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.

中文翻译：

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用于管理临时拥塞的双索引规则


最近在医疗保健运营方面的工作为拥堵导致服务质量恶化提供了经验证据。在这些发现的启发下，我们制定了一个新的调度问题，以研究服务提供商应该如何优先考虑工作，以减轻临时拥堵相关问题的影响。我们分析了该模型，并表明最佳策略可以解释为分两个阶段运行的动态优先级规则。当系统过载时，最好根据一个索引来处理作业，该索引通过合并拥塞成本来推广 Smith 规则。一旦系统不再过载，史密斯规则就成为最佳规则。然而，关于早处理和晚处理哪个作业的决定似乎很有挑战性（我们从分区问题中建立了多项式时间减少）。我们的研究表明，为了应对拥堵，决策者应该偏离默认的调度做法，并在拥堵时调整作业的紧迫性，以考虑潜在的拥堵相关成本。这增加了应优先考虑较短作业的优先级（从而减少系统拥塞的时间），同时仍考虑其他作业特征。