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2020, 16(5): 2369-2387.
doi: 10.3934/jimo.2019058
Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case
| 1. | Faculty of Engineering and Sciences, Universidad Diego Portales, Av. Ejercito 441, Santiago Centro, Santiago, Chile |
| 2. | Diagonal Las Torres 2300, Santiago, Chile |
Emergency logistics is crucial to ameliorate the impact of large earthquakes on society. We present a modeling framework to assist decision makers in strategic and tactical planning for effective relief operations after an earthquake's occurrence. The objective is to perform these operations quickly while keeping its total expenses under a budget. The modeling framework locates/allocates resources in potentially affected zones, and transportation capacity is dynamically deployed in those zones. Demand uncertainty is directly incorporated through an impulse stochastic process. The novelty of this approach is threefold. It incorporates temporo-spatial dependence and demands heterogeneity. It incorporates the availability of transportation capacity at different zones. It incorporates tight budget constraints that precludes the total satisfaction of demands. The resulting model is a large size stochastic mixed-integer programming model, which can be approximately solved through Sample Average Approximation. An example is provided and a thorough sensitivity analysis is performed. The numerical results suggest that that the response times are highly sensitive to the availability of inventory at each period. In addition, all logistics parameters (except for inventory capacity) have approximately the same impact on the total response time. The elasticity for all these parameters indicate constant returns to scale.
Keywords:
OR in disaster relief,
OR in developing countries,
humanitarian logistics,
stochastic programming,
distribution.
Mathematics Subject Classification:
Primary: 90C15, 90C11; Secondary: 90B15.
Citation:
Rodrigo A. Garrido, Ivan Aguirre. Emergency logistics for disaster management under spatio-temporal demand correlation: The earthquakes case. Journal of Industrial and Management Optimization,
2020, 16
(5)
: 2369-2387.
doi: 10.3934/jimo.2019058
![]()
References:
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M. Ahmadi, A. Seifi and B. Tootooni,
A humanitarian logistics model for disaster relief operation considering network failure and standard relief time: A case study on san francisco district, Transportation Research Part E: Logistics and Transportation Review, 75 (2015), 145-163.
doi: 10.1016/j.tre.2015.01.008. |
| [2] |
A. R. Akkihal, Inventory Pre-positioning for Humanitarianoperations, Master's thesis, Massachusetts Institute of Technology, USA, 2006. |
| [3] |
D. Alem, A. Clark and A. Moreno,
Stochastic network models for logistics planning in disaster relief, European Journal of Operational Research, 255 (2016), 187-206.
doi: 10.1016/j.ejor.2016.04.041. |
| [4] |
N. Altay and W. G. Green Ⅲ,
Or/ms research in disaster operations management, European Journal of Operational Research, 175 (2006), 475-493.
doi: 10.1016/j.ejor.2005.05.016. |
| [5] |
T. Anagnos and A. Kiremidjian,
A review of earthquake occurrence models for seismic hazard analysis, Probabilistic Engineering Mechanics, 3 (1988), 3-11.
doi: 10.1016/0266-8920(88)90002-1. |
| [6] |
J. G. Anderson and M. D. Trifunac, On uniform risk functionals which describe strong earthquake ground motion: Definition, numerical estimation, and an application to the fourier amplitude spectrum of acceleration, Report CE 77-02 University of Southern California, Los Angeles, U.S.A., 1977. |
| [7] |
J. G. Anderson and M. D. Trifunac,
Uniform risk functionals for characterization of strong earthquake ground motion, Bulletin of the Seismological Society of America, 68 (1978), 205-218.
|
| [8] |
A. Ben-Tala, B. Do Chung, S. R. Mandala and T. Yao,
Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains, Transportation Research Part B: Methodological, 45 (2011), 1177-1189.
doi: 10.1016/j.trb.2010.09.002. |
| [9] |
C. Boonmee, M. Arimura and T. Asada,
Facility location optimization model for emergency humanitarian logistics, International Journal of Disaster Risk Reduction, 24 (2017), 485-498.
doi: 10.1016/j.ijdrr.2017.01.017. |
| [10] |
A. M. Caunhyea, X. Niea and S. Pokharel,
Optimization models in emergency logistics: A literature review, Socio-Economic Planning Sciences, Special Issue: Disaster Planning and Logistics: Part 1, 46 (2012), 4-13.
doi: 10.1016/j.seps.2011.04.004. |
| [11] |
C. A. Cornell,
Engineering seismic risk analysis, Bulletin of the Seismological Society of America, 58 (1968), 1583-1606.
|
| [12] |
A. Coskun, W. Elmaghraby, M. Karaman and F. S. Salman, Relief aid stocking decisions under bilateral agency cooperation, Socio-Economic Planning Sciences, 2018.
doi: 10.1016/j.seps.2018.10.009. |
| [13] |
V. Del Gaudio and J. Wasowski,
Time probabilistic evaluation of seismically induced landslide hazard in irpinia (southern italy), Soil Dynamics and Earthquake Engineering, 24 (2004), 915-928.
|
| [14] |
F. Fiedrich, F. Gehbauer and U. Rickers,
Optimized resource allocation for emergency response after earthquake disasters, Safety Science, 35 (2000), 41-57.
doi: 10.1016/S0925-7535(00)00021-7. |
| [15] |
G. Galindo and R. Batta,
Review of recent developments in or/ms research in disaster operations management, European Journal of Operational Research, 230 (2013), 201-211.
doi: 10.1016/j.ejor.2013.01.039. |
| [16] |
R. A. Garrido, Optimal emergency resources deployment under a terrorist threat: The hazmat case and beyond, In Handbook of OR/MS Models in Hazardous Materials Transportation, International Series in Operations Research and Management Science, chapter 8, pages 245–267. Springer, New York, 2013.
doi: 10.1007/978-1-4614-6794-6_8. |
| [17] |
R. A. Garrido and P. Lamas, Optimal logistics and transportation decisions for emergency response to natural disasters, In World Academy of Science, Engineering and Technology 76, chapter 8, pages 201–213. WASET, Johannesburg, South Africa, 2013. |
| [18] |
R. A. Garrido, P. Lamas and F. J. Pino,
A stochastic programming approach for floods emergency logistics, Transportation Research Part E: Logistics and Transportation Review, 75 (2015), 18-31.
doi: 10.1016/j.tre.2014.12.002. |
| [19] |
I. D. Gupta,
Probabilistic seismic hazard analysis method for mapping of spectral amplitudes and other design-specific quantities to estimate the earthquake effects on man-made structures, ISET Journal of Earthquake Technology, 44 (2007), 127-167.
|
| [20] |
J. Holguin-Veras, N. Pérez, S. Ukkusuri, T. Wachtendorf and B. Brown,
Emergency Logistics Issues Affecting the Response to Katrina: A Synthesis and Preliminary Suggestions for Improvement, Transportation Research Record: Journal of the Transportation Research Board, 2022 (2007), 76-82.
doi: 10.3141/2022-09. |
| [21] |
E. L. Krinitzsky,
Earthquake probability in engineering – part 1: The use and misuse of expert opinion: The third richard h. jahns distinguished lecture in engineering geology, Engineering Geology, 33 (1993), 257-288.
doi: 10.1016/0013-7952(93)90030-G. |
| [22] |
J. Luedtke and S. Ahmed,
A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
| [23] |
E. Mas, A. Suppasri, Sh. Koshimura and F. Imamura,
Agent based simulation of the 2011 great east japan earthquake tsunami evacuation procedure. introduction to an integrated model of tsunami inundation and evacuation, Journal of Natural Disaster Science, 34 (2012), 41-57.
|
| [24] |
T. Matisziw, A. Murray and T. Grubesic,
Strategic network restoration, Networks and Spatial Economics, 10 (2010), 345-361.
doi: 10.1007/s11067-009-9123-x. |
| [25] |
R. K. McGuire,
Seismic design spectra and mapping procedures using hazard analysis based directly on oscillator response, Earthquake Engineering and Structural Dynamics, 5 (1977), 211-234.
doi: 10.1002/eqe.4290050302. |
| [26] |
A. Nemirovski and A. Shapiro,
Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2007), 969-996.
doi: 10.1137/050622328. |
| [27] |
L. Ozdamar, D. Tuzun-Aksu, E. Yasa and B. Ergunes,
Disaster relief routing in limited capacity road networks with heterogeneous flows, Journal of Industrial and Management Optimization, 14 (2018), 1367-1380.
doi: 10.3934/jimo.2018011. |
| [28] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro,
Sample average approximation method for chance constrained programming: Theory and applications, Journal of Optimization Theory and Applications, 142 (2009), 399-416.
doi: 10.1007/s10957-009-9523-6. |
| [29] |
B. Papazachos, E. E. Papadimitriou, A. A. Kiratzi, Ch. A. Papaioannou and G. F. Karakaisis,
Probabilities of occurrence of large earthquakes in the aegean and surrounding area during the period 1986–2006, Pure and Applied Geophysics, 125 (1987), 597-612.
doi: 10.1007/BF00879574. |
| [30] |
B. C. Papazachos, Ch. A. Papaioannou, V. N. Margaris and N. P. Theodulidis,
Seismic hazard assessment in greece based on strong motion duration, Proceedings of the Tenth World Conference on Earthquake Engineeing, 2 (1992), 425-430.
|
| [31] |
T. Parsons,
Recalculated probability of m greater than 7 earthquakes beneath the sea of marmara, turkey, Journal of Geophysical Research, 109 (2004), 1-21.
|
| [32] |
T. Parsons,
Significance of stress transfer in time-dependent earthquake probability calculations, Journal of Geophysical Research: Solid Earth, 110 (2005), 1978-2012.
doi: 10.1029/2004JB003190. |
| [33] |
M. Peng, Y. Peng and H. Chen,
Post-seismic supply chain risk management: A system dynamics disruption analysis approach for inventory and logistics planning, Computers & Operations Research, Special issue Multiple Criteria Decision Making in Emergency Management, 42 (2014), 14-24.
doi: 10.1016/j.cor.2013.03.003. |
| [34] |
D. Richardson, S. de Leeuw and I. F. A. Vis, Conceptualising inventory prepositioning in the humanitarian sector, In Luis M. Camarinha-Matos, Xavier Boucher, and Hamideh Afsarmanesh, editors, Collaborative Networks for a Sustainable World, pages 149–156, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg.
doi: 10.1007/978-3-642-15961-9_17. |
| [35] |
D. A. Richardson, S. Leeuw and W. Dullaert,
Factors affecting global inventory prepositioning locations in humanitarian operations–a delphi study, Journal of Business Logistics, 37 (2016), 59-74.
doi: 10.1111/jbl.12112. |
| [36] |
F. S. Salman and E. Yücel,
Emergency facility location under random network damage: Insights from the istanbul case, Computers & Operations Research, 62 (2015), 266-281.
doi: 10.1016/j.cor.2014.07.015. |
| [37] |
J.-B. Sheu,
Dynamic relief-demand management for emergency logistics operations under large-scale disasters, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 1-17.
doi: 10.1016/j.tre.2009.07.005. |
| [38] |
J.-B. Sheu,
An emergency logistics distribution approach for quick response to urgent relief demand in disasters, Transportation Research Part E: Logistics and Transportation Review, 43 (2010), 687-709.
doi: 10.1016/j.tre.2006.04.004. |
| [39] |
J. Tobita, N. Fukuwa and M. Mori,
Integrated disaster simulator using webgis and its application to community disaster mitigation activities, Journal of Natural Disaster Science, 30 (2008), 71-82.
doi: 10.2328/jnds.30.71. |
| [40] |
M. I. Todorovska and M. D. Trifunac,
Liquefaction opportunity mapping via seismic wave energy, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125 (1999), 1032-1042.
doi: 10.1061/(ASCE)1090-0241(1999)125:12(1032). |
| [41] |
S. Tofighi, S. A. Torabi and S. A. Mansouri,
Humanitarian logistics network design under mixed uncertainty, European Journal of Operational Research, 250 (2016), 239-250.
doi: 10.1016/j.ejor.2015.08.059. |
| [42] |
H. Wang, L. Du and S. Ma,
Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake, Transportation Research Part E Logistics and Transportation Review, 69 (2014), 160-179.
doi: 10.1016/j.tre.2014.06.006. |
| [43] |
T. Yao, S. R. Mandala and B. D. Chung,
Evacuation transportation planning under uncertainty: A robust optimization approach, Networks and Spatial Economics, 9 (2009), 171-189.
doi: 10.1007/s11067-009-9103-1. |
| [44] |
E. Yücel, F. S. Salman and I. Arsik,
Improving post-disaster road network accessibility by strengthening links against failures, European Journal of Operational Research, 269 (2018), 406-422.
doi: 10.1016/j.ejor.2018.02.015. |
| [45] |
W. Yushimito, M. Jaller and S. Ukkusuri,
A voronoi-based heuristic algorithm for locating distribution centers in disasters, Networks and Spatial Economics, 12 (2012), 21-39.
doi: 10.1007/s11067-010-9140-9. |
show all references
References:
| [1] |
M. Ahmadi, A. Seifi and B. Tootooni,
A humanitarian logistics model for disaster relief operation considering network failure and standard relief time: A case study on san francisco district, Transportation Research Part E: Logistics and Transportation Review, 75 (2015), 145-163.
doi: 10.1016/j.tre.2015.01.008. |
| [2] |
A. R. Akkihal, Inventory Pre-positioning for Humanitarianoperations, Master's thesis, Massachusetts Institute of Technology, USA, 2006. |
| [3] |
D. Alem, A. Clark and A. Moreno,
Stochastic network models for logistics planning in disaster relief, European Journal of Operational Research, 255 (2016), 187-206.
doi: 10.1016/j.ejor.2016.04.041. |
| [4] |
N. Altay and W. G. Green Ⅲ,
Or/ms research in disaster operations management, European Journal of Operational Research, 175 (2006), 475-493.
doi: 10.1016/j.ejor.2005.05.016. |
| [5] |
T. Anagnos and A. Kiremidjian,
A review of earthquake occurrence models for seismic hazard analysis, Probabilistic Engineering Mechanics, 3 (1988), 3-11.
doi: 10.1016/0266-8920(88)90002-1. |
| [6] |
J. G. Anderson and M. D. Trifunac, On uniform risk functionals which describe strong earthquake ground motion: Definition, numerical estimation, and an application to the fourier amplitude spectrum of acceleration, Report CE 77-02 University of Southern California, Los Angeles, U.S.A., 1977. |
| [7] |
J. G. Anderson and M. D. Trifunac,
Uniform risk functionals for characterization of strong earthquake ground motion, Bulletin of the Seismological Society of America, 68 (1978), 205-218.
|
| [8] |
A. Ben-Tala, B. Do Chung, S. R. Mandala and T. Yao,
Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains, Transportation Research Part B: Methodological, 45 (2011), 1177-1189.
doi: 10.1016/j.trb.2010.09.002. |
| [9] |
C. Boonmee, M. Arimura and T. Asada,
Facility location optimization model for emergency humanitarian logistics, International Journal of Disaster Risk Reduction, 24 (2017), 485-498.
doi: 10.1016/j.ijdrr.2017.01.017. |
| [10] |
A. M. Caunhyea, X. Niea and S. Pokharel,
Optimization models in emergency logistics: A literature review, Socio-Economic Planning Sciences, Special Issue: Disaster Planning and Logistics: Part 1, 46 (2012), 4-13.
doi: 10.1016/j.seps.2011.04.004. |
| [11] |
C. A. Cornell,
Engineering seismic risk analysis, Bulletin of the Seismological Society of America, 58 (1968), 1583-1606.
|
| [12] |
A. Coskun, W. Elmaghraby, M. Karaman and F. S. Salman, Relief aid stocking decisions under bilateral agency cooperation, Socio-Economic Planning Sciences, 2018.
doi: 10.1016/j.seps.2018.10.009. |
| [13] |
V. Del Gaudio and J. Wasowski,
Time probabilistic evaluation of seismically induced landslide hazard in irpinia (southern italy), Soil Dynamics and Earthquake Engineering, 24 (2004), 915-928.
|
| [14] |
F. Fiedrich, F. Gehbauer and U. Rickers,
Optimized resource allocation for emergency response after earthquake disasters, Safety Science, 35 (2000), 41-57.
doi: 10.1016/S0925-7535(00)00021-7. |
| [15] |
G. Galindo and R. Batta,
Review of recent developments in or/ms research in disaster operations management, European Journal of Operational Research, 230 (2013), 201-211.
doi: 10.1016/j.ejor.2013.01.039. |
| [16] |
R. A. Garrido, Optimal emergency resources deployment under a terrorist threat: The hazmat case and beyond, In Handbook of OR/MS Models in Hazardous Materials Transportation, International Series in Operations Research and Management Science, chapter 8, pages 245–267. Springer, New York, 2013.
doi: 10.1007/978-1-4614-6794-6_8. |
| [17] |
R. A. Garrido and P. Lamas, Optimal logistics and transportation decisions for emergency response to natural disasters, In World Academy of Science, Engineering and Technology 76, chapter 8, pages 201–213. WASET, Johannesburg, South Africa, 2013. |
| [18] |
R. A. Garrido, P. Lamas and F. J. Pino,
A stochastic programming approach for floods emergency logistics, Transportation Research Part E: Logistics and Transportation Review, 75 (2015), 18-31.
doi: 10.1016/j.tre.2014.12.002. |
| [19] |
I. D. Gupta,
Probabilistic seismic hazard analysis method for mapping of spectral amplitudes and other design-specific quantities to estimate the earthquake effects on man-made structures, ISET Journal of Earthquake Technology, 44 (2007), 127-167.
|
| [20] |
J. Holguin-Veras, N. Pérez, S. Ukkusuri, T. Wachtendorf and B. Brown,
Emergency Logistics Issues Affecting the Response to Katrina: A Synthesis and Preliminary Suggestions for Improvement, Transportation Research Record: Journal of the Transportation Research Board, 2022 (2007), 76-82.
doi: 10.3141/2022-09. |
| [21] |
E. L. Krinitzsky,
Earthquake probability in engineering – part 1: The use and misuse of expert opinion: The third richard h. jahns distinguished lecture in engineering geology, Engineering Geology, 33 (1993), 257-288.
doi: 10.1016/0013-7952(93)90030-G. |
| [22] |
J. Luedtke and S. Ahmed,
A sample approximation approach for optimization with probabilistic constraints, SIAM Journal on Optimization, 19 (2008), 674-699.
doi: 10.1137/070702928. |
| [23] |
E. Mas, A. Suppasri, Sh. Koshimura and F. Imamura,
Agent based simulation of the 2011 great east japan earthquake tsunami evacuation procedure. introduction to an integrated model of tsunami inundation and evacuation, Journal of Natural Disaster Science, 34 (2012), 41-57.
|
| [24] |
T. Matisziw, A. Murray and T. Grubesic,
Strategic network restoration, Networks and Spatial Economics, 10 (2010), 345-361.
doi: 10.1007/s11067-009-9123-x. |
| [25] |
R. K. McGuire,
Seismic design spectra and mapping procedures using hazard analysis based directly on oscillator response, Earthquake Engineering and Structural Dynamics, 5 (1977), 211-234.
doi: 10.1002/eqe.4290050302. |
| [26] |
A. Nemirovski and A. Shapiro,
Convex approximations of chance constrained programs, SIAM Journal on Optimization, 17 (2007), 969-996.
doi: 10.1137/050622328. |
| [27] |
L. Ozdamar, D. Tuzun-Aksu, E. Yasa and B. Ergunes,
Disaster relief routing in limited capacity road networks with heterogeneous flows, Journal of Industrial and Management Optimization, 14 (2018), 1367-1380.
doi: 10.3934/jimo.2018011. |
| [28] |
B. K. Pagnoncelli, S. Ahmed and A. Shapiro,
Sample average approximation method for chance constrained programming: Theory and applications, Journal of Optimization Theory and Applications, 142 (2009), 399-416.
doi: 10.1007/s10957-009-9523-6. |
| [29] |
B. Papazachos, E. E. Papadimitriou, A. A. Kiratzi, Ch. A. Papaioannou and G. F. Karakaisis,
Probabilities of occurrence of large earthquakes in the aegean and surrounding area during the period 1986–2006, Pure and Applied Geophysics, 125 (1987), 597-612.
doi: 10.1007/BF00879574. |
| [30] |
B. C. Papazachos, Ch. A. Papaioannou, V. N. Margaris and N. P. Theodulidis,
Seismic hazard assessment in greece based on strong motion duration, Proceedings of the Tenth World Conference on Earthquake Engineeing, 2 (1992), 425-430.
|
| [31] |
T. Parsons,
Recalculated probability of m greater than 7 earthquakes beneath the sea of marmara, turkey, Journal of Geophysical Research, 109 (2004), 1-21.
|
| [32] |
T. Parsons,
Significance of stress transfer in time-dependent earthquake probability calculations, Journal of Geophysical Research: Solid Earth, 110 (2005), 1978-2012.
doi: 10.1029/2004JB003190. |
| [33] |
M. Peng, Y. Peng and H. Chen,
Post-seismic supply chain risk management: A system dynamics disruption analysis approach for inventory and logistics planning, Computers & Operations Research, Special issue Multiple Criteria Decision Making in Emergency Management, 42 (2014), 14-24.
doi: 10.1016/j.cor.2013.03.003. |
| [34] |
D. Richardson, S. de Leeuw and I. F. A. Vis, Conceptualising inventory prepositioning in the humanitarian sector, In Luis M. Camarinha-Matos, Xavier Boucher, and Hamideh Afsarmanesh, editors, Collaborative Networks for a Sustainable World, pages 149–156, Berlin, Heidelberg, 2010. Springer Berlin Heidelberg.
doi: 10.1007/978-3-642-15961-9_17. |
| [35] |
D. A. Richardson, S. Leeuw and W. Dullaert,
Factors affecting global inventory prepositioning locations in humanitarian operations–a delphi study, Journal of Business Logistics, 37 (2016), 59-74.
doi: 10.1111/jbl.12112. |
| [36] |
F. S. Salman and E. Yücel,
Emergency facility location under random network damage: Insights from the istanbul case, Computers & Operations Research, 62 (2015), 266-281.
doi: 10.1016/j.cor.2014.07.015. |
| [37] |
J.-B. Sheu,
Dynamic relief-demand management for emergency logistics operations under large-scale disasters, Transportation Research Part E: Logistics and Transportation Review, 46 (2010), 1-17.
doi: 10.1016/j.tre.2009.07.005. |
| [38] |
J.-B. Sheu,
An emergency logistics distribution approach for quick response to urgent relief demand in disasters, Transportation Research Part E: Logistics and Transportation Review, 43 (2010), 687-709.
doi: 10.1016/j.tre.2006.04.004. |
| [39] |
J. Tobita, N. Fukuwa and M. Mori,
Integrated disaster simulator using webgis and its application to community disaster mitigation activities, Journal of Natural Disaster Science, 30 (2008), 71-82.
doi: 10.2328/jnds.30.71. |
| [40] |
M. I. Todorovska and M. D. Trifunac,
Liquefaction opportunity mapping via seismic wave energy, Journal of Geotechnical and Geoenvironmental Engineering, ASCE, 125 (1999), 1032-1042.
doi: 10.1061/(ASCE)1090-0241(1999)125:12(1032). |
| [41] |
S. Tofighi, S. A. Torabi and S. A. Mansouri,
Humanitarian logistics network design under mixed uncertainty, European Journal of Operational Research, 250 (2016), 239-250.
doi: 10.1016/j.ejor.2015.08.059. |
| [42] |
H. Wang, L. Du and S. Ma,
Multi-objective open location-routing model with split delivery for optimized relief distribution in post-earthquake, Transportation Research Part E Logistics and Transportation Review, 69 (2014), 160-179.
doi: 10.1016/j.tre.2014.06.006. |
| [43] |
T. Yao, S. R. Mandala and B. D. Chung,
Evacuation transportation planning under uncertainty: A robust optimization approach, Networks and Spatial Economics, 9 (2009), 171-189.
doi: 10.1007/s11067-009-9103-1. |
| [44] |
E. Yücel, F. S. Salman and I. Arsik,
Improving post-disaster road network accessibility by strengthening links against failures, European Journal of Operational Research, 269 (2018), 406-422.
doi: 10.1016/j.ejor.2018.02.015. |
| [45] |
W. Yushimito, M. Jaller and S. Ukkusuri,
A voronoi-based heuristic algorithm for locating distribution centers in disasters, Networks and Spatial Economics, 12 (2012), 21-39.
doi: 10.1007/s11067-010-9140-9. |
Table 1.
Sensitivity scenarios and parameters' variations
| Parameters | Base | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 4 | 2 | 3 | 5 | 6 |
| Number of Products | 2 | 1 | 3 | 4 | 5 |
| Number of Zones | 6 | 2 | 4 | 8 | 10 |
| Inventory capacity per period (units) | 100 | 90 | 95 | 105 | 110 |
| Parameters | Base | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 4 | 2 | 3 | 5 | 6 |
| Number of Products | 2 | 1 | 3 | 4 | 5 |
| Number of Zones | 6 | 2 | 4 | 8 | 10 |
| Inventory capacity per period (units) | 100 | 90 | 95 | 105 | 110 |
Table 2.
Sensitivity of the average objective function with respect to each parameter's variation
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | -52% | -27% | 26% | 52% |
| Number of Products | -52% | 52% | 105% | 158% |
| Number of Zones | -69% | -35% | 34% | 69% |
| Inventory Capacity per Period | 9% | 6% | -8% | -19% |
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | -52% | -27% | 26% | 52% |
| Number of Products | -52% | 52% | 105% | 158% |
| Number of Zones | -69% | -35% | 34% | 69% |
| Inventory Capacity per Period | 9% | 6% | -8% | -19% |
Table 3.
Objective function's Coefficient of Variation for each sensitivity scenario
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 0.08 | 0.06 | 0.05 | 0.04 |
| Number of Products | 0.08 | 0.04 | 0.04 | 0.06 |
| Number of Zones | 0.11 | 0.08 | 0.04 | 0.04 |
| Inventory Capacity per Period | 0.03 | 0.04 | 0.07 | 0.10 |
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 0.08 | 0.06 | 0.05 | 0.04 |
| Number of Products | 0.08 | 0.04 | 0.04 | 0.06 |
| Number of Zones | 0.11 | 0.08 | 0.04 | 0.04 |
| Inventory Capacity per Period | 0.03 | 0.04 | 0.07 | 0.10 |
Table 4.
Elasticity of the average objective function with respect to each parameter's variation
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 1.04 | 1.08 | 1.04 | 1.04 |
| Number of Products | 1.04 | 1.04 | 1.05 | 1.05 |
| Number of Zones | 1.03 | 1.06 | 1.03 | 1.03 |
| Inventory Capacity per Period | -0.87 | -1.20 | -1.60 | -1.85 |
| Parameters | Scen. 1 | Scen. 2 | Scen. 3 | Scen. 4 |
| Number of Periods | 1.04 | 1.08 | 1.04 | 1.04 |
| Number of Products | 1.04 | 1.04 | 1.05 | 1.05 |
| Number of Zones | 1.03 | 1.06 | 1.03 | 1.03 |
| Inventory Capacity per Period | -0.87 | -1.20 | -1.60 | -1.85 |
Table 5.
Variation of the solution under different probabilities of earthquake's occurrence
| Total Access Time | Earthquake Pr. = 20% |
Earthquake Pr. = 10% |
PEarthquake Pr. = 2% |
Earthquake Pr. = 1% |
| Lower Bound | 500 | 700 | 2,900 | 4,000 |
| Upper Bound | 1,000 | 1,200 | 3,900 | 4,800 |
| Relative Gap | 100% | 71% | 34% | 20% |
| Absolute Gap | 500 | 700 | 1000 | 800 |
| Total Access Time | Earthquake Pr. = 20% |
Earthquake Pr. = 10% |
PEarthquake Pr. = 2% |
Earthquake Pr. = 1% |
| Lower Bound | 500 | 700 | 2,900 | 4,000 |
| Upper Bound | 1,000 | 1,200 | 3,900 | 4,800 |
| Relative Gap | 100% | 71% | 34% | 20% |
| Absolute Gap | 500 | 700 | 1000 | 800 |
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