One heuristic method to solve call center schedule problem

After thinking for a while, I find the following method may work

1. Divide a day into hourly block
2. Based on the predetermined performance measure, compute how many servers needed
3. Use these request of servers in each hour as demand, and then treat the whole schedule problem as LP

This method only suitable for the case that average service time is much less than an hour so that PSA(Pointwise Stationary Approximation) rule is fit. Otherwise, the interation among consecutive hours will destroy the whole formulation.