Abstract In this paper we consider a distribution planning problem in a transshipment network under stochastic customer demand, to account for uncertainty faced in real-life applications when planning distribution activities. To date, considerations of randomness in distribution planning networks with intermediate facilities have received very little attention in the literature. We address this gap by modeling uncertainty in a distribution network with an intermediate facility, and providing insight on the benefit of accounting for randomness at the distribution planning phase. The problem is studied from the perspective of a third-party logistics provider (3PL) that is outsourced to handle the logistics needs of its customers; the 3PL uses a consolidation center to achieve transportation cost savings. We formulate a two-stage stochastic programming model with recourse that aims to minimize the sum of transportation cost, expected inventory holding cost and expected outsourcing cost. The recourse variables ensure that the problem is feasible regardless of the realization of demand, by allowing the option of using a spot market carrier if demand exceeds capacity. We propose a flow-based formulation with a nonlinear holding cost component in the objective function. We then develop an alternative linear path-based formulation that models the movement of freight in the network as path variables. We apply Sample Average Approximation (SAA) to solve the problem, and show that it results in reasonable optimality gaps for problem instances of different sizes. We conduct extensive testing to evaluate the benefits of our proposed stochastic model compared to its deterministic counterpart. Our computational experiments provide managerial insight into the robustness and cost-efficiency of the distribution plans of our proposed stochastic model, and the conditions under which our model achieves significant distribution cost savings.

中文翻译：

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转运网络中具有随机需求和资源的分配计划

摘要在本文中，我们考虑了在随机客户需求下的转运网络中的分销计划问题，以解决在计划分销活动时实际应用中面临的不确定性。迄今为止，在具有中间设施的配电计划网络中对随机性的考虑在文献中很少受到关注。我们通过对带有中间设施的分销网络中的不确定性进行建模，并在分配计划阶段就考虑随机性的好处提供了见解，从而解决了这一差距。从第三方物流供应商（3PL）的角度研究该问题，该第三方物流供应商将其处理来满足其客户的物流需求；3PL使用整合中心来节省运输成本。我们制定了一种具有资源的两阶段随机规划模型，旨在最小化运输成本，预期库存持有成本和预期外包成本之和。资源变量通过允许在需求超过容量时选择使用现货市场载体来确保无论需求如何实现，该问题都是可行的。我们提出了一种基于流量的公式，该公式在目标函数中具有非线性持有成本成分。然后，我们开发一种基于线性路径的替代公式，该模型将网络中的货物移动建模为路径变量。我们应用样本平均逼近度（SAA）来解决该问题，并表明对于不同大小的问题实例，它会导致合理的最优差距。与确定性模型相比，我们进行了广泛的测试，以评估我们提出的随机模型的优势。我们的计算实验为我们提出的随机模型的分配计划的鲁棒性和成本效率提供了管理方面的见识，并为我们的模型在很大程度上节省了分配成本的条件下提供了管理依据。