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Stochastic clearing theory has wide spread applications in the context ofsupply chain and service operations management. Historical application domainsinclude bulk service queues, inventory control, and transportation planning(e.g., vehicle dispatching and shipment consolidation). In this paper,motivated by a fundamental application in shipment consolidation, we revisitthe notion of service performance for stochastic clearing system operation.More specifically, our goal is to evaluate and compare service performance ofalternative operational policies for clearing decisions, as quantified by ameasure of timely service referred as \emph{Average Order Delay} ($AOD$). Allstochastic clearing systems are subject to service delay due to the inherentclearing practice, and $AOD$ can be thought of as a benchmark for evaluatingtimely service. Although stochastic clearing theory has a long history,existing literature on the analysis of $AOD$ as a service measure has severallimitations. Hence, we extend the previous analysis by proposing a more generalmethod for a generic analytical derivation of $AOD$ for any renewal-typeclearing policy, including but not limited to alternative shipmentconsolidation policies in the previous literature. Our proposed method utilizesa new martingale point of view and lends itself for a generic analyticalcharacterization of $AOD$, leading to a complete comparative analysis ofalternative renewal-type clearing policies. Hence, we also close the gaps inliterature on shipment consolidation via a complete set of analyticallyprovable results regarding $AOD$ which were only illustrated through numericaltests previously.

Analytical Results on the Service Performance of Stochastic Clearing Systems