A Constraint Programming Approach for Solving a Queueing Design and Control Problem

A facility with frontroom and backroom operations has the option of hiring specialized or cross-trained workers. Cross-trained workers can be switched between the two rooms depending on demand but are more expensive than specialized ones. Assuming stochastic customer arrival and service times, we seek a smallest-cost combination of cross-trained and specialized workers, together with a policy for switching the cross-trained workers between the rooms, which satisfies 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.