Suppose you plan to visit a region in a foreign country, and you need to decide where to stay.(adsbygoogle = window.adsbygoogle || []).push({});

You're going to stay for a week, and don't fancy moving from town to town with your luggage.

So you prefer to find a hotel in one appropriately chosen location, and you'll do round-trips to the places you want to visit each day.

My question is: what's the best way to select the hotel location?

I guess the answer depends on what objective you want to achieve.

For instance, you may want to minimise thetimespent travelling or thedistancetravelled; and that either on a daily basis or on the total over your stay (if it makes a difference, which I'm not sure about).

Suppose the places you want to visit are 5 points on the map.

Assume that for any point X on the map corresponding to a hotel you can easily calculate the shortest travel time and road distance to each of the 5 places.

How would you go about estimating the 'best' X?

Would you start from the centroid of the 5 points and optimise from there?

Is the best X necessarily only one, or could one find multiple ones?

Can the best X be close (in time or space) to most places and far from one or two of them, or is it always going to be 'centrally' located?

Do you know if there is already an algorithm that does this, for instance in GPS navigation systems?

Thank you!

L

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# Where to stay?

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