1. Raimo P. Hämäläinen Juha Mäntysaari
A Dynamic Interval Goal Programming Approach to the Regulation of a Lake-River System
Raimo P. Hämäläinen
Juha Mäntysaari
Systems Analysis Laboratory
Helsinki University of Technology
S ystems
Analysis Laboratory
Helsinki University of Technology

2. Päijänne-Kymijoki lake river system
KONNIVESI
RUOTSALAINEN
RIVER
KYMIJOKI 10 20 30 40 50 km
Jyväskylä
PYHÄJÄRVI
Lahti
Kotka
Finland

3. Päijänne-Kymijoki lake river system
4:th largest in Finland
Control: Outflow from Päijänne to the river Kymijoki
Inflows: forecasted
Regulation policies: Water levels at six time points

4. Need for modelling
Development of feasible regulation strategies is a dynamic control problem
No intuitive solutions
Planning againts long historical inflow data
Analysis of regulation impacts
Many interest groups
multicriteria optimization in a dynamic system

5. Goals in terms of water levels
Users give desired water levels at:
six different points during one year
ideal level + acceptable interval (min, max)

6. Constraints Max change in outflow: Outflow from Päijänne: Min/max flow
Fixed and hard
Max change in outflow:
Soft, violation penalties
Water level in the lake Pyhäjärvi:
Fixed rule based regulation
Part of the dynamics

7. Criteria and penalty functions
Criterion for goal levels:
Quadratic cost for differences of goal points from regulated water levels
Penalty outside the goal interval:
Quadratic difference from the limits (min or max)
Penalty for violation of change
in outflow rate:
Quadratic cost outside the maximum flow limit, otherwise zero

8. Criteria and penalty functions
Cost function minimized = Sum of deviations from goal + penalty outside goal intervals

9. Model assumptions Lake dynamics
Optimization against one to four year history
Lower dam regulation by a given rule
Regulator uses a rolling two goal optimization principle
Adjustment rules

10. Generation of the optimal regulation strategy

11. Goal programming Goal (infeasible point)d
Goal point/set
cost function
Goal programming
Goal (infeasible point)
Problem: Find a point in the feasible set closest to the goal point/set
Weighted, Min Max, Lexicographic
Aspects in regulation:
Dynamic problem
Goal interval (set)

12. Why goal programming ?
Economic, social and environmental impacts
37 primary + 20 secondary = 57 different impacts
For example: Power production, flood damages, number of destroyed loon nests
Some impacts are interdependent: energy produced and the value of energy
Use of tradeoff comparison questions or criteria classification becomes difficult

13. ISMO spreadsheet application

14. ISMO spreadsheet application
Minimizes deviations from goal levels and goal intervals
Satisfies flow constraints
Simulates the regulator’s operating principles
Preference model
Set of goal levels + acceptability intervals
Optimization againts history data for a selected one to four year period
Modifiable parameters
Flow constraints in the river
steepness of the penalty function

15. Use of ISMO

16. ISMO example

17. Inflow

18. Utopia and realistic solutions

19. Utopia and realistic solutions

20. Impacts Nature Social Economic Spawning areas for pike fish
Water level when ice melts
number of destroyed loon nests
Social
Recreational losses
Professional fishing: Reduction of the water level during 10-Dec and 28-Feb
Economic
Power production
Flood damages
Days infavourable for log floating

21. Comparison of impacts:
User evaluates and modifies goal levels

22. Spreadsheet modelling works !
ISMO is implemented in MS Excel 7.0 (MS Office 95)
Solver provides optimization routines
10-20 minutes for one solution
Benefits
Rapid development
Easy: data input, model modification, visualisation and printing
Users accept easily
Excel is a commonly used office program

23. Added value Generation of alternative regulation strategies
Impact tables of regulation
a key info material in decision analysis interviews and conferences
Sensitivity tool
individual changes for water levels and related impacts
helps representatives to better understand the restrictions of the system

24. Further development Different information patterns
Iterative optimization of the goal levels to produce maximum amount/value of the energy
Now used to develop new regulation policies and their impacts

25. References www.paijanne.hut.fi
Marttunen, M., Järvinen, E. A., Saukkonen, J. and Hämäläinen, R. P., “Regulation of Lake Päijänne - a Learning Process Preceding Decision-Making”, Finnish Journal of Water Economy, 6:29-37, 1999.
Hämäläinen, R. P., Kettunen, E., Marttunen, M. and Ehtamo, H., “Evaluating a framework for multi-stakeholder decision support in water resources management”, Manuscript, (Downloadable from
Hämäläinen, R. P. and Mäntysaari, J., “A Dynamic Interval Goal Programming Approach the Regulation of a Lake-River System”, Manuscript, (Downloadable from Publications/pdf-files/mhama.pdf)
Hämäläinen, R. P., “Interactive Multiple Criteria Decision Analysis in Water Resources Planning”, Home pages of the Lake Päijänne project, 1998,