I’m trying to reduce a real world problem to something that might be solvable by folks who know more about strange maths than I do.
Workers A, B, C, D, E, and F are based out of a central office. They need to schedule meetings in a time period with customers around the country, to which they will most likely fly. They want to optimize their travel.
This sounds like a Traveling Salesman Problem (TSP), but it gets weird:
Because they are a flying, not all paths between nodes are available.
Paths are also restricted temporally, as flights availability is limited, more or less so depending on the airport.
To make matters worse, due to differing expertise among the workers, different combinations of workers are required at different meetings. E.g., the meeting in LA may require workers A and B, but the meeting in Chicago requires workers A, C, and F.
Finally, the customers have limited availability.
Is there an established way of solving this sort of problem? Does this problem have a name? Are there commercial products that help with this? Searching for “travel optimization software” brings up many hits, IBM being a prominent one, but they don’t quite seem to address this scenario.
Note that I said the workers want to “optimize” their travel. That’s a bit intangible. They first need to fit all the meetings into their schedule. Then they want to minimize travel time. But then they probably want to avoid any variety of travel headaches, e.g. wrong-coast meetings on Monday and Friday, travel to Fairbanks in January vs March (as if that’s much better), flights at uncomfortable times, etc.