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I am working on an OR scheduling problem where OR opening cost is considered a fixed cost when a surgery is scheduled. If OR is used beyond a certain time, overtime cost is incurred.

I would like to know how the ratio affects the problem difficulty. I understand that for ridiculously higher OR opening costs, one would try to first minimize the number of ORs open. What happens in other cases? How does a solver perceive this?

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    $\begingroup$ Using "OR" for "operating room" on an Operations Research forum is an invitation to confusion -- especially for older folks like me. (We confuse easily.) :-) $\endgroup$
    – prubin
    Commented Mar 3, 2022 at 20:48

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If by "problem difficulty" you mean how much time / how many nodes are required to solve the problem, I don't know that the effect of the ratio can be anticipated. I would not be surprised if extremely high or extremely low ratios made for easier problems (fewer nodes worth looking at), while some intermediate ratio might bring the objective values of high- and low-overtime solutions closer to each other, forcing more nodes to be explored. That's just a guess.

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