Stochastic clearing theory has wide-spread applications in the context of supply chain and service operations management. Historical application domains include 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 revisit the notion of service performance for stochastic clearing system operation. More specifically, our goal is to evaluate and compare service performance of alternative operational policies for clearing decisions, as quantified by a measure of timely service referred to as Average Order Delay ( $AOD$ ). All stochastic clearing systems are subject to service delay due to the inherent clearing practice, and $\textrm {AOD}$ can be thought of as a benchmark for evaluating timely service. Although stochastic clearing theory has a long history, the existing literature on the analysis of $\textrm {AOD}$ as a service measure has several limitations. Hence, we extend the previous analysis by proposing a more general method for a generic analytical derivation of $\textrm {AOD}$ for any renewal-type clearing policy, including but not limited to alternative shipment consolidation policies in the previous literature. Our proposed method utilizes a new martingale point of view and lends itself for a generic analytical characterization of $\textrm {AOD}$ , leading to a complete comparative analysis of alternative renewal-type clearing policies. Hence, we also close the gaps in the literature on shipment consolidation via a complete set of analytically provable results regarding $\textrm {AOD}$ which were only illustrated through numerical tests previously.

中文翻译：

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随机清算系统服务绩效分析结果

随机清算理论在供应链和服务运营管理方面有着广泛的应用。历史应用领域包括批量服务队列、库存控制和运输计划（例如，车辆调度和装运整合）。在本文中，受装运合并中的基本应用的启发，我们重新审视了随机清算系统操作的服务性能概念。更具体地说，我们的目标是评估和比较清算决策的替代运营政策的服务绩效，通过称为及时服务的度量来量化平均订单延迟( $AOD$ ）。由于固有的清算做法，所有随机清算系统都会出现服务延迟，并且 $\textrm {AOD}$ 可以被认为是评估及时服务的基准。尽管随机清算理论有着悠久的历史，但现有的关于分析的文献 $\textrm {AOD}$ 作为一种服务措施有几个限制。因此，我们通过提出一种更通用的方法来扩展先前的分析 $\textrm {AOD}$ 适用于任何续订类型的清算政策，包括但不限于以前文献中的替代货运合并政策。我们提出的方法利用了一种新的鞅观点，并适用于对 $\textrm {AOD}$ ，从而对替代续订型清算政策进行了完整的比较分析。因此，我们还通过一套完整的可分析证明的结果来填补关于装运整合的文献中的空白。 $\textrm {AOD}$ 之前仅通过数值测试说明了这一点。