A Dynamic Interval Goal Programming Approach to the

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 www. sal. hut. fi S ystems Analysis Laboratory 6/18/2021 Helsinki University of Technology

Päijänne-Kymijoki lake river system Jyväskylä LAKE PÄIJÄNNE Finland RUOTSALAINEN KONNIVESI LAKE PYHÄJÄRVI Lahti RIVER KYMIJOKI 0 10 20 30 40 50 km Kotka

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

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 Þ multicriteria optimization in a dynamic system

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

Constraints 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

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

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

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

Generation of the optimal regulation strategy

Goal programming • Goal (infeasible point) • Problem: Find a point in the feasible set closest to the goal point/set Þ Weighted, Min Max, Lexicographic • Aspects in regulation: – Dynamic problem – Goal interval (set)

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 ðUse of tradeoff comparison questions or criteria classification becomes difficult

ISMO spreadsheet application

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

Use of ISMO

ISMO example

Inflow 1980 -1984

Utopia and realistic solutions

Utopia and realistic solutions

Impacts • Nature – 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

Comparison of impacts: ðUser evaluates and modifies goal levels

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

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

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

References – 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, 1999. (Downloadable from http: //www. sal. hut. fi/Publications/pdf-files/mhamb. pdf) – Hämäläinen, R. P. and Mäntysaari, J. , “A Dynamic Interval Goal Programming Approach the Regulation of a Lake-River System”, Manuscript, 2000. (Downloadable from http: //www. sal. hut. fi/ Publications/pdf-files/mhama. pdf) – Hämäläinen, R. P. , “Interactive Multiple Criteria Decision Analysis in Water Resources Planning”, Home pages of the Lake Päijänne project, www. paijanne. hut. fi 1998,