Solving a Stochastic Queueing Control Problem with Constraint Programming

Authors:
Daria Terekhov;J. Christopher Beck
Affiliations:
Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada;Department of Mechanical and Industrial Engineering, University of Toronto, Toronto, Ontario, Canada
Venue:
CPAIOR '07 Proceedings of the 4th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2007

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Abstract

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 a shaving algorithm are presented. Experimental results show that the best constraint programming model, using shaving, is able to find and prove optimal solutions for almost all problem instances within a reasonable run-time, but that an existing heuristic algorithm performs better in terms of solution quality over time. A hybrid method combining the heuristic and the best constraint programming method is shown to perform better than either of these approaches separately. This is the first work of which we are aware that solves a queueing control problem with constraint programming.