Solving a Stochastic Queueing Design and Control Problem with Constraint Programming

A facility with front room and back room operations has the option of hiring specialized or, more expensive, cross-trained workers. Assuming stochastic customer arrival and service times, we seek a smallest-cost combination of cross-trained and specialized workers satisfying constraints on the expected customer waiting time and expected number of workers in the back room. A constraint programming approach using logic-based Benders’ decomposition is presented. Experimental results demonstrate the strong performance of this approach across a wide variety of problem parameters. This paper provides one of the first links between queueing optimization problems and constraint programming.