A control-chart-based queueing approach for service facility maintenance with energy-delay tradeoff

Maintenance planning and energy consumption control are critical issues in facility operations management. In practice, the energy consumption of a facility, which will be affected by the operation condition, is closely connected with the associated maintenance policy. Specifically, for an energy-consuming service system, though a frequent maintenance activity can keep the facility in a good condition with low energy consumption, it makes the delay time longer and leads to a poor customer experience. In this paper, we study a single-server queueing system with different energy consumption levels in the associated running states to address the conflict between energy consumption and customer delay. Two types of maintenance activities are implemented for the server, i.e., the planned maintenance and the reactive maintenance. The planned maintenance is adopted based on a frequency parameter at the beginning of an idle period, and the reactive maintenance is initialized by the Shewhart's individual control chart (condition-based maintenance). To capture the energy-delay tradeoff, our objective is to develop an optimal maintenance policy that minimizes the long-run expected total cost of the system under a customer waiting time constraint. Numerical experiments are conducted to analyze the problem, in which useful managerial insights are obtained for the optimal maintenance policy. The results demonstrate the robustness of the proposed maintenance model, its advantage over the model without control chart, and its applicability in general situations.