Solving a Stochastic Queueing Control Problem with Constraint Programming

In this paper, a retail facility which has front room and back room operations, and crosstrained workers, is considered. In particular, it is of interest to the facility to determine optimal times for switching workers between the two rooms under stochastic customer arrival so that expected customer waiting time is minimized, but all work in the back room is performed. Three constraint programming models and several shaving procedures that can be used in conjunction with 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 runtime. 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 finding and proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such stochastic problems with constraint programming.