A seismic-risk-based bi-objective stochastic optimization framework for the pre-disaster allocation of earthquake search and rescue units

Year 2024, Volume: 4 Issue: 3, 370 - 394, 30.09.2024

Nadi Serhan Aydın

https://doi.org/10.53391/mmnsa.1517843

Abstract

Accurately predicting earthquakes' time, location and size is nearly impossible with today’s technology. Severe earthquakes require prompt and effective mobilization of available resources, as the speed of intervention has a direct impact on the number of people rescued alive. This, in turn, calls for a strategic pre-disaster allocation of search and rescue (SAR) units, both teams and equipment, to make the deployment of resources as quick and equitable as possible. In this paper, a seismic risk-based framework is introduced that takes into account distance-based contingencies between cities. This framework is then integrated into a mixed-integer non-linear programming (MINLP) problem for the allocation of SAR units under uncertainty. The two minimization objectives considered are the expected maximum deployment time of different SAR units and the expected mean absolute deviation of the fulfillment rates. We recover the best vulnerability-adjusted routes for each size-location scenario as input to the optimization model using the dynamic programming (DP) approach as part of the broader area of reinforcement learning (RL). The results of the hypothetical example indicate that the comprehensive model is feasible in various risk scenarios and can be used to make allocation-deployment decisions under uncertainty. The results of the sensitivity analysis verify that the model behaves reasonably against changes in selected parameters, namely the number of allowed facilities and weights of individual objectives. Under the assumption that the two objectives are equally important, the model achieves a total deviation of %3.5 from the objectives with an expected maximum dispatch time of 1.1327 hours and an expected mean absolute deviation of 0.01.

Keywords

Earthquake response, SAR units allocation, mixed-integer nonlinear programming (MINLP), stochastic optimization, dynamic programming

References

• [1] World Health Organization (WHO), Earthquakes, (2024). https://www.who.int/ health-topics/earthquakes#tab=tab_1
• [2] Schweier, C. Geometry based estimation of trapped victims after earthquakes. In Proceedings International Symposium on Strong Vrancea Earthquakes and Risk Mitigation, pp. 4-6, Bucharest, Romania, (2007, October).
• [3] Weber, M. Rural areas may suffer disproportionately in quakes. Temblor, (2020).
• [4] Noji, E.K. The public health consequences of disasters. Prehospital and Disaster Medicine, 15(4), 21-31, (2000).
• [5] Kunkle, R. Medical care of entrapped patients in confined spaces. In Proceedings, International Workshop on Earthquake Injury Epidemiology: Implications for Mitigation and Response, pp. 338-344, Baltimore, Maryland, USA, (1989, July).
• [6] Ahmadi, G., Tavakkoli-Moghaddam, R., Baboli, A. and Najafi, M. A decision support model for robust allocation and routing of search and rescue resources after earthquake: a case study. Operational Research, 22, 1039–1081, (2022).
• [7] Klibi, W., Ichoua, S. and Martel, A. Prepositioning emergency supplies to support disaster relief: a case study using stochastic programming. INFOR: Information Systems and Operational Research, 56(1), 50-81, (2018).
• [8] Chiu, Y.Y., Omura, H., Chen, H.E. and Chen, S.C. Indicators for post-disaster search and rescue efficiency developed using progressive death tolls. Sustainability, 12(19), 8262, (2020).
• [9] Condeixa, L.D., Leiras, A., Oliveira, F. and De Brito Jr, I. Disaster relief supply pre-positioning optimization: A risk analysis via shortage mitigation. International Journal of Disaster Risk Reduction, 25, 238-247, (2017).
• [10] Arnette, A.N. and Zobel, C.W. A risk-based approach to improving disaster relief asset pre-positioning. Production and Operations Management, 28(2), 457-478, (2019).
• [11] Caunhye, A.M., Nie, X. and Pokharel, S. Optimization models in emergency logistics: A literature review. Socio-Economic Planning Sciences, 46(1), 4-13, (2012).
• [12] Kaveh, A., Javadi, S.M. and Moghanni, R.M. Emergency management systems after disastrous earthquakes using optimization methods: A comprehensive review. Advances in Engineering Software, 149, 102885, (2020).
• [13] Boonmee, C., Arimura, M. and Asada, T. Facility location optimization model for emergency humanitarian logistics. International Journal of Disaster Risk Reduction, 24, 485-498, (2017).
• [14] Chen, L. and Miller-Hooks, E. Optimal team deployment in urban search and rescue. Transportation Research Part B: Methodological, 46(8), 984-999, (2012).
• [15] Döyen, A., Aras, N. and Barbaroso˘glu, G. A two-echelon stochastic facility location model for humanitarian relief logistics. Optimization Letters, 6, 1123-1145, (2012).
• [16] Zhang, L., Liu, T. and Huang, J. Relief equipment layout model for natural disaster with uncertain demands. In Proceedings, 2009 International Conference on Management and Service Science, pp. 1-4, Beijing, China, (2009, September).
• [17] Ghasemi, P., Khalili-Damghani, K., Hafezalkotob, A. and Raissi, S. Stochastic optimization model for distribution and evacuation planning (A case study of Tehran earthquake). SocioEconomic Planning Sciences, 71, 100745, (2020).
• [18] Mohammadi, R., Ghomi, S.F. and Jolai, F. Prepositioning emergency earthquake response supplies: A new multi-objective particle swarm optimization algorithm. Applied Mathematical Modelling, 40(9-10), 5183-5199, (2016).
• [19] Paul, J.A. and MacDonald, L. Location and capacity allocations decisions to mitigate the impacts of unexpected disasters. European Journal of Operational Research, 251(1), 252-263, (2016).
• [20] Zhang, S., Guo, H., Zhu, K., Yu, S. and Li, J. Multistage assignment optimization for emergency rescue teams in the disaster chain. Knowledge-Based Systems, 137, 123-137, (2017).
• [21] Vahdani, B., Veysmoradi, D., Shekari, N. and Mousavi, S.M. Multi-objective, multi-period location-routing model to distribute relief after earthquake by considering emergency roadway repair. Neural Computing and Applications, 30, 835-854, (2018).
• [22] Khayal, D., Pradhananga, R., Pokharel, S. and Mutlu, F. A model for planning locations of temporary distribution facilities for emergency response. Socio-Economic Planning Sciences, 52, 22-30, (2015).
• [23] Sebatli, A., Cavdur, F. and Kose-Kucuk, M. Determination of relief supplies demands and allocation of temporary disaster response facilities. Transportation Research Procedia, 22, 245-254, (2017).
• [24] Aghaie, S. and Karimi, B. Location-allocation-routing for emergency shelters based on geographical information system (ArcGIS) by NSGA-II (case study: Earthquake occurrence in Tehran (District-1)). Socio-Economic Planning Sciences, 84, 101420, (2022).
• [25] Tirkolaee, E.B., Aydın, N.S., Ranjbar-Bourani, M. and Weber, G.W. A robust bi-objective mathematical model for disaster rescue units allocation and scheduling with learning effect. Computers & Industrial Engineering, 149, 106790, (2020).
• [26] Wex, F., Schryen, G., Feuerriegel, S. and Neumann, D. Emergency response in natural disaster management: Allocation and scheduling of rescue units. European Journal of Operational Research, 235(3), 697-708, (2014).
• [27] Fiedrich, F., Gehbauer, F. and Rickers, U. Optimized resource allocation for emergency response after earthquake disasters. Safety Science, 35(1-3), 41-57, (2000).
• [28] Sharif, S.V., Moshfegh, P.H. and Kashani, H. Simulation modeling of operation and coordination of agencies involved in post-disaster response and recovery. Reliability Engineering & System Safety, 235, 109219, (2023).
• [29] Chen, W. and Zhang, L. An automated machine learning approach for earthquake casualty rate and economic loss prediction. Reliability Engineering & System Safety, 225, 108645, (2022).
• [30] Zhang, L. and Cui, N. Pre-positioning facility location and resource allocation in humanitarian relief operations considering deprivation costs. Sustainability, 13(8), 4141, (2021).
• [31] Edrisi, A. and Askari, M. Probabilistic budget allocation for improving efficiency of transportation networks in pre-and post-disaster phases. International Journal of Disaster Risk Reduction, 39, 101113, (2019).
• [32] Bommer, J.J., Stafford, P.J., Alarcón, J.E. and Akkar, S. The influence of magnitude range on empirical ground-motion prediction. Bulletin of the Seismological Society of America, 97(6), 2152-2170, (2007).
• [33] Menichini, G., Nistri, V., Boschi, S., Del Monte, E., Orlando, M. and Vignoli, A. Calibration of vulnerability and fragility curves from moderate intensity Italian earthquake damage data. International Journal of Disaster Risk Reduction, 67, 102676, (2022).
• [34] Lallemant, D., Kiremidjian, A. and Burton, H. Statistical procedures for developing earthquake damage fragility curves. Earthquake Engineering & Structural Dynamics, 44(9), 1373-1389, (2015).
• [35] Sutton, R.S. and Barto, A.G. Reinforcement Learning: An Introduction. MIT Press: USA, (2018).