The route is the budget
Travelers usually pick cities first and order them by feel: fly into the famous one, end wherever the return flight is cheapest. But transport between cities is typically the second-largest cost line of a trip, and it is the one most sensitive to ordering. Lisbon → Seville → Porto → home crosses Iberia twice; Lisbon → Porto → Seville → home crosses it once. Same cities, same days, one leg fewer — often a three-digit saving per person before anyone has compared a hotel price.
The right mental model is the traveling-salesman problem with two twists: you do not have to return to the start (an open-jaw flight home from the last city is often cheaper than backtracking), and legs are not priced by distance alone. A 90-minute budget flight can cost less than a taxi; a 300-kilometer train on the wrong day can cost more than either.
What a machine checks that you will not
A human plans a route once. A good planner re-prices every permutation — and for five cities there are 120 of them. That is tedious for you and trivial for software, which is exactly the division of labor you want.
- Open-jaw by default: price flying home from the last city before assuming a loop.
- Mode per leg, not per trip: trains win under roughly 500 km city-center to city-center; flights win over water and over mountains.
- Day-of-week asymmetry: the same leg can differ 40% between Tuesday and Friday — sequencing decides which leg lands on which day.
- Diminishing returns: the fourth city in nine days costs you a half-day of transit for every day of presence. Sometimes the best route edit is deletion.
Days per city is a routing decision too
How long each city deserves depends on what you care about, not on its fame. A food-first traveler needs three evenings in San Sebastián and one afternoon in a cathedral town; a history-first traveler flips that. When day allocation is decided together with the route, the itinerary stops feeling rushed — pace, not coverage, is what people remember as a good trip.
This is why Pardal's Report explains every leg and every day count with a reason: cheaper Tuesday flight, museum density, your own stated pace. If the reasoning is visible, you can argue with it — swap a city, trade a day — and the plan re-prices around your edit instead of collapsing.