In stochastic programming, the correlation gap is the worst-case ratio between the cost when the random variables are correlated to the cost when the random variables are independent.
If no students attend, then the teacher can stay at home and his cost is 0.
This is a stochastic-programming problem, because the constraints are not known in advance – only their probabilities are known.
[1] prove that the correlation gap is bounded in several cases.
For example, suppose we have a stochastic programming problem with a submodular cost function.
If we just ignore the correlation and solve the problem as if the variables are independent, the resulting solution is a