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The optimal stopping time for the collection of emergency materials for disaster relief operations

The purpose of this study is to explore the optimal stopping time in the process of collecting emergency materials for disaster-affected victims. In practice, the procedures of dealing with the collection of emergency materials can be wrong due to improper stopping control which could cause heavy losses of property, such as the significant amount of unnecessary wasteful redundancies of resources after the relief operations of some large-scale earthquakes in China. Based on the theory of optimal stopping, this paper builds a mathematical model to explore the optimal stopping time from a practical and realistic perspective. The proposed method considers two combined standards to obtain a more reasonable optimal stopping time for the collection of emergency materials. Under the proposed framework, a cost index related to the solution is introduced, which is combined with optimal stopping theory whereby the optimal point to terminate the collection of emergency materials is obtained. Compared with existing measures, the strength of the proposed models provide scientific methods to explore the optimal stopping point for the collection of emergency materials with a qualitative and quantitative approach. Exploring the optimal stopping time could help set up an effective emergency plan to practically reduce the effects of an earthquake disaster.