Cross-docking is a strategy to facilitate a persistent process from suppliers to the consumer points, without long-term storage of products at a distribution warehouse. Products are collected from various origins by inbound trucks, unloaded to the cross-dock, reconsolidated with other products, and finally loaded onto outbound trucks within the same or next day. Because of the limited number of dock-doors as the main resources and the uncertain arrival time of trucks at the cross-dock, queue problems in such environments are unavoidable. This study considers a vehicle routing problem (VRP) for a multi-door cross-docking system with a queuing approach. A real application of the proposed model can be found in congestion conditions at the cross-docking yard, when the queuing time of the vehicles (i.e., the queuing delay) may reduce the quality of service. Moreover, in some cases, improper queue management at a facility such as a cross-dock may incur an economic cost associated with the waiting time in the queue. In this study, we focus on the receiving doors of a cross-dock and assume that the rate of truck arrivals at the cross-dock is a random variable. Moreover, the cross-dock is not able to provide service to all vehicles simultaneously; it has some limitations such as capacity constraints and service time restrictions. Thus, an M/M/c queuing formulation is proposed to model this cross-docking environment, in which the vehicles’ dispatch plan for starting the pickup process would also be determined. In the proposed multi-channel queuing system, the arrival flow of trucks to the cross-docking terminal can be deemed as a Poisson process, resulting in a nonlinear mathematical formulation to optimize the problem. The model is then linearized. To handle its computational complexity, we develop a new Genetic Algorithm (GA) to obtain near-optimal solutions to the problem and compare them with those of the optimization software GAMS. Then, a sensitivity analysis is done on different parameters of the model, and their effect on transportation cost and waiting cost of vehicles in the queue is investigated. The results show that considering a queuing approach in this problem, even for a small-scale problem derived from a real case study, can improve the average waiting time of trucks in the queue considerably compared with the situation in which all parameters are assumed deterministic.

交叉对接是一种促进从供应商到消费者点的持续过程的策略，无需在分销仓库长期存储产品。产品由入库卡车从各个来源收集，卸载到交叉码头，与其他产品重新整合，最终在同一天或次日内装上出库卡车。由于作为主要资源的码头门数量有限，并且卡车到达交叉码头的时间不确定，在这种环境下排队问题是不可避免的。本研究考虑了采用排队方法的多门交叉对接系统的车辆路径问题 (VRP)。该模型的实际应用可以在交叉对接场的拥堵情况下找到，此时车辆的排队时间（即排队延迟）可能会减少 服务质量。此外，在某些情况下，在诸如跨站台之类的设施中不当的队列管理可能会导致与队列中的等待时间相关的经济成本。在这项研究中，我们专注于交叉码头的接收门，并假设卡车到达交叉码头的速度是一个随机变量。此外，跨站台无法同时为所有车辆提供服务；它有一些限制，例如容量限制和服务时间限制。因此，提出了 M/M/c 排队公式来模拟这种交叉对接环境，其中也将确定车辆开始取货过程的调度计划。在提出的多通道排队系统中，货车到越库码头的到达流量可视为泊松过程，产生非线性数学公式来优化问题。然后将模型线性化。为了处理其计算复杂性，我们开发了一种新的遗传算法 (GA) 来获得问题的近乎最优解，并将它们与优化软件 GAMS 的解进行比较。然后，对模型的不同参数进行敏感性分析，研究它们对排队车辆的运输成本和等待成本的影响。结果表明，与假设所有参数都是确定性的情况相比，在该问题中考虑排队方法，即使对于源自真实案例研究的小规模问题，也可以显着改善队列中卡车的平均等待时间。为了处理其计算复杂性，我们开发了一种新的遗传算法 (GA) 来获得问题的近乎最优解，并将它们与优化软件 GAMS 的解进行比较。然后，对模型的不同参数进行敏感性分析，研究它们对排队车辆的运输成本和等待成本的影响。结果表明，与假设所有参数都是确定性的情况相比，在该问题中考虑排队方法，即使对于源自真实案例研究的小规模问题，也可以显着改善队列中卡车的平均等待时间。为了处理其计算复杂性，我们开发了一种新的遗传算法 (GA) 来获得问题的近乎最优解，并将它们与优化软件 GAMS 的解进行比较。然后，对模型的不同参数进行敏感性分析，研究它们对排队车辆的运输成本和等待成本的影响。结果表明，与假设所有参数都是确定性的情况相比，在该问题中考虑排队方法，即使对于源自真实案例研究的小规模问题，也可以显着改善队列中卡车的平均等待时间。对模型的不同参数进行了敏感性分析，研究了它们对排队车辆的运输成本和等待成本的影响。结果表明，与假设所有参数都是确定性的情况相比，在该问题中考虑排队方法，即使对于源自真实案例研究的小规模问题，也可以显着改善队列中卡车的平均等待时间。对模型的不同参数进行了敏感性分析，研究了它们对排队车辆的运输成本和等待成本的影响。结果表明，与假设所有参数都是确定性的情况相比，在该问题中考虑排队方法，即使对于源自真实案例研究的小规模问题，也可以显着改善队列中卡车的平均等待时间。