Can we use GA to find solution to a scheduling problem when the objective function (or fitness function) is stochastic in nature?

[Vikas Agrawal]

Hello All:

I am working on an assignment problem in a healthcare setting. Given a set of "operations" with their mean and std. deviation and a set of "operating room ", the objective it to assign these operations to given set of operating room in such a way that it will minimize the maximum time to complete all the operations.

My objective function is stochastic in nature since I will have to run a separate simulation to generate 1000 random values from the joint normal distribution of operations for each operating room and find the maximum and minimize that. 

Can GA be used under such scenarios? Or we must have deterministic objective function so that fitness scores stay same generation over generation if same candidate solution is chosen by elitism. 

Thanks,

Vikas