Abstract: 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.

Key words: emergency medical service, facility location, robust optimization, mixed integer programming, demand uncertainty