Evacuation shelters, which are urgently required during natural disasters, are designed to minimize the burden of evacuation on human survivors. However, the larger the scale of the disaster, the more costly it becomes to operate shelters. When the number of evacuees decreases, the operation costs can be reduced by moving the remaining evacuees to other shelters and closing shelters as quickly as possible. On the other hand, relocation between shelters imposes a huge emotional burden on evacuees.In this study, we formulate the "Evacuation Shelter Scheduling Problem," which allocates evacuees to shelters in such a way to minimize the movement costs of the evacuees and the operation costs of the shelters. Since it is difficult to solve this quadratic programming problem directly, we show its transformation into a 0-1 integer programming problem. In addition, such a formulation struggles to calculate the burden of relocating them from historical data because no payments are actually made. To solve this issue, we propose a method that estimates movement costs based on the numbers of evacuees and shelters during an actual disaster. Simulation experiments with records from the Kobe earthquake (Great Hanshin-Awaji Earthquake) showed that our proposed method reduced operation costs by 33.7 million dollars: 32%.

Evacuation shelters, which are urgently required during natural disasters, are designed to minimize the burden of evacuation on human survivors. However, the larger the scale of the disaster, the more costly it becomes to operate shelters. When the number of evacuees decreases, the operation costs can be reduced by moving the remaining evacuees to other shelters and closing shelters as quickly as possible. On the other hand, relocation between shelters imposes a huge emotional burden on evacuees.In this study, we formulate the "Evacuation Shelter Scheduling Problem," which allocates evacuees to shelters in such a way to minimize the movement costs of the evacuees and the operation costs of the shelters. Since it is difficult to solve this quadratic programming problem directly, we show its transformation into a 0-1 integer programming problem. In addition, such a formulation struggles to calculate the burden of relocating them from historical data because no payments are actually made. To solve this issue, we propose a method that estimates movement costs based on the numbers of evacuees and shelters during an actual disaster. Simulation experiments with records from the Kobe earthquake (Great Hanshin-Awaji Earthquake) showed that our proposed method reduced operation costs by 33.7 million dollars: 32%.2 https://www.bousai.metro.tokyo.lg.jp/ bousai/1000026/1000316.html (accessed June 14, 2021)3 On January 17, 1995, a major earthquake of magnitude 6.9 occurred in southern Hyogo Prefecture, Japan. Buildings were severely damaged, mainly in Kobe City, and about 300 fires broke out. A total of 6,434 people were killed. https://en.wikipedia. org/wiki/Great_Hanshin_earthquake (accessed June 14, 2021)4 We used the exchange rate in January 1995: 100 yen to one dollar. 5 For example, in the earthquake off the coast of Fukushima Prefecture on February 13, 2021, no fatalities were confirmed, 70 evacuation centers were opened, and 120 people were evacuated.https://www.asahi.com/articles/ ASP2F7XHXP2FDIFI00D.html