed cut costs in tonnage.
A liner service string is the fixed rotation of ports served at a published frequency by a set number of ships. Sizing it is the arithmetic that decides whether a speed reduction actually saves money on a scheduled service.
A weekly service needs one ship on berth in each port every seven days, so the number of ships required is the round-voyage time in days divided by seven, rounded up, where round-voyage time is the round-trip distance divided by the service speed plus total port and canal time. On an Asia to North Europe loop of about 21,000 nautical miles with about 14 days in port and canals, that gives nine ships at 18 knots, ten at 16 knots and eleven at 14 knots.
The consequence is that the cost of slowing is a step function, because the ship count is an integer. There are speed bands within which a further knot costs no additional tonnage at all, and boundaries at which one further knot costs a whole ship’s capital and operating cost. That is why carriers cut speed in coordinated moves across an entire string rather than ship by ship, and why the same fuel saving is worth different amounts on either side of a boundary. See slow steaming and container ship .