I am trying to model a modified location-allocation problem where each facility acts as a M/M/s queuing system (similar to J Wang et al. 2020). The objective is to minimize the waiting time spent at each facility, and because of that, the problem becomes very non-linear.
where W is the expected waiting time, k (number of servers) and mu (service rate) are constants depending on j and s, while lambda (arrival rate) is part of the optimization and defined through many more constraints.
I'm having trouble defining W and P as constraints. Is this kind of problem something that Gurobi can solve? I've read that I can use Model.addGenConstrPow() for more general powers, but I'm not sure how I would implement it. If this is possible, how do I go about doing it? Else, are there suggestions of other methods I can use to solve the problem?
Any help is appreciated, thank you!
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