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6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
A multi-objective goal
programming approach for locating
emergency shelters under damage
uncertainty
Ashish Trivedi
Amol Singh
Indian Institute of Management Rohtak, India
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Agenda
• Significance of earthquakes
• Shelter management
• Location planning
• Factors
• Proposed model
• Implications and contributions
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Devastating Disasters
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Natural disasters’ trend
Source: EM-DAT
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Earthquakes’ trend
Source: EM-DAT
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Shelter planning
• Emergency Shelter: Provision of basic and immediate shelter
needs necessary to ensure the survival of disaster affected
persons, including rapid response solutions such as tents,
insulation materials, other temporary emergency shelter
solutions and shelter related non-food items” (Memorandum
of Understanding between IFRC and UN OCHA).
• Promote self-recovery and early recovery of those affected.
• complex natural disasters with prolonged mass displacement
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Why Shelters?
• Sphere Project
• Shelter and settlement standard 1: strategic planning
Existing shelter and settlement solutions are prioritised through
the return or hosting of disaster affected households, and the
security, health, safety and well-being of the affected population
are ensured.
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
• Shelters provide safety, security, climate protection, and
resistance to disease and ill health.
• Shelter provision and performance is not up to the mark &
poor location selection is one of the reasons for the same.
• Selection of a suitable site for locating shelters from potential
alternatives is of critical importance.
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Classification of shelters
Types of
shelters
Unplanned
Urban self
settlement
Self settled
camps
Planned
Temporary
shelters
Core
shelters
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Factors considered
Criteria Sub-criteria
Favourability of terrain Soil hardness
Topography
Slope
Presence of trees
Wood/timber availability for construction
purposes
Electrical infrastructure Electricity
Telecommunication facility
Hygiene and sanitary system Drinking water
Drainage system & sewage infrastructure
Solid waste disposal
Burial/cremation sites
Community infrastructure Educational facilities
Recreational facilities
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Factors continued..
Safety and security
Access to livelihood
Livestock accommodation
Fire safety
Safety from landslides, flooding, etc.
Warning systems
Transportation capacity Air traffic handling
Condition of local road infrastructure
Proximity Distance from market/warehouses
Distance from main roads
Distance from healthcare facility
Distance from transportation hubs
Distance from Disaster debris storage sites
Type of ownership
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Proposed model objectives
• Maximization of weights assigned to candidate sites based on
subjective evaluation criteria.
• Minimization of total distance covered by affected
households.
• Minimization of number of households who are not provided
shelters.
• Minimization of the number of shelter sites.
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
constraints
• Capacity constraints
• Demand constraints
• Utilization constraints
• Threshold proximity constraints
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Illustration & results
scen
ario
(no.
of
hous
ehol
ds)
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13
500 1 0 0 0 0 0 0 0 0 0 0 0 0
1000 1 0 1 0 1 0 0 0 0 0 1 0 0
1500 1 1 1 1 1 1 1 0 1 0 1 1 0
2000 1 1 1 1 1 1 1 1 1 0 1 1 1
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
cluster
site
S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13
C1 22 0 0 0 125 63 8 0 0 0 0 0 0
C2 52 30 8 19 0 0 0 0 0 0 16 0 13
C3 40 0 0 0 0 0 16 13 34 0 0 0 0
C4 25 0 0 0 21 0 11 0 4 0 0 0 0
C5 17 8 52 19 0 0 0 0 0 0 38 38 0
C6 457 0 0 0 2 0 0 0 0 0 3 0 0
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
ADDED VALUE FOR INTEGRATIVE RISK
MANAGEMENT AND URBAN RESILIENCE
• This study proposes a decision model to prepare hazard prone
societies in becoming more resilient against disasters.
• The present work contributes towards the realisation of
sustainable development and recovery of affected community
as temporary shelter locations play a significant role in speedy
rehabilitation in a post disaster situation.
• Address of multiple objectives while planning for shelter
locations
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Goal programming model
Sets
• 𝐼 : set of clusters affected
• 𝐽 : set of candidate shelter locations
• 𝐾 : set of objectives
• 𝑆 ∶ set of scenarios
Decision Variables
• 𝑦𝑗 : Binary variable, 1 if site 𝑗 is selected as shelter area, 0 otherwise
• 𝑋𝑖𝑗 : Binary variable, 1 if people from cluster 𝑖 can be relocated to
site 𝑗, 0 otherwise
• 𝑛𝑖𝑗 : Number of households moved from cluster 𝑖 to site 𝑗
• 𝑑 𝑘
+
: Over-achievement of goal 𝑘
• 𝑑 𝑘
−
: Under-achievement of goal 𝑘
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Parameters
• 𝑤𝑗 : Weight of shelter sites based on subjective factors
• 𝑑𝑖𝑗: Distance between shelter sites and clusters
• 𝐶𝑗 : Capacity of shelter site (number of households)
• 𝐷𝑖𝑠 : Number of affected household at cluster 𝑖 under scenario s
• 𝐷𝐻𝑗 : Distance of site 𝑗 to nearest healthcare facility
• 𝐷𝑊𝑗 : Distance of site 𝑗 to nearest relief warehouse/market
• 𝑇𝐷ℎ : Threshold distance to nearest healthcare facility
• 𝑇𝐷 𝑤 : Threshold distance to nearest relief warehouse/market
• 𝛽 : Threshold value for minimum utilization of shelter site capacity
• 𝐺 𝑘
+
: Ideal value for goal 𝑘
• 𝐺 𝑘
−
: Anti-ideal value for goal 𝑘
• U : Number of households not getting shelters
• 𝑤 𝑘
𝑔
: Weight associated with goal 𝑘
• 𝑝𝑠 : probability of scenario s
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Formulation
• Minimize
𝑍 = 𝑘
𝑑 𝑘
∗
×𝑤 𝑘
𝑔
𝐺 𝑘
+−𝐺 𝑘
−
• Where 𝑑 𝑘
∗
= 𝑑 𝑘
−
𝑓𝑜𝑟 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑔𝑜𝑎𝑙; 𝑎𝑛𝑑 𝑑 𝑘
+
𝑓𝑜𝑟 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑔𝑜𝑎𝑙
• Subject to:
• 𝑗 𝑦𝑗 𝑤𝑗 + 𝑑1
−
− 𝑑1
+
= 𝐺1
+
• 𝑖 𝑗 𝑛𝑖𝑗𝑠 𝑑𝑖𝑗 + 𝑑2
−
− 𝑑2
+
= 𝐺2
+
• 𝑈 + 𝑑3
−
− 𝑑3
+
= 𝐺3
+
• 𝑗 𝑦𝑗 + 𝑑4
−
− 𝑑4
+
= 𝐺4
+
• 𝑖 𝑛𝑖𝑗𝑠 ≤ 𝑦𝑗 𝐶𝑗 Ɐ 𝑗, 𝑠
• 𝑗 𝑛𝑖𝑗𝑠 ≤ 𝐷𝑖𝑠 Ɐ 𝑖, 𝑠
• 𝑖 𝑗 𝑛𝑖𝑗 𝑠 + 𝑈 = 𝑖 𝐷𝑖𝑠
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
• 𝑖 𝑋𝑖𝑗 ≤ 𝑦𝑗 𝑀 Ɐ 𝑗
• 𝑖 𝑋𝑖𝑗 ≥ 𝑦𝑗 Ɐ 𝑗
• 𝑛𝑖𝑗𝑠 ≤ 𝑋𝑖𝑗 𝑀 Ɐ 𝑖, 𝑗, 𝑠
• 𝑖 𝑛 𝑖𝑗𝑠
𝐶 𝑗
≥ 𝑦𝑗× 𝛽 Ɐ 𝑗
• 𝑦𝑗 × 𝐷𝐻𝑗 ≤ 𝑇𝐷 𝐻 Ɐ 𝑗
• 𝑦𝑗 × 𝐷𝑊𝑗 ≤ 𝑇𝐷 𝑊 Ɐ 𝑗
• 𝑗 𝑋𝑖𝑗 ≥ 1 Ɐ 𝑖
• 𝑋𝑖𝑗, 𝑦𝑗 = 𝐵𝑖𝑛𝑎𝑟𝑦
• 𝑛𝑖𝑗 = 𝐼𝑛𝑡𝑒𝑔𝑒𝑟
• 𝑀 = 𝐵𝑖𝑔 𝑛𝑢𝑚𝑏𝑒𝑟
6th
International Disaster and Risk Conference IDRC 2016
‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland
www.grforum.org
Thank you
Questions

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A Multi-objective Goal Programming Approach for Locating Emergency Shelters under Damage Uncertainty, Ashish TRIVEDI

  • 1. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org A multi-objective goal programming approach for locating emergency shelters under damage uncertainty Ashish Trivedi Amol Singh Indian Institute of Management Rohtak, India
  • 2. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Agenda • Significance of earthquakes • Shelter management • Location planning • Factors • Proposed model • Implications and contributions
  • 3. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Devastating Disasters
  • 4. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Natural disasters’ trend Source: EM-DAT
  • 5. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Earthquakes’ trend Source: EM-DAT
  • 6. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Shelter planning • Emergency Shelter: Provision of basic and immediate shelter needs necessary to ensure the survival of disaster affected persons, including rapid response solutions such as tents, insulation materials, other temporary emergency shelter solutions and shelter related non-food items” (Memorandum of Understanding between IFRC and UN OCHA). • Promote self-recovery and early recovery of those affected. • complex natural disasters with prolonged mass displacement
  • 7. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Why Shelters? • Sphere Project • Shelter and settlement standard 1: strategic planning Existing shelter and settlement solutions are prioritised through the return or hosting of disaster affected households, and the security, health, safety and well-being of the affected population are ensured.
  • 8. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org • Shelters provide safety, security, climate protection, and resistance to disease and ill health. • Shelter provision and performance is not up to the mark & poor location selection is one of the reasons for the same. • Selection of a suitable site for locating shelters from potential alternatives is of critical importance.
  • 9. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Classification of shelters Types of shelters Unplanned Urban self settlement Self settled camps Planned Temporary shelters Core shelters
  • 10. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Factors considered Criteria Sub-criteria Favourability of terrain Soil hardness Topography Slope Presence of trees Wood/timber availability for construction purposes Electrical infrastructure Electricity Telecommunication facility Hygiene and sanitary system Drinking water Drainage system & sewage infrastructure Solid waste disposal Burial/cremation sites Community infrastructure Educational facilities Recreational facilities
  • 11. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Factors continued.. Safety and security Access to livelihood Livestock accommodation Fire safety Safety from landslides, flooding, etc. Warning systems Transportation capacity Air traffic handling Condition of local road infrastructure Proximity Distance from market/warehouses Distance from main roads Distance from healthcare facility Distance from transportation hubs Distance from Disaster debris storage sites Type of ownership
  • 12. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Proposed model objectives • Maximization of weights assigned to candidate sites based on subjective evaluation criteria. • Minimization of total distance covered by affected households. • Minimization of number of households who are not provided shelters. • Minimization of the number of shelter sites.
  • 13. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org constraints • Capacity constraints • Demand constraints • Utilization constraints • Threshold proximity constraints
  • 14. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Illustration & results scen ario (no. of hous ehol ds) S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 500 1 0 0 0 0 0 0 0 0 0 0 0 0 1000 1 0 1 0 1 0 0 0 0 0 1 0 0 1500 1 1 1 1 1 1 1 0 1 0 1 1 0 2000 1 1 1 1 1 1 1 1 1 0 1 1 1
  • 15. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org cluster site S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12 S13 C1 22 0 0 0 125 63 8 0 0 0 0 0 0 C2 52 30 8 19 0 0 0 0 0 0 16 0 13 C3 40 0 0 0 0 0 16 13 34 0 0 0 0 C4 25 0 0 0 21 0 11 0 4 0 0 0 0 C5 17 8 52 19 0 0 0 0 0 0 38 38 0 C6 457 0 0 0 2 0 0 0 0 0 3 0 0
  • 16. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org ADDED VALUE FOR INTEGRATIVE RISK MANAGEMENT AND URBAN RESILIENCE • This study proposes a decision model to prepare hazard prone societies in becoming more resilient against disasters. • The present work contributes towards the realisation of sustainable development and recovery of affected community as temporary shelter locations play a significant role in speedy rehabilitation in a post disaster situation. • Address of multiple objectives while planning for shelter locations
  • 17. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Goal programming model Sets • 𝐼 : set of clusters affected • 𝐽 : set of candidate shelter locations • 𝐾 : set of objectives • 𝑆 ∶ set of scenarios Decision Variables • 𝑦𝑗 : Binary variable, 1 if site 𝑗 is selected as shelter area, 0 otherwise • 𝑋𝑖𝑗 : Binary variable, 1 if people from cluster 𝑖 can be relocated to site 𝑗, 0 otherwise • 𝑛𝑖𝑗 : Number of households moved from cluster 𝑖 to site 𝑗 • 𝑑 𝑘 + : Over-achievement of goal 𝑘 • 𝑑 𝑘 − : Under-achievement of goal 𝑘
  • 18. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Parameters • 𝑤𝑗 : Weight of shelter sites based on subjective factors • 𝑑𝑖𝑗: Distance between shelter sites and clusters • 𝐶𝑗 : Capacity of shelter site (number of households) • 𝐷𝑖𝑠 : Number of affected household at cluster 𝑖 under scenario s • 𝐷𝐻𝑗 : Distance of site 𝑗 to nearest healthcare facility • 𝐷𝑊𝑗 : Distance of site 𝑗 to nearest relief warehouse/market • 𝑇𝐷ℎ : Threshold distance to nearest healthcare facility • 𝑇𝐷 𝑤 : Threshold distance to nearest relief warehouse/market • 𝛽 : Threshold value for minimum utilization of shelter site capacity • 𝐺 𝑘 + : Ideal value for goal 𝑘 • 𝐺 𝑘 − : Anti-ideal value for goal 𝑘 • U : Number of households not getting shelters • 𝑤 𝑘 𝑔 : Weight associated with goal 𝑘 • 𝑝𝑠 : probability of scenario s
  • 19. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Formulation • Minimize 𝑍 = 𝑘 𝑑 𝑘 ∗ ×𝑤 𝑘 𝑔 𝐺 𝑘 +−𝐺 𝑘 − • Where 𝑑 𝑘 ∗ = 𝑑 𝑘 − 𝑓𝑜𝑟 𝑚𝑎𝑥𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑔𝑜𝑎𝑙; 𝑎𝑛𝑑 𝑑 𝑘 + 𝑓𝑜𝑟 𝑚𝑖𝑛𝑖𝑚𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑔𝑜𝑎𝑙 • Subject to: • 𝑗 𝑦𝑗 𝑤𝑗 + 𝑑1 − − 𝑑1 + = 𝐺1 + • 𝑖 𝑗 𝑛𝑖𝑗𝑠 𝑑𝑖𝑗 + 𝑑2 − − 𝑑2 + = 𝐺2 + • 𝑈 + 𝑑3 − − 𝑑3 + = 𝐺3 + • 𝑗 𝑦𝑗 + 𝑑4 − − 𝑑4 + = 𝐺4 + • 𝑖 𝑛𝑖𝑗𝑠 ≤ 𝑦𝑗 𝐶𝑗 Ɐ 𝑗, 𝑠 • 𝑗 𝑛𝑖𝑗𝑠 ≤ 𝐷𝑖𝑠 Ɐ 𝑖, 𝑠 • 𝑖 𝑗 𝑛𝑖𝑗 𝑠 + 𝑈 = 𝑖 𝐷𝑖𝑠
  • 20. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org • 𝑖 𝑋𝑖𝑗 ≤ 𝑦𝑗 𝑀 Ɐ 𝑗 • 𝑖 𝑋𝑖𝑗 ≥ 𝑦𝑗 Ɐ 𝑗 • 𝑛𝑖𝑗𝑠 ≤ 𝑋𝑖𝑗 𝑀 Ɐ 𝑖, 𝑗, 𝑠 • 𝑖 𝑛 𝑖𝑗𝑠 𝐶 𝑗 ≥ 𝑦𝑗× 𝛽 Ɐ 𝑗 • 𝑦𝑗 × 𝐷𝐻𝑗 ≤ 𝑇𝐷 𝐻 Ɐ 𝑗 • 𝑦𝑗 × 𝐷𝑊𝑗 ≤ 𝑇𝐷 𝑊 Ɐ 𝑗 • 𝑗 𝑋𝑖𝑗 ≥ 1 Ɐ 𝑖 • 𝑋𝑖𝑗, 𝑦𝑗 = 𝐵𝑖𝑛𝑎𝑟𝑦 • 𝑛𝑖𝑗 = 𝐼𝑛𝑡𝑒𝑔𝑒𝑟 • 𝑀 = 𝐵𝑖𝑔 𝑛𝑢𝑚𝑏𝑒𝑟
  • 21. 6th International Disaster and Risk Conference IDRC 2016 ‘Integrative Risk Management – Towards Resilient Cities‘ • 28 Aug – 1 Sept 2016 • Davos • Switzerland www.grforum.org Thank you Questions