This paper develops a mathematical model for post-disaster planning with human casualties, which can be considered as operational guidance for the proper use of emergency resources. For this purpose, a stochastic mixed-integer programming model is provided to formulate the problem. The objective functions of the model are (1) maximizing the survival probability of patients, (2) minimizing the maximum of completion time of treatment of all patients, and (3) minimizing the total cost of operations. The model is solved with the ϵ-constraint method. Due to the NP-hardness of the problem which is a significant challenge in the literature, two innovative meta-heuristic algorithms are proposed, i.e. a non-dominated sorting genetic algorithm (NSGA-II) and a multi-objective simulated annealing (MOSA). Finally, a comprehensive computational analysis is performed for evaluation purposes. Also, a case study is made on the earthquake in Iran, which illustrates the real-world application of the model.

Highlights

• A stochastic multi-objective mathematical programming model to allocate patients to hospitals and treat them.

• NSGA-II and MOSA are proposed, in addition to ϵ-constraint method as solution methods.

• Performance of two meta-heuristic algorithms is measured with five evaluation metrics.

• The study showed that NSGA-II is more effective than MOSA.

• The model was implemented on a real-world case, Tabriz earthquake in Iran.

本文建立了一个具有人员伤亡的灾后规划数学模型，可以作为正确使用应急资源的操作指南。为此，提供了一个随机混合整数规划模型来制定问题。该模型的目标函数是（1）最大化患者的生存概率，（2）最小化所有患者的最大治疗完成时间，以及（3）最小化总手术成本。该模型是用 ϵ-constraint 方法求解的。由于该问题的NP-hardness是文献中的一个重大挑战，因此提出了两种创新的元启发式算法，即非支配排序遗传算法（NSGA-II）和多目标模拟退火（MOSA） . 最后，为评估目的进行了全面的计算分析。此外，还对伊朗地震进行了案例研究，说明了该模型的实际应用。

强调

• 一种随机多目标数学规划模型，用于将患者分配到医院并进行治疗。

• 提出了 NSGA-II 和 MOSA，除了 ε-约束方法作为求解方法。

• 两种元启发式算法的性能是用五个评估指标来衡量的。

• 研究表明，NSGA-II 比 MOSA 更有效。

• 该模型是在伊朗大不里士地震的真实案例中实施的。