  In a facility with front room and back room operations, it is useful to
switch workers between the rooms in order to cope with changing customer
demand. Assuming stochastic customer arrival and service times, we seek a
policy for switching workers such that the expected customer waiting time is
minimized while the expected back room staffing is sufficient to perform all
work. Three novel constraint programming models and several shaving procedures
for these models are presented. Experimental results show that a model based on
closed-form expressions together with a combination of shaving procedures is
the most efficient. This model is able to find and prove optimal solutions for
many problem instances within a reasonable run-time. Previously, the only
available approach was a heuristic algorithm. Furthermore, a hybrid method
combining the heuristic and the best constraint programming method is shown to
perform as well as the heuristic in terms of solution quality over time, while
achieving the same performance in terms of proving optimality as the pure
constraint programming model. This is the first work of which we are aware that
solves such queueing-based problems with constraint programming.
