The 'optimal transportation' is misleading in this case : People are not interchangeable, so you are actually trying to find a map between the space of { peopl

The 'optimal transportation' is misleading in this case : People are not interchangeable, so you are actually trying to find a map between the space of { people who have to go places } and {routes they might take } . Once everybody has chosen a route, there is a measure on the space of routes. The cost of each route to each person depends on the measure on the route space. Once you have this pairing of measures, you can ask if it's optimal or not.