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From the PIP procedure to MODSSs MNRL03 Andrea Castelletti Politecnico di Milano

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2 Planning actions and management actions Planning actions: Planning actions: decided once forever or over a long time horizon. Management actions Management actions: decided frequently or even periodically, often on a daily basis. Planning actions: Planning actions: by means of a Project, i.e. by evaluating different alternatives (i.e. mix of planning actions) with the aim of individuating those that better satisfy the DM and/or Stakeholders’ point of views. Management actions Management actions: taken on the basis of the Regulator’s experience, i.e. somehow empirically. Does not work!!! How are they taken?

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3 t inflows t levels GD t releases capacity Planning a new reservoir Deciding to build the reservoir does require deciding how it will be daily regulated, otherwise it is not possible to evaluate if and how the farmers are satisfied. The management must be always considered when either the planning requires it or it change the context in which the current managemt is performed. Planning the management t inflows t levels GD t releases capacity Planning decision: Planning decision: to build the reservoir Management decision: Management decision: water volume to be released in the next 24 hours

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4 Planning the management Simplification: when the system is a periodic one, only 365 management decisions have to be defined. planning decision. IDEA: we can define the management decision for each day of the Project horizon (N years) by specifying the sequence of decisions (N*365) over that horizon. This sequence constitutes a planning decision. Release plan Is this the best solution? To reply let’s consider the management only, i.e. let’s assume the reservoir has already been built. Is this the best solution? To reply let’s consider the management only, i.e. let’s assume the reservoir has already been built.

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5 Taking decisions in full rationality model Cabora Bassa MOZAMBIQUE irrigation Decision: volume of water to release every day from the dam in order to satisfy the farmers’ demand utut stst a t+1

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6 catchment reservoir + users s t+1 w t+1 utut ItIt a t+1 The release plan m 0 … m 364 ?

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7 a * t+1 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt The rule curve s t+1 t s * s * t+1

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8 a * t+1 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt The rule curve t s * s * t+1 ? s t s*s*

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9 The rule curve Rule curve for Cabora Bassa Actual path

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10 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt The control policy t s * t s * p= {m t () t = 0,1,…,h} delay mt(st)mt(st) a * t+1 s * t+1

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11 s t+1 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt a t+1 The control policy m t (s t ) delay m t (s t,w t ) m t (s t,w t,I t,a t ) forecaster â t+1 m t (s t,w t,â t+1 ) delay m t (s t,w t,I t,a t ) delay

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12 s t+1 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt a t+1 The control policy m t (s t ) delay m t (s t,w t ) m t (s t,w t,I t,a t ) forecaster â t+1 m t (s t,w t,â t+1 ) delay m t (s t,w t,I t,a t ) delay Why a single decision u t ? It’s more rational a whole set M t ! MtMt

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13 s t+1 m 0 … m 364 catchment reservoir + users w t+1 utut ItIt a t+1 The control policy m t (s t ) delay m t (s t,w t ) m t (s t,w t,I t,a t ) m t (s t,w t,a t+1 ) delay

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14 performanc e indexes comparison & generation of policies catchment reservoir + users s t+1 w t+1 a t+1 utut manag. policy model of the physical system ItIt scenario choice ANALYST manag. policy Simulation delay model of the manag. system

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15 performanc e indexes catchment reservoir + users s t+1 w t+1 a t+1 manag. policy model of the manag. system model of the physical system ItIt scenario choice ANALYST Set-valued simulation delay utut set valued manage policy MtMt DM

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16 In a deterministic world Let’s introduce a simplification: We are dealing with deterministic inflows We know {a 1,…,a h } for any time horizon {1,…,h}

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17 3. Designing policy Single-Objective control problem x t+1 = f t (x t, u t, a t+1 ) p = {m t () t = 0,1,…,h} u t = m t (x t ) u t U t (x t ) a t+1 ~ t () Design Procedure 2. Conceptualisation Defining criteria and indicators Identifying the model 1. Reconnaissance Defining actions (measures) ** Problem formulation MOZAMBIQUE B* mz. = utopia p* mz. history optimization

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Single-Objective control problem Design Procedure Integrated Modelling Framework 3. Designing policy 2. Conceptualisation Identifying the model 1. Reconnaissance Defining actions (measures) Defining criteria and indicators

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19 Full rationality x t+1 = f t (x t, u t, a t+1 ) Cabora Bassa MOZAMBIQUE irrigation Kafue Kariba Cabora Bassa MOZAMBIQUE ZIMBABWE ZAMBIA irrigation hydropower Taking decisions in partial rationality Partial rationality Many interests Many DMs Many interests Many DMs

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20 B Zim B Moz B Zam (B Zam opt ;B Zim opt ) today B Moz con Present situation

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21 B Zim B Moz B Zam (B Zam ott ;B Zim ott ) today utopia B Moz con B Moz ott D F E The optimal solution for Mozambique B Moz

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22 B Zim B Moz B Zam (B Zam ott ;B Zim ott ) today B Moz con B Moz ott D F E The Pareto frontier Pareto frontier utopia

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23 B Moz B Zam B Zim B Zam B Moz utopia today alternative The Pareto frontier

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24 Multi-objective control problem x t+1 = f t (x t, u t, a t+1 ) p = {m t () t = 0,1,…,h} u t = m t (x t ) u t U t (x t ) a t+1 ~ t () ** Pareto frontier mozambique zimbabwe zambia Formulation

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25 In an uncertain world Considering the inflows as deterministic is an unrealitsic assumption. However, we can not simply say that future inflows are unknow Rational decision EvaluationPrediction Predicting the future requires some past characteristic of the process to keep in the future: modelling the inflow as a random process (stochastic). THE STEADY STATE PARADIGM

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26 Decision-making in uncertain condition - example Knowing exactly what will happen, we would select alternative A 2 that returns 1500 €. Indicator value Occurrence 11 Decisions A1A A2A2 1500

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27 Risk aversion Laplace criterion provide alternative A 2 as the best choice. And you, what would you select? Maybe the worst case: min Indicator value Occurrences 11 22 Alternatives A1A A2A Probability of occurrence j 0,80,2 E j [i ij ]

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28 Partial rationality + Uncertain world The Multi-Objective Control problem B Zim B Moz B Zam Generating the whole Frontier is not always possible. In some cases, interacting with the Stakeholders is more appropriate, thus generating the Front point by point. NEGOTIATIONS.

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29 Negotiations B Zim B Moz B Zam B Moz B Zim B Zam afflussi domanda irrigua Just showing the value of the objectives could be not enough, in some cases showing the associated trajectories can be more useful ….

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30 no Mitigation and compensation, Multi-objective control problem 5. Evaluation6. Comparison and negotiations Agreement? reasonable alternatives 3. Policy design 2. Conceptualisation 1. Reconnessaince 4. Estimating the effects Design Procedure Pareto frontier mozambique zimbabwe zambia 3. Designing policy 2. Conceptualisation 5. Evaluation 6. Comparison and negotiations Agreement? 4. Estimating effects yes Final decision

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31 MODSS 6. Comparison or negotiation reasonable alternatives 2. Conceptualisation 3. Designing alternatives 4. Estimating effects Stakeholders 1. Reconnaissance 5. Evaluation no Mitigation and compensation Agreement? yes Final (political) decision TwoLe Daily management Planning Management TwoLe/P TwoLe/M

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32 planning management analyst DM stakeholders DM users operational control models and policies release decision TwoLe/P TwoLe /M TwoLe: a 2 level MODSS

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