Mainline container shipping gets the headlines, but a large share of the world's boxes ride the last few hundred nautical miles on feeder vessels: smaller ships connecting hub ports to regional ports on tight rotations. Feeder economics are unforgiving. Margins are thin, port calls are expensive, schedules interlock with mainline arrivals that themselves slip, and a single missed connection can strand hundreds of containers for days.
The routing problem is correspondingly nasty. It is a vehicle routing problem where the depots move (mainline arrival times are stochastic), the demand is lumpy (a hub discharge is not a smooth flow), the time windows are hard (berth slots and tides), and the cost structure is dominated by fixed port call charges that reward consolidation and punish frequency. Deterministic schedules built on published mainline timetables are fiction within a week of the season starting.
What the stochastic formulation buys
Treat mainline arrivals as distributions, fitted per service and per port from AIS history and carrier performance, and the feeder rotation becomes a recourse problem: which port calls to fix, which to keep swappable, where to hold buffer against a late hub arrival, and when to run an extra sailing versus rolling cargo to the next rotation. The optimizer can weigh a schedule that saves one port call against the probability-weighted cost of the connections it puts at risk, which is the actual trade the planner faces every week.
Small ships, hard math.
Choose which ports the loop serves and size the vessel.
Dropping a small port shortens the loop and can still raise cost per TEU. The denominator moves too.
The hub interaction
Feeder routing cannot be solved in isolation, because the feeder network is the hub's shock absorber. When the mainline schedule degrades, a well-run feeder layer converts a systemic delay into a manageable one; a rigid feeder layer amplifies it into missed cutoffs across the region. This coupling is why we treat feeder optimization as part of network-level stochastic planning rather than a standalone tour problem. The mathematics is harder. So is the money: in a thin-margin trade, the operator whose rotations survive a bad week takes share from the operator whose rotations do not.