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First time asking question, apologies if incorrect.

What would be the best way to approach this problem (Similar to travelling salesman, but I'm not sure if it runs into the same issues).

You have a list of "tasks" at certain locations (Cities) and a group of "people" that can complete those tasks (Salesmen). This is structured over a day, where some tasks may need to be completed before a specific time and may require specific "tools" (Set number available). The difference is that the length between each location is the same in all circumstances, but they all have to return to the start. Therefore, rather than trying to minimise the distance travelled, instead you want to maximise the time each salesmen spends moving and stays at the initial staring node. This also gives you pre-defined requirements.

The program doesn't need to find an optimal solution, just an acceptable one (Greater than a certain value.) Would you just bash out each case? If so, what would be the best language to use for bashing out the solutions?

Thanks

EDIT - Just to confirm, the pre-requisite where all the cities are the same distance from each other is just for simplification of the problem, not reflective of real life.

Lukas123213
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    "if the cities were all the same distances from each other?". Once you hit four cities, I don't think that's possible of a two-dimensional grid so you need to move to three dimensions (three cities are okay since you can make an equilateral triangle). As you add more and more cities, you will need more dimensions to maintain this property. How many dimensions are you allowed to *have?* :-) – paxdiablo Oct 06 '20 at 02:56
  • @paxdiablo can you do it with 4? I would have thought 3 was the limit – Evert Oct 06 '20 at 03:07
  • When all the edge weights in the undirected graph are the same, I think this might devolve into finding a [Hamiltonian path](https://en.wikipedia.org/wiki/Hamiltonian_path). – concision Oct 06 '20 at 04:41
  • @Evert, three cities in two dimensions is a equilateral triangle and, yes, that's the limit. Four cities in three dimensions is a triangular pyramid (each face being an equilateral triangle). I guess the next step would be four dimensions with a triangular hyper-pyramid with each hyper-face being a triangular pyramid. After that, ... oops, it appears my brain just exploded :-) – paxdiablo Oct 06 '20 at 04:50
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    @paxdiablo thank you! I actually misread your original comment and it all makes sense now =) – Evert Oct 06 '20 at 04:55

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