Authors: Beate Rottkemper Kathrin Fischer Institute for Operations Research and Information Systems Hamburg University of Technology

1. Decision Making in Humanitarian Logistics
A multi-objective optimization model for relocating relief goods during
disaster recovery operations
Beate Rottkemper
Kathrin Fischer
Institute for Operations Research and Information Systems
Hamburg University of Technology

2. Agenda
Overlapping disaster
situations
Scenario planning and
model building
Solutions and decision
support

3. Overlapping disasters
What happens if the relief action does not proceed smoothly?
Relief action
Disruption
Disruption
Disruption
Overlapping disasters

4. Overlapping disastersCharacteristics
• Relief infrastructure established
• Relief items in stock
• Aid workers in field
• Budget is tight
• Transportation network is known
• Infrastructure damages (partly) known
• Shorter time horizon
• Huge uncertainty

5. Problem description
Imbalance of
needs and
supply
Disruption
Relief item
relocation
Risk of
Decision making
Leads to

6. Distribution structure Problem description

7. Future A
Future B
Future C
Future D
Future E
Scenario planning
Factors influencing the future development
Future A
Future B
Future C
Future D
Future E
Initial situation

8. Key
Biological factors
Environmental factors
Human related factors
Predictor variable
Dependent variable
Influencing factors Scenario planning
Protopopoff et al., 2009
Longevity
Density Malaria infection
Immunity
Intermittent
preventive
treatment
Drug resistance
Health status
Age
Health access
Treatment
Migration
Gender
Socio economic
status
Breeding sites
Insecticide
resistance
Insecticide
treated nets
Indoor residual
spraying
Livestock
Land use
Human-vector
contact
Biological factors
Human related factors
Precipitation
Temperature
Altitude

9. Risk states Scenario planning
0 disruption
1 disruption
2 disruptions
3 disruptions
RD 3, Period 2
RD 3, Period 2,
RD 4, Period 4
RD 2, Period 4,
RD 3, Period 4,
RD 4, Period 6
RD 3, Period 2,
RD 4, Period 5,
RD 5, Period 7
RD 4, Period 5
...
Sub-scenariosMain scenarios
Initial situation
Low risk
High risk

10. Modelling uncertainty
• Forecasted needs for the relief action
• Risk of disruptions and therefore uncertain part of needs
…1 2 3 4 T
Uncertain needs
Certain needs
period

11. Unmet needs
Met needs
Certain needs
Period 1 Period 2
Uncertain needs
Handling unmet needs Modelling uncertainty

12. Optimization process

13. Network flow model
Network model based on Herer et al. (2006):
Mathematical model

14. Mathematical modelThree objective functions
1. Unmet certain needs
2. Unmet uncertain needs
3. Logistics costs
Transportation costsTransshipment costs
Inventory holding costsReplenishment costs

15. Mathematical modelConstraints
• Stock balance constraints
• For each depot, each period and total inventory balance
• Balance of needs (each region, each period)
• Capacity limitations (of trucks) for all relations and
periods
• Calculation of unmet need
• Certain and uncertain needs

16. Mathematical modelConstraint method
2. Cost constraint
1. Weighted objective function

17. Dynamic solution selectionConstraint method

18. Dynamic solution selectionConstraint method

19. Computational results

20. Computational results

21. Decision making rules
Replenishments Reference model Critical value = 1 Critical value = 0.7
Low risk 20,770 21,220 29,943
High risk 40,539 41,094 42,490
• The decision depends on the available budget and on the risk state
• Low risk state: Results of reference model and critical value = 1 similar
• High risk state: All results similar

22. • Scenario planning helps to deal with uncertainties in overlapping disaster
situations
• Multiobjective optimization model with a rolling horizon solution approach
integrates uncertainties in the planning process
• Decisions can be made mainly based on environmental settings and on the
monitoring of the relevant risk factors
• Future research concentrates on the development of rules to support decision
making in overlapping disaster situations
Conclusion and outlook
beate.rottkemper@tu-harburg.de

23. Title:
http://www.flickr.com/photos/icrc/4520631916/in/pool-relief#/photos/icrc/4520631916/in/pool-108
Slide 8: Protopopoff, N.; Van Bortel, W.; Speybroeck, N.; Van Geertruyden, J.-P.; Baza, D.; D’Alessandro U. &
Coosemans, M.: Ranking Malaria Risk Factors to Guide Malaria Control Efforts in African
Highlands. In: PLoS ONE 4 (2009), number 11, P. 1–10
Slide 13: Herer, Y. T.; Tzur, M. & Yücesan, E.: The multilocation transshipment problem. In: IIE Transactions 38 (2006),
P. 185-200
Sources

24. Mathematical model
Decision variables
• Flow variables to balance the stocks
• Integer variables to calculate the required vehicles
• Variables to calculate the penalty costs

25. Mathematical model
Objective function
Grid point constraint

26. Mathematical model
Stock-balance at every regional depot (2) and at the central depot (3)
Demand-balance

27. Mathematical model
Total inventory balance
Calculation of fix transportation costs

28. Mathematical model
Calculation of certain unsatisfied demand in period t
Calculation of unsatisfied demand which occurred before period t + 1
Calculation of max(0, UDitk) and max(0, UD2
itk)

29. Mathematical model
Calculation of the unsatisfied demand in period k which occured in
period t