We study a variant of dynamic pickup and delivery crowd-shipping operation for delivering online orders within a few hours from a brick-and-mortar store. This crowd-shipping operation is subject to a high degree of uncertainty due to the stochastic arrival of online orders and crowd-shippers that impose several challenges for efficient matching of orders to crowd-shippers. We formulate the problem as a Markov decision process and develop an Approximate Dynamic Programming (ADP) policy using value function approximation for obtaining a highly scalable and real-time matching strategy while considering temporal and spatial uncertainty in arrivals of online orders and crowd-shippers. We incorporate several algorithmic enhancements to the ADP algorithm, which significantly improve the convergence. We compare the ADP policy with an optimization-based myopic policy using various performance measures. Our numerical analysis with varying parameter settings shows that ADP policies can lead to up to 25.2% cost savings and a 9.8% increase in the number of served orders. Overall, we find that our proposed framework can guide crowd-shipping platforms for efficient real-time matching decisions and enhance the platform delivery capacity.

中文翻译：

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众筹提货问题的近似动态规划


我们研究了一种动态取货和交付众包操作的变体，用于在几个小时内从实体店交付在线订单。由于在线订单和众包商的随机到达，这种众包操作具有高度的不确定性，这给订单与众包商的高效匹配带来了一些挑战。我们将问题表述为马尔可夫决策过程，并使用价值函数近似开发近似动态规划（ADP）策略，以获得高度可扩展和实时的匹配策略，同时考虑在线订单和众包商到达的时间和空间不确定性。我们对 ADP 算法进行了多项算法增强，显着提高了收敛性。我们使用各种性能指标将 ADP 策略与基于优化的短视策略进行比较。我们对不同参数设置的数值分析表明，ADP 策略可节省高达 25.2% 的成本，并使所服务的订单数量增加 9.8%。总的来说，我们发现我们提出的框架可以指导众包平台进行高效的实时匹配决策并增强平台的交付能力。