Abstract: In recent years, various frequently-occurred disasters has brought severe threats to human life and property security. As for the humanitarian-based emergency relief operations, in addition to the efficiency, effectiveness and equity issues, the impact of heterogeneous behaviors of emergency participants on the entire humanitarian relief decision-makings also draws much attention, such as the differentiated psychological pains or negative emotions suffered by victims in the face of disasters, or the diverse decision preferences shown by various decision-makers, etc.
The impact of heterogeneous behaviors on emergency relief operations is explored from two perspectives. On one hand, we focus on the psychological sufferings of different levels resulted from the unmet resource needs in time in the multi-stage emergency relief. By using the deprivation cost as economic loss valuation of the psychological sufferings, we quantitatively characterize diverse victims' pains or differentiated trauma and incorporate its effect into the social cost, i.e., the decision-making goal in emergency relief operations. On the other hand, in the decision-making process of post-disaster emergency resourcerouting-allocation, the joint chance-constrained programming is used to characterize decision-makers' requirements for the balance of multi-stage rescue supply and demand. By means of different confidence levels, we pay attention to different relief attitudes of decision-makers with heterogeneous preferences in post-disaster operational decisions. Combining with the dynamic balance constraints between supply and demand captured by the joint chance-constrained programming, a multi-stage post-disaster routing-allocation optimization model is built considering heterogeneous behaviors of victims and decision-makers, for minimizing the social costs composed of emergency transportation cost and heterogeneous psychological cost of victims.By taking 2008 WenChuan earthquake as a case, a genetic algorithm is applied for model solution. By combining real data with some set parameters, our model is compared with traditional emergency routing-allocation solutions without considering heterogeneous behaviors. Based on the analytical results, the effectiveness of our model and algorithm is verified. Besides, sensitivity analysis of key parameters is also performed, including relief frequency, number of rescue points, the waiting-time period of relief service, and heterogeneous preference of decision-makers.
Through model solving and parameter analysis, the following conclusions are demonstrated:(1) The traditional emergency decision-making models that do not consider the heterogeneous psychological sufferings of victims may only be suitable for the fast and efficient emergency relief operations.If the relief frequency is not fast enough, the impact of the victims' heterogeneous psychological sufferings cannot be ignored. (2) Compared with the traditional fixed penalty (FP) model, our routing and allocation (RAP)model has more advantages in rescue investment, rescue in time, and relief demand satisfaction.In particular, our emergency decision-making can give priority to rescue in severe disaster areas, mainly due to our consideration of the psychological sufferings of victims who have not been rescued in a timely manner.(3) In order to improve the efficiency in emergency relief operations, it is necessary to emphasize some prevention and control measures, such as increasing emergency resource investment and strengthening regional disaster-resistant capacityin the normal state of emergency management.As long as sufficient resources are available,the emergency needs can be met within a certain time limit.However, decision-makers still need to comprehensively think about whether it is worth investing in emergency resource, according to the marginal efficiency of resource investment in emergency relief decision-makings.Our research results provide some managerial suggestions for establishing an effective and efficient emergency relief system.

Key words: emergency, routing-allocation, heterogeneity, dynamics, genetic algorithm