Energy-saving policies for temperature-controlled production systems with state-dependent setup times and costs

There are numerous practical examples of production systems with servers that require heating in order to process jobs. Such production systems may realize considerable energy savings by temporarily switching off the heater and building up a queue of jobs to be processed later, at the expense of extra queueing costs. In this paper, we optimize this trade-off between energy and queueing costs. We model the production system as an M/G/1 queue with a temperature controlled server that can only process jobs if a minimum production temperature is satisfied. The time and energy required to heat a server depend on its current temperature, hence the setup times and setup costs for starting production are state dependent. We derive the optimal policy structure for a fluid queue approximation, called a wait-heat-clear policy. Building upon these insights, for the M/G/1 queue we derive exact and approximate costs for various intuitive types of wait-heat-clear policies. Numerical results indicate that the optimal wait-heat-clear policy yields average cost savings of over 40% compared to always keeping the server at the minimum production temperature. Furthermore, an encouraging result for practice is that simple heuristics, depending on the queue length only, have near-optimal performance.