A Constraint Programming Approach for Solving a Queueing Control Problem

TL;DR

This paper introduces three novel constraint programming models and a hybrid approach to optimize worker switching policies in a stochastic queueing system, significantly improving solution quality and proving optimality for complex instances.

Contribution

It presents the first constraint programming models for queueing control problems, demonstrating their effectiveness and introducing a hybrid method combining heuristics and CP for better performance.

Findings

The CP model with closed-form expressions is most efficient.

The hybrid method matches heuristic solution quality and proves optimality.

The approach can solve many instances within reasonable time.

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 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.