This study investigates how a hinterland consignee (importer) makes decisions regarding the storage of empty containers for reuse by a shipper (exporter). The system is modeled as a double-ended queue with non-zero matching times, limited truck resources, and both consignee and shipper having fixed withholding capacities. The consignee’s withholding threshold is strategically set to minimize overall transport and detention costs. We derive closed-form expressions for performance measures in the case of a single storage facility at the shipper, utilizing a matrix-based approach. We extend this methodology numerically to the general case. Additionally, we present an accurate fixed-point approximation facilitating the determination of performance measures and optimal threshold. Our findings show the importance of withholding decisions in import and balanced areas for cost reduction. In export areas, a policy of full reuse proves nearly optimal. Analyzing dynamic state-dependent consignee decisions via a Markov decision process, we establish that the optimal policy involves withholding thresholds increasing with stored quantity at the shipper. While optimal, state-dependent thresholds yield limited cost savings compared to a fixed threshold, suggesting minimal impact from consignee-shipper information sharing. Additionally, we examine the influence of variability in matching and production times, observing decreased costs with reduced variability, particularly in export areas, but with minor impacts on withholding decisions.

中文翻译：

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如何优化集装箱扣留决策以便在内陆地区重复使用？

本研究调查了内陆收货人（进口商）如何做出有关存储空集装箱以供托运人（出口商）重复使用的决策。该系统被建模为双端队列，匹配时间非零，卡车资源有限，收货人和托运人都有固定的扣留能力。收货人的预扣税门槛经过战略性设置，以最大限度地降低总体运输和滞留成本。我们利用基于矩阵的方法，在托运人的单个存储设施的情况下得出性能测量的封闭式表达式。我们将这种方法在数值上扩展到一般情况。此外，我们提出了准确的定点近似，有助于确定性能指标和最佳阈值。我们的研究结果表明，在进口和平衡领域保留决策对于降低成本的重要性。在出口领域，充分再利用的政策被证明几乎是最佳的。通过马尔可夫决策过程分析动态的状态相关收货人决策，我们确定最佳策略涉及预扣阈值随着托运人存储数量的增加而增加。虽然最佳的、与状态相关的阈值与固定阈值相比产生的成本节省有限，这表明收货人-托运人信息共享的影响最小。此外，我们还研究了匹配和生产时间变异性的影响，观察到成本随着变异性的降低而降低，特别是在出口地区，但对扣留决策的影响较小。