The cost of the last mile ★

The economics of networks is fascinating. One recurring feature is the costly last mile. I’m borrowing this term from telecommunications, where it refers to the final part of the network, which actually reaches the consumer—e.g. the copper cables that carry your ADSL services from the exchange. Most ‘transport’ (loosely interpreted to include electricity, water, internet) benefits from economies of scale. For example, a bus fare is less than a taxi fare for the same route in part because the cost of the driver’s time is divided between 50 passengers rather than 4. For this reason, transport networks tend to be planned as (or evolve to) a branching structure—think the hub & spoke structure of US airlines—with very high capacity ‘trunk’ routes and lower capacity branches.

A consequence of this structure is that the high-capacity trunks, although expensive in per-distance terms, are very cheap in terms of units-carried-per-distance. The edges of the network tend to be cheap in per-distance terms, but very expensive in units-carried-per-distance—in part because they carry relatively few units, and in part because they tend to traverse difficult, expensive territory (e.g. power transmission lines cut straight swathes through the air above forests and farmland, whereas distribution lines follow city grids and may even be buried in expensive underground trenches).

A second consequence is that there tends to be much more of the edge-network than of the trunk-network. For example, my home state of Queensland has 14,000km of high voltage transmission network but 200,000km of distribution network. It’s hard to find a good estimate, but it seems like an average Queensland house needs something like 3000 feet of electrical wiring, or around 1km. At the 2011 census, Queensland had 1.8m private dwellings, so the total amount of in-building wiring is likely on the order of 2 million km. So there is a an order of magnitude increase in distance covered as we move towards the edge of the network.

These two consequences combine to make the last mile relatively costly: both costly in a unit sense that a consumer would care about, and costly in an aggregate sense that a government might care about (because there is so much of it).

This fact was driven home to me quite forcefully recently when I shipped some possessions from London to Washington DC. I shipped around 100 cu ft of items, and the base quote was around £1000 ($US 1500). When I finally found a flat in DC, it was on the third floor, and it turned out the original quote was only up to the 2nd floor. The movers insisted on a $50 extra charge to go to the 3rd floor, which seemed insane since the building has an elevator in any case. The extra moving distance was, say, 3m, on a 6000km journey—or one 2-millionth part extra. The extra cost was $50 / $1500, or 1/30th extra. It seemed like straightforward overcharging—by a factor of 100,000—but was it?

I’ve been meaning to do this calculation for a while.

The table below takes an incredibly simplistic view, accounting only for the labour involved in my shipment. As you can see, the total labour in moving 100 cu ft from central London to central Washington was around 3 hours. At $1500, my shipment cost $500/hour, or $8/minute (this alone should signal to us that labour is not the most important cost, but we’ll keep playing the game anyway…). Let’s generously say the elevator took an extra 3 seconds to travel from the 2nd to the 3rd floor, and there were 10 trips. Then the extra floor cost 30 seconds, or around $4. So perhaps the extra floor charge is off by a factor of 10, not a factor of 100,000.

A more accurate model would of course include capital costs (container ships aren’t cheap, nor are ports), fuel costs and non-transport labour costs (repackaging, customs processing, admin, etc.). And then the $50 charge probably looks even worse.

But still, it’s remarkable that perhaps somewhere between 1/3 and 2/3 of the labour time in moving my possessions 6000km from London to DC was the time spent at my home, on either end. That’s the cost of the last mile.