Cruise call clustering

Why do four cruise ships crowd one small port on a Tuesday morning and none of them appear on Wednesday?

A small harbour town wakes on Tuesday to four ships at once: long tender queues, a shuffling line along the one cliff path, restaurants out of everything by two. On Wednesday the quay is empty and those restaurants sit idle.

The usual explanations are that the lines arranged it, or that the port sold the day to the highest bidders. But pause on the incentives. A cruise line's product on a port day is a pleasant morning ashore, and four ships in one bay wreck it — coaches run short, the good sites are mobbed, satisfaction scores come back bruised. Every one of those four would rather have been there alone. So how does an outcome nobody wants arrive so reliably, and on the same weekday, year after year?

Begin with the unit the product is sold in. A cruise is overwhelmingly a seven-night thing, and that is not a maritime fact — it is a fact about the buyer, whose leave, school holidays and flights are organised in weeks. Seven nights means the ship returns to its home port on a fixed weekday, and turnaround consumes a whole day: several thousand people off, the ship stored and fuelled and cleaned, several thousand on. So one weekday in seven belongs to the homeport, and it is the same weekday every week, because the inbound flights, the crew changes and the provisioning contracts are all built around it.

Now the shape of the days between, just as constrained. Passengers want daylight ashore, so the ship arrives around seven in the morning and sails around five, leaving the dark hours for moving. Fourteen hours between sailing and arrival, minus manoeuvring, pilotage and a margin, gives roughly thirteen hours of open-sea steaming. At a typical eighteen knots, that is a little over two hundred and thirty nautical miles.

Notice what has happened to the map. A ship cannot arrive at an arbitrary distance from the last port; it arrives at a whole number of overnight hops. Ports sort themselves into rings around a homeport — a first at roughly two hundred-odd miles, a second at twice that — and a port falling between rings either gets a slow passage or is not called at all.

Put the two constraints together and the answer falls out with nobody coordinating anything. Every ship on a seven-night loop from the same homeport leaves on the same weekday. Every one covers roughly the same distance each night, because they are shaped by the same daylight window and the same fuel curve. Therefore every one reaches the second-ring island on the same weekday — not because they conferred, but because they solved an identical problem under identical constraints and got the identical answer.

Would competition not push them apart? Only if a line could move without losing something. Shifting a day means either sailing the leg in daylight, which spends a port day at sea, or moving the turnaround off its weekend, which breaks the flight bookings. The cost of deviating is concentrated and immediate; the benefit — an emptier quay — is shared with competitors who did not. So each line does the individually sensible thing and the fleet collides.

There is a quieter second reason it is not competed away: nobody holds the lever that would spread it. Berths at small ports are commonly allocated by request and precedent, first come, at fees that do not vary with the day — and a price higher on Tuesday than Wednesday would do the work directly, but small ports compete hard for calls and fear charging a ship away.

The conspiracy reading and the venality reading both point the wrong way. A port maximising fees would want calls spread across the week, since a spread earns the same money with less congestion and better spend ashore; and lines colluding would have colluded on something that benefited them. What we have instead is emergence — a pattern produced by independent actors under shared constraints, an explanation that needs no decision-maker in it.

Next, a correction to my own arithmetic. Two hundred and thirty nautical miles is illustrative, assembled from typical inputs — an eighteen-knot passage and a thirteen-hour night — not a measured average, and both vary by ship, sea state and route. I would decline to state fleet-wide speeds, port fees or passenger counts, which differ by source and definition. What survives is the quantisation, not the number: whatever the hop length is, distance is consumed in nightly units, and that turns a continuous map into a set of rings.

Worth adding, because it cuts against the intuition that the industry is diversifying: fuel burn rises steeply with speed, so lines have converged on economical passage speeds — and converging on a speed tightens the rings and sharpens the clustering. The efficiency measure and the crowding have one cause.

Two complications. Itineraries are not all seven nights; ten and fourteen-night loops drift against the weekly pattern, which is why a port's calendar has structure rather than one spike. And some clustering really is demand-led. The geometric account explains the base pattern, not every peak.

What would refute it? The account predicts a port's crowded weekday is derivable from the turnaround days of the homeports feeding it and its distance from them in whole overnight hops — so a port fed from two homeports with different turnaround days should show two distinct busy days, and two ports at the same ring distance from one homeport should peak together. Find crowded days spread evenly through the week, or two equidistant ports on the same circuit peaking three days apart, and the geometry is not what is driving it.

Every term the collection defines is gathered in the glossary.