灾后不确定需求下应急医疗移动医院鲁棒选址问题研究

我国灾害医学救援主要采用"现场救治"模式，应急医疗移动医院的选址是否合理直接影响救援效率，但各受灾点伤员数量的不确定性增加了决策的困难。本文引入多面体不确定集合刻画伤员数量的不确定性，同时考虑伤员分类及移动医院分型，构建一个以伤员总生存概率最大化为目标的鲁棒选址模型。利用鲁棒优化理论，将模型转化为等价的混合整数规划问题，通过GAMS软件编程并调用CPLEX求解器求解。最后，以四川芦山地震应急医疗救援为例，验证模型和求解方法的可行性和鲁棒性。结果表明，扰动比例和不确定水平对移动医院的选址和伤员的分配方案有显著影响，决策者可根据自己对不确定性风险的偏好程度选择最佳的扰动比例和不确定水平组合，以获得最优的选址分配方案。

Emergency Medical Mobile Hospital Robust Location Problem in Post-disaster under Demand Uncertainty

The key of disaster medical rescue is to make casualties get treatment as soon as possible. If the rescue efficiency could be improved, the mortality caused by disaster would be reduced. Due to the complex natural environment, frequent natural disasters, large number of casualties and so on, disaster medical rescue in China mainly adopts the "on-site treatment" mode, in which the locations of emergency medical mobile hospitals directly affects the rescue efficiency. However, the uncertainty of casualties increases difficulty of location decision-making. Therefore, how to make a scientific and reasonable location decision of emergency medical mobile hospital under the condition of limited resources and uncertain information is the main problem of this paper. In view of this, a polyhedron uncertain sets is introduced to characterize the uncertainty of casualties. Meanwhile considering different types of casualties and mobile hospitals, a robust location model aiming at maximizing the total survival probability of casualties is established. Applying robust optimization theory, the model is transformed into an equivalent mixed integer programming problem, which is programmed by GAMS and solved by CPLEX solver. At last, a case study of emergency medical rescue of Sichuan Lushan earthquake is proposed to verify the feasibility and robustness of the model and solution method. The numerical results show that:(1) The disturbance proportion and uncertainty level have significant impacts on the location of mobile hospitals and the allocation of casualties. Decision makers could choose the best combination of disturbance proportion and uncertainty level according to their risk preference, so as to obtain the optimal location-allocation solution. (2) Although the optimal objective function value are different under different disturbance proportion and uncertainty level, there are only four location schemes, corresponding to nominal location scheme and location schemes with low, medium and high uncertainty respectively, which shows that the model has good robustness and could simplify the decision-making process of decision makers. (3) In the case of limited emergency resources and high level of uncertainty, the model will give priority to the treatment of life-threatening and serious wounded, and give up the treatment of some walking wounded, which is accord with the actual situation and humanitarianism. In summary, the model proposed in this paper could solve the emergency medical mobile hospital location problem under demand uncertainty, and provide auxiliary decision support for emergency management department.