We consider a logistics planning problem of prepositioning relief commodities in preparation for an impending hurricane landfall. We model the problem as a multi-period network flow problem where the objective is to minimize the total expected logistics cost of operating the network to meet the demand for relief commodities. We assume that the hurricane’s attributes evolve over time according to a Markov chain model, and the demand quantity at each demand point is calculated based on the hurricane’s attributes (intensity and location) at the terminal stage, which corresponds to the hurricane’s landfall. We introduce a fully adaptive multi-stage stochastic programming (MSP) model that allows the decision-maker to adapt their logistics decisions over time according to the evolution of the hurricane’s attributes. In addition, we develop a novel extension of the standard MSP model to address the challenge of having a random number of stages in the planning horizon due to the uncertain landfall time of the hurricane. We benchmark the performance of the adaptive decision policy given by the MSP models with alternative decision policies, including a static policy, a rolling-horizon policy, a wait-and-see policy, and a decision-tree-based policy, all based on two-stage stochastic programming models. Our numerical results and sensitivity analyses provide key insights into the value of MSP in the hurricane disaster relief logistics planning problem.

中文翻译：

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具有随机阶段数的多阶段随机规划：在飓风救灾物流规划中的应用


我们考虑了一个物流规划问题，即预先部署救援商品，为即将到来的飓风登陆做准备。我们将问题建模为多周期网络流问题，其目标是最小化运营网络的总预期物流成本，以满足对救济商品的需求。我们假设飓风的属性根据马尔可夫链模型随时间演变，并且每个需求点的需求量是根据飓风在终端阶段的属性（强度和位置）计算的，这与飓风的登陆相对应。我们引入了一个完全自适应的多阶段随机规划 （MSP） 模型，该模型允许决策者根据飓风属性的演变随着时间的推移调整他们的物流决策。此外，我们还开发了标准 MSP 模型的新扩展，以解决由于飓风登陆时间的不确定性而在规划范围内具有随机阶段数的挑战。我们将 MSP 模型给出的自适应决策策略的性能与替代决策策略进行基准测试，包括静态策略、滚动视野策略、观望策略和基于决策树的策略，所有这些都基于两阶段随机规划模型。我们的数值结果和敏感性分析为 MSP 在飓风救灾物流规划问题中的价值提供了关键见解。