A dual-index rule for managing temporary congestion

Recent work in healthcare operations provide empirical evidence for the deterioration of service quality due to congestion. Motivated by these findings, we formulate a novel scheduling problem to study how a service provider should prioritize jobs in order to mitigate the impact of temporary congestion-related issues. We analyze the model and show that the optimal policy can be interpreted as a dynamic priority rule that operates in two phases. When the system is overloaded, it is optimal to process jobs according to an index that generalizes Smith’s rule by incorporating the congestion cost. Once the system is no longer overloaded, Smith’s rule becomes optimal. However, the decision about which job to process earlier versus later appears to be challenging (we establish a polynomial time reduction from the partition problem). Our work shows that to respond to congestion, the decision maker should deviate from default scheduling practices and adjust jobs’ urgency at times of congestion to account for potential congestion-related costs. This increases the priority that should be given to shorter jobs (which reduces the time the system is congested), while still taking into account other job characteristics.