- Every order of your cities is enumerated. Six cities is 720 orders, seven is 5,040. A must-start or must-end city cuts the list before anything is priced.
- For each order, a small dynamic program walks the window day by day and picks the cheapest stay length in every city, inside the minimum and maximum nights you set.
- Prices come from a matrix that already holds every city pair on every day of your window, built from two free fare grids before the optimizer runs — so “one more night here for a cheaper flight there” is decided on real fares, not a per-route average.
- Ties are nudged toward using your whole window instead of collapsing every city to its minimum. The nudge is deliberately tiny — under a dollar across the whole trip, however long the window — so any real fare difference wins outright.
- The three cheapest orders are kept. The recommended one is priced leg by leg with a live search; the runners-up get their long-haul legs checked so the comparison is honest.
- Order chosen
- Dallas → London → Paris → Budapest → Athens → Rome → Madrid → Dallas
- Flights, per person
- $1,214
- Runner-up order
- $1,215, a dollar more
- Third order kept
- $1,236, $22 more
- Nights it picked
- 3 in Athens, 2 in each of the other five, inside a 2–3 range
On this trip the top two orders came out a dollar apart, and the plan prints that rather than dressing it up: here the order barely mattered and you can pick on taste. The gap is what you are being told, and it grows with the number of cities and the slack in your window.
- Two cities and fixed dates leaves almost nothing to optimise. The win grows with the number of cities and the slack in your window.
- Locking the order, or pinning a start and end city, means you are asking for a specific trip rather than the cheapest one. Legitimate — the plan just costs more.
- Nights are allocated from departure dates at day granularity, so the night spent on an overnight transatlantic leg is charged to the city you have not landed in yet. The optimizer solves in those terms, because that is what your own minimums are expressed in — but the calendar file, the printed sheet and the itinerary card all count from the flights instead, and say so where the two differ.
- More than seven cities is not supported: the number of orders grows faster than any budget for pricing them.
One booking, normal rules. Nothing here can be taken away from you.