A stochastic multi-objective model based on the classical optimal search model for searching for the people who are lost in response stage of earthquake

Document Type : Article


1 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran

2 Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran

3 Department of Industrial Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran.


Although after an earthquake the injured person should be equipped with food, shelter and hygiene activities, before anything must be searched and rescued. But disaster management (DM) has focused heavily on emergency logistics and developing an effective strategy for search operations has been largely ignored. In this study, we suggest a stochastic multi-objective optimization model to allocate resource and time for searching the individuals who are trapped in disaster regions. Since in disaster conditions the majority of information is uncertain, our model assumes ambiguity for the locations where the missing people may exist. Fortunately, the suggested model fits nicely into the structure of the classical optimal search model. Hence, we use a stochastic dynamic programming approach to solve this problem. On the other hand, through a computational experiment, we have observed that this model needs heavy computation. Therefore, we reformulate the suggested search model as a multi-criteria decision making (MCDM) problem and employ two efficient MCDM techniques, i.e. TOPSIS and COPRAS to tackle this ranking problem. Consequently, the computational effort is decreased significantly and a promising solution is produced.


Main Subjects

1. Aldrich, D.P. \The power of people: social capital's role in recovery from the 1995 Kobe earthquake", Natural Hazards, 56(3), pp. 595-611 (2011). 2. Tseng, C.P. and Chen, C.W. \Natural disaster management mechanisms for probabilistic earthquake loss", Natural Hazards, 60(3), pp. 1055-1063 (2012). 3. Wei, Y.M., Jin, J.L., andWang, Q. \Impacts of natural disasters and disasters risk management in China: The case of China's experience in wenchuan earthquake", In Resilience and Recovery in Asian Disasters, Springer, Tokyo (2015). 4. Sagha_nia, M., Araghizade, H., Na_ssi, N., and Asadollahi, R. \Treatment management in disaster: A review of the Bam earthquake experience", Prehospital and Disaster Medicine, 22(6), pp. 517-521 (2007). 5. Lantada, N., Pujades, L.G., and Barbat, A.H. \Vulnerability index and capacity spectrum based methods for urban seismic risk evaluation: A comparison", Natural Hazards, 51, pp. 501-524 (2009). 6. Naghii, M.R. \Public health impact and medical consequences of earthquakes", Revista Panamericana de Salud P_ublica, 18(3), pp. 216-221 (2005). 7. Nateghi-A, F. \Earthquake scenario for the mega-city of Tehran", Disaster Prevention and Management: An International Journal, 10(2), pp. 95-100 (2001). 8. Kahn, M.E. \The death toll from natural disasters: the role of income, geography, and institutions", Review of Economics and Statistics, 87(2), pp. 271-284 (2005). 9. Lay, T. \The surge of great earthquakes from 2004 to 2014", Earth and Planetary Science Letters, 409, pp. 133-146 (2015). 10. Singh, A. \An overview of the optimization modelling applications", Journal of Hydrology, 466-467, pp. 167- 182 (2012). 11. Hou, L. and Shi, P. \Haiti 2010 earthquake - how to explain such huge loses", International Journal of Disaster Risk Science, 2(1), pp. 25-33 (2011). 12. Altay, N. and Green, W.G. \OR/MS research in disaster operations management", European Journal of Operational Research, 175(1), pp. 475-493 (2006). 13. Narayanan, R.G.L. and Ibe, O.C. \A joint network for disaster recovery and search and rescue operations", Computer Networks, 56(14), pp. 3347-3373 (2012). 14. Lien, Y.N., Jang, H.C., and Tsai, T.C. \A MANET based emergency communication and information system for catastrophic natural disasters", 29th IEEE International Conference on Distributed Computing Systems Workshops, Montreal, Canada, pp. 412-417 (2009). 15. Chang, S.E. and Nojima, N. \Measuring post-disaster transportation system performance: the 1995 Kobe earthquake in comparative perspective", Transportation Research Part A: Policy and Practice, 35(6), pp. 475-494 (2001). 16. Chen, L. and Miller-Hooks, E. \Optimal team deployment in urban search and Rescue", Transportation Research Part B: Methodological, 46(8), pp. 984-999 (2012). 17. Fiedrich, F., Gehbauer, F., and Rickers, U. \Optimized resource allocation for emergency response after earthquake disasters", Safety Science, 35(1-3), pp. 41-57 (2000). 18. Stone, L.D. \Search theory", In Encyclopedia of Operations Research and Management Science, Springer, Boston (2013). 19. Stone, L.D., Theory of Optimal Search, Academic Press, New York (1975). 20. Abounacer, R., Rekik, M., and Renaud, J. \An exact solution approach for multiobjective locationtransportation problem for disaster response", Computers and Operations Research, 41, pp. 83-93 (2014). 21. Black, W.L. \Discrete sequential search", Information and Control, 8(2), pp. 159-162 (1965). 22. Ross, S.M., Introduction to Stochastic Dynamic Programming, Academic Press, Amsterdam (1983). 23. Bellman, R. and Dreyfus, S., Applied Dynamic Programming, Princeton University Press, Princeton (1962). 24. Lazarev, A.A. and Werner, F. \A graphical realization of the dynamic programming method for solving NPhard combinatorial problems", Computers and Mathematics with Applications, 58(4), pp. 619-631 (2009). 25. Sadjadi, S.J., Aryanezhad, M.B., and Moghaddam, B.F. \A dynamic programming approach to solve e_cient frontier", Mathematical Methods Operations Research, 60(2), pp. 203-214 (2004). 26. Gutjahr, W.J. and Nolz, P.C. \Multicriteria optimization in humanitarian aid", European Journal of Operational Research, 252(2), pp. 351-366 (2016). 27. Bozorgi-Amiri, A., Jabalameli, M.S., and Mirzapour Al-e-Hashem, S.M.J. \A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty", OR Spectrum, 35(4), pp. 905-933 (2013). 28. Cervellera, C., Chen, V.C.P, and Wen, A. \Optimization of a large-scale water reservoir network by stochastic dynamic programming with e_cient state space discretization", European Journal of Operational Research, 171(3), pp. 1139-1151 (2006). 29. Garey, M.R. and Johnson, D.S., Computers and Intractability: A Guide to the Theory of NPCompleteness, W.H. Freeman and Company, New York (1979). 30. Afshar, A. and Haghani, A. \Modeling integrated supply chain logistics in real-time large-scale disaster relief operations", Socio-Economic Planning Sciences, 46(4), pp. 327-338 (2012). 31. Berkoune, D., Renaud, J., Rekik, M., and Ruiz, A. \Transportation in disaster response operations", Socio-Economic Planning Sciences, 46(1), pp. 23-32 (2012). 32. Naja_, M., Eshghi, K., and Dullaert, W. \A multiobjective robust optimization model for logistics planning in the earthquake response phase", Transportation Research Part E: Logistic and Transportation Review, 49(1), pp. 217-249 (2013). 33. Bozorgi-Amiri, A. and Asvadi, S. \A prioritization model for locating relief logistic centers using analytic hierarchy process with interval comparison matrix", Knowledge-Based Systems, 86, pp. 173-181 (2015). 34. Sheu, J.B. \An emergency logistics distribution approach for quick response to urgent relief demand in disasters", Transportation Research Part E: Logistics and Transportation Review, 43(6), pp. 687-709 (2007). 35. Ma, X., Song, Y., and Huang, J. \Min-max robust optimization for the wounded transfer problem in largescale emergencies", Control and Design Conference, Xuzhou, China, pp. 901-904 (2010). 36. Galindo, G. and Batta, R. \Review of recent developments in OR/MS research in disaster operations management", European Journal of Operational Research, 230(2), pp. 201-211 (2013). 37. Jotshi, A. and Batta, R. \Search for an immobile entity on a network", European Journal of Operational Research, 191(2), pp. 347-359 (2008). 38. Berger, J. and Lo, N. \An innovative multi-agent search-and-rescue path planning approach", Computers & Operations Research, 53, pp. 24-31 (2015). 39. Caunhye, A.M., Nie, X., and Pokharel, S. \Optimization model in emergency logistics: a literature review", Socio-Economic Planning Sciences, 46(1), pp. 4-13 (2012). 40. Hoyos, M.C., Morales, R.S., and Akhavan-Tabatabaei, R. \OR models with stochastic components in disaster operations management: A literature survey", Computers & Industrial Engineering, 82, pp. 183-197 (2015). 41. Koopman, B.O. \The theory of search, Part II. Target detection", Operations Research, 4(5), pp. 503-531 (1956). 42. Kress, M., Lin, K.Y., and Szechtman, R. \Optimal discrete search with imperfect speci_city", Mathematical Methods of Operations Research, 68(3), pp. 539-549 (2008). 43. Sadi-Nezhad, S., Sotoudeh-Anvari, A., and Khalili- Damghani, K. \A fuzzy optimal search approach: Real applications in crisis and mine detection", International Journal of Management and Decision Making, 13(3), pp. 318-334 (2014). 44. Kriheli, B. and Levner, E. \Search and detection of failed components in repairable complex systems under imperfect inspections", Mexican International Conference on Arti_cial Intelligence, San Luis Potos__, Mexico, pp. 399-410 (2013). 45. Benkoski, S.J., Monticino, M.G., and Weisinger, J.R. \A survey of the search theory literature", Naval Research Logistics, 38(4), pp. 469-494 (1991). 46. Washburn, A.R., Search and Detection, INFORMS, Maryland, USA (2002). 47. Assaf, D. and Zamir, S. \Continuous and discrete search for one of many objects", Operations Research Letters, 6(5), pp. 205-209 (1987). 48. Trummel, K.E. and Weisinger, J.R. \The complexity of the optimal searcher path problem", Operations Research, 34(2), pp. 324-327 (1986). 49. Gal, S., Search Games, Academic Press, New York (1980). 50. Chudnovsky, D.V. and Chudnovsky, G.V., Search Theory: Some Recent Developments, Marcel Dekker, New York (1989). 51. Chung, T.H., Hollinger, G.A., and Isler, V. \Search and pursuit-evasion in mobile robotics", Autonomous Robots, 31, pp. 299-316 (2011). 52. Chew, M.C. \A sequential search procedure", The Annals of Mathematical Statistics, 38(2), pp. 494-502 (1967). 53. Ross, S.M. \A problem in optimal search and stop", Operations Research, 17(6), pp. 984-992 (1969). 54. Smith, F.H. and Kimeldorf, G. \Discrete sequential search for one of many objects", Annals of Statistics, 3(4), pp. 906-915 (1975). 55. Wegener, I. \Optimal search with positive switch cost is NP-Hard", Information Processing Letters, 21(1), pp. 49-52 (1985). 56. Kadane, J.B. \Optimal discrete search with technological choice", Mathematical Methods of Operations Research, 81(3), pp. 317-336 (2015). 57. Zahl, S. \An allocation problem with applications to operations research and statistics", Operations Research, 11(3), pp. 426-441 (1963). 58. Kadane, J.B. \Discrete search and the neymanpearson lemma", Journal of Mathematical Analysis and Applications, 22(1), pp. 156-171 (1968). 59. Gutjahr, W.J. and Pichler, A. \Stochastic multiobjective optimization: a survey on non-scalarizing methods", Annals of Operations Research, 236(2), pp. 475-499 (2016). 60. Li, C., Liu, F., Cao, H., and Wang, Q. \A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system", International Journal of Production Research, 47(13), pp. 3657-3668 (2009). 61. Marescot, L., Chapron, G., Chad_es, I., and Fackler, P.L. \Complex decisions made simple: a primer on stochastic dynamic programming", Methods in Ecology and Evolution, 4(9), pp. 872-884 (2013). 62. Richardson, H.R. and Discenza, J.H. \The united states coast guard computer-assisted search planning system (CASP)", Naval Research Logistics Quarterly, 27(4), pp. 659-680 (1980). 63. Hwang, C.L. and Masud, A.S.M., Multiple Objective Decision Making Methods and Applications, Springer- Verlag, New York (1979). 64. Chinchuluun, A. and Pardalos, P.M. \A survey of recent developments in multiobjective optimization", Annals of Operations Research, 154(1), pp. 29-50 (2007). 65. Branke, J., Deb, K., Miettinen, K., and Slowi_nski, R., Multiobjective Optimization: Interactive and Evolutionary Approaches, Springer, Berlin (2008). 66. Li, R. and Leung, Y. \Multi-objective route planning for dangerous goods using compromise programming", Journal of Geographical Systems, 13(3), pp. 249-271 (2011). A. Sotoudeh-Anvari et al./Scientia Iranica, Transactions E: Industrial Engineering 26 (2019) 1842{1864 1863 67. Romero, C., Tamiz, M., and Jones, D.F. \Goal programming, compromise programming and reference point method formulations: Linkages and utility theorems", Journal of the Operational Research Society, 49(9), pp. 989-991 (1998). 68. Zeleny, M. \A concept of compromise solutions and the method of the displaced ideal", Computers & Operations Research, 1(3-4), pp. 479-496 (1974). 69. Azaron, A., Brown, K.N., Tarim, S.A., and Modarres, M. \A multi-objective stochastic programming approach for supply chain design considering risk", International Journal of Production Economics, 116(1), pp. 129-138 (2008). 70. Fangohr, H. \A comparison of C, MATLAB, and Python as teaching languages in engineering", International Conference on Computational Science, Baton Rouge, LA, USA, pp. 1210-1217 (2004). 71. Su, Z., Zhang, G., Liu, Y., Yue, F., and Jiang, J. \Multiple emergency resource allocation for concurrent incidents in natural disasters", International Journal of Disaster Risk Reduction, 17, pp. 199-212 (2016). 72.  Ozcan, T., C_ elebi, N., and Esnaf, S_. \Comparative analysis of multi-criteria decision making methodologies and implementation of a warehouse location selection problem", Expert Systems with Applications, 38(8), pp. 9773-9779 (2011). 73. Jahan, A. and Edwards, K.L. \A state-of-the-art survey on the inuence of normalization techniques in ranking: improving the materials selection process in engineering design", Materials & Design, 65, pp. 335- 342 (2015). 74. Lot_, F.H. and Fallahnejad, R. \Imprecise Shannon's entropy and multiple attribute decision making", Entropy, 12(1), pp. 53-62 (2010). 75. Sun, X. and Li, Y. \An intelligent multi-criteria decision support system for systems design", 10th AIAA Aviation Technology, Integration, and Operations (ATIO) Conference, Texas, USA, pp. 1-11 (2010). 76. Zanakis, S.H., Solomon, A., Wishart, N., and Dublish, S. \Multi-attribute decision making: a simulation comparison of select methods", European Journal of Operational Research, 107(3), pp. 507-529 (1998). 77. Vincke, P., Multiattributes Decision Aid, Wiley, New York (1992). 78. L_ken, E. \Use of multi criteria decision analysis methods for energy planning problems", Renewable and Sustainable Energy Reviews, 11(7), pp. 1584-1595 (2007). 79. Mela, K., Tiainen, T., and Heinisuo, M. \Comparative study of multiple criteria decision making methods for building design", Advanced Engineering Informatics, 26(4), pp. 716-726 (2012). 80. Chatterjee, P., Athawale, V.M., and Chakraborty, S. \Materials selection using complex proportional assessment and evaluation of mixed data methods", Materials & Design, 32(2), pp. 851-60 (2011). 81. Antucheviciene, J., Zakarevicius, A., and Zavadskas, E.K. \Measuring congruence of ranking results applying particular MCDM methods", Informatica, 22(3), pp. 319-338 (2011). 82. Huang, J.J., Tzeng, G.H., and Liu, H.H. \A revised VIKOR model for multiple criteria decision makingthe perspective of regret theory", 20th International Conference, MCDM 2009, Chengdu/Jiuzhaigou, China, pp. 761-768 (2009). 83. Mulliner, E., Malys, N., and Maliene, V. \Comparative analysis of MCDM methods for the assessment of sustainable housing a_ordability", Omega, 59, pp. 146- 156 (2016). 84. Peng, Y. \Regional earthquake vulnerability assessment using a combination of MCDM methods", Annals of Operations Research, 234(1), pp. 95-110 (2015). 85. Mousavi-Nasab, S.H. and Sotoudeh-Anvari, A. \A comprehensive MCDM-based approach using TOPSIS, COPRAS and DEA as an auxiliary tool for material selection problems", Materials & Design, 121, pp. 237- 253 (2017). 86. Athawale, V.M. and Chakraborty, S. \A comparative study on the ranking performance of some multicriteria decision-making methods for industrial robot selection", International Journal of Industrial Engineering Computations, 2(4), pp. 831-850 (2011). 87. Poorzahedy, H. and Rezaei, A. \Peer evaluation of multi-attribute analysis techniques: case of a light rail transit network choice", Scientia Iranica, 20(3) pp. 371-386 (2013). 88. Jahan, A., Bahraminasab, M., and Edwards, K.L. \A target-based normalization technique for materials selection", Materials & Design, 35, pp. 647-654 (2012). 89. Velasquez, M. and Hester, P.T. \An analysis of multicriteria decision making methods", International Journal of Operations Research, 10(2), pp. 56-66 (2013). 90. Millet, I. and Schoner, B. \Incorporating negative values into the analytic hierarchy process", Computers and Operations Research, 32(12), pp. 3163-3173 (2005). 91. Lai, S.K. \A preference-based interpretation of AHP", Omega, 23(4), pp. 453-462 (1995). 92. Hwang, C.L. and Yoon, K., Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag, New York (1981). 93. Mikaeil, R., Youse_, R., and Ataei, M. \Sawability ranking of carbonate rock using fuzzy analytical hierarchy process and TOPSIS approaches", Scientia Iranica, 18(5), pp. 1106-1115 (2011). 94. Sotoudeh-Anvari, A. and Sadi-Nezhad, S. \A new approach based on the level of reliability of information to determine the relative weights of criteria in fuzzy TOPSIS", International Journal of Applied Decision Sciences, 8(2), pp. 164-178 (2015). 95. Zavadskas, E.K., Kaklauskas, A., and Sarka, V. \The new method of multicriteria complex proportional assessment of projects", Technological and Economic Development of Economy, 1, pp. 131-139 (1994).