Πρακτικέςκαι καιµέθοδοισυστηµάτων βελτιστοποίησηςδιαχειριστικών διαχειριστικώνµέτρων ρ. Χρίστος Τµήµα Πολιτικών Μηχανικών Πανεπιστήµιο Frederick 1
Presentation Outline What is Operations Research? Why is it (Optimization) needed? Optimization in Environmental Management Approaches / Procedures / Models Types of Results to be expected Current Status Next Steps 2
Jargon, jargon, and more jargon Operations Research Optimization Mathematical Programming Systems Analysis 3
What is Operations Research? Operations Research is the application of advanced analytical methods to help make better decisions. Alternative Definition The science of decision making. 4
A brief history lesson (born out of necessity) World War II problems Deployment of radar, management of convoys, bombing, mining, training schedules, resupplying the front lines, World War II solutions Scientists and Engineers were called in to apply mathematics and the scientific method to these Military Operations problems What since then? Transportation Industry Telecommunications Industrial Production And finally 5
Optimization in Environmental Management 6
Descriptive models Descriptive model of the system as a hypothesis of how the system could work, or try to estimate how an unforeseeable event could affect the system. 7
Water Management Issues (a world of complexity) Watershed Water Quality Water Quantity Impacts on Pollutants Users Ecosystems Agriculture Tourism Other BOD Nutrients Nutrients Industry Agriculture Tourism Other Technological Solutions Cost Unquantifiable Objectives 8
Water Management Stakeholders (a world of conflict) Farmers Industry Homeowners Public Officials Watershed Environmental Activists Scientific Community Mass media Local Government Local Businesses & Activities 9
How it all ties together (the architecture of a DSS applied to an environmental system) GIS Simulation Modules Optimization Modules DB Database Hydraulic Model Hydrologic Model Water Quality Model Black Box Models Ecological Models Etc Decision Variables Objectives Constraints Economic, social, legislative & environmental aspects 10
Decision models Decision model for the decision maker to develop insight into the decision and determine a clear course of action 11
How does an Optimization Model look like? The following is a mathematical formulation of a decision model: Minimize: N n f = 1 t= 1 C f X (1), t f, t Subject to: n t= 1 X f, = 1 f (2) t N n p p [ X f, t ( % R ) W ] t f f = 1 t= 1 f, t { 0, 1} p 100 T p (3) X f, t (4) 12
Types of results to be expected from Optimization Procedure 13
A bunch of numbers 14
Benefits of Optimization (the Objective Space) 15
Benefits of Optimization (the Decision Space) 16
The Tradeoff Curves $3,000,000 Lowest Possible Risk $2,500,000 $2,000,000 Cost / year $1,500,000 $1,000,000 $500,000 Highest Possible Risk $0 0 5,000,000 10,000,000 15,000,000 20,000,000 25,000,000 Risk Index 17
Examination of Alternatives 18
Uncertainty Analysis 19
Optimization Work Task; Current status A working dilemma: A new model? Probably a Mixed Integer Programming Procedure Not a DSS (especially as GUIs are concerned) An existing model / DSS (appropriately modified) WEAP (Stockholm Environmental Institute) WSM300 (German university group) Elbe-DSS (U. of Osnabruck) USEPA s Framework for Identifying Optimal TMDL Allocations Questionnaire - information from stakeholders 20
Optimization Work Task; Future Steps (we ve only just began) Reinforcement of research team Conceptual model finalization 21
I need you!! (Importance of Stakeholder input in model definition) Objectives Minimization of costs Maximization of benefits Constraints Environmental regulations and TMDLs Other Red-lines Parameters & coefficients of decision variables Unit costs Correlations between pollutants and functions of ecosystems Management Scenarios Definition 22
Questions? Comments? Insults? 23