While discussing who wants to sit next to whom in a new office I wondered if this isn't some kind of general class of problems that can be helped by software.

Imagine we have X employees and Y rooms and e1 prefers to be with e2 who prefers equally e3 and e1 and e2 dislikes e4 a bit and room r1 has a capacity of only 2 people while r2 and r3 can hold 3... etc. pp. with some additional constraints which could all be modelled somehow.

That could as well be applied to storage room management or many other szenarios. I imagine that some of them have several equally good solutions.

How is this class of problems called? What should I google for? Is there software which accepts a simple set of rules and can calculate the best solutions?

  • You could probably ask at Mathematics Meta what this class of problem is called. I am unsure if it would be on topic at the main Mathematics site, but Meta should help you. – Mawg Sep 14 at 10:13

These are Constrained optimization problems can be furthered classified according to the nature of the constraints (e.g., linear, nonlinear, convex).

The constraints on the variables can vary widely from simple bounds to systems of equalities and inequalities that model complex relationships among the variables.

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