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Energy-efficient technology investments using a decision support system framework

This document presents an integrated framework for decision support systems using R. It describes using R and related packages to represent stochastic energy optimization problems, generate input files for solvers, analyze results, and produce reproducible reports. Stochastic models are developed and solved within this framework. The framework allows statistical analysis, graphical output, model equations, solver inputs/outputs, and comprehensive reports to be combined for modeling, analysis, and stakeholder communication.

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DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Energy-efficient technology investments using a decision support system framework Emilio L. Cano1 Javier M. Moguerza1 Tatiana Ermolieva2 Yurii Yermoliev2 1Rey Juan Carlos University 2International Institute for Applied Systems Analysis (IIASA) Salamanca, May 31 - June 2 2016 Computational Management Science 2016 1/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 2/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 3/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Algorithms Model Symbolic model Variables, relations Underlying theory Methodology, technique Uncertainty modelling Data Deterministic data Uncertain data - Stochastic processes Data analysis Solution Data treatment Analysis Visualization DSS Interpretation Computational Management Science 2016 4/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Algorithms Model Symbolic model Variables, relations Underlying theory Methodology, technique Uncertainty modelling Data Deterministic data Uncertain data - Stochastic processes Data analysis Solution Data treatment Analysis Visualization DSS Stakeholders Dialog Interpretation Computational Management Science 2016 4/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Computational Management Science 2016 4/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Computational Management Science 2016 5/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Computational Management Science 2016 5/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Copy-paste Inconsistencies Errors Out-of-date non-reproducible Painful changes Computational Management Science 2016 5/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Black box Compiled software for specific solutions Changes require re-programming Not reproducible Computational Management Science 2016 5/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Framework Reproducible Research & Literate Programming omptimr R package & Algebraic Modeling Languages (AMLs) “The goal of RR is to tie specific instructions to data analysis and experimental data [and modeling] so that results can be recreated, better understood and verified” “LP: a document that is a combination of content and data analysis code [and models]” Computational Management Science 2016 5/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions R as an Integrated Environment Advantages Open Source Reproducible Research and Literate Programming capabilities. Integrated framework for SMS, data, equations and solvers. Data Analysis (pre- and post-), graphics and reporting. Computational Management Science 2016 6/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions optimr Package Computational Management Science 2016 7/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions optimr Package Computational Management Science 2016 7/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions optimr Package getEq(model1SMS, 4, format = "gams") ## [1] "eqDemand(j,t) ..nt Sum((i), y(i,j,t)) =e= D(j,t) n;n" Computational Management Science 2016 7/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Solution and Analysis wProblem(mod1Instance, "mod1.gms", "gams", "lp") library(gdxrrw) igdx(" /Programs/gams") gams("mod1.gms") importGams(mod1Instance) <- "outSolDeterministic1.gdx" 0 50 100 150 200 0 50 100 150 200 scenario1scenario2 1 2 Period Units a 0 1 Available units profile1 profile2 profile3 profile4 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Node3Node4Node5 time2 time3 time4 time5 time2 time3 time4 time5 time2 time3 time4 time5 time2 time3 time4 time5 t Supply(kWh) i PV Electricity generation Computational Management Science 2016 8/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Integration Sweave("comprehensiveExample.Rnw") library(tools) texi2pdf("comprehensiveExample.tex") Computational Management Science 2016 9/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Integration Sweave("comprehensiveExample.Rnw") library(tools) texi2pdf("comprehensiveExample.tex") Comprehensive Example for “An Integrated Framework for the Representation and Solution of Stochastic Energy Optimization Problems” Emilio L. Cano January 6, 2014 1 Introduction This document is an example on how to use R as an integrated environment for optimization. It is assumed that the optimr package is installed. Here we can include any statistical analysis, for example a time series analysis to forecast the future energy prices, saving the values as parameters. We can also show graphical representations of the parameter values, as in Figure 1, or tables with data, e.g. Table 1. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Figure 1: Parameter values for the stochastic parameters. The equations or any item of the model can be printed automatically from the model2SMS object. For example, the following command fetches the objec- tive function: > cat("$$", getEq(model2SMS, 6, "tex", only = "rExpr"), "$$") n∈N Pn · t∈T   i∈I CI t i,n · xt i + i∈I,j∈J COt i,j,n · DTt j · yt i,j,n   1 j n t value 1 winter 1 2013 17.06 2 spring 1 2013 21.93 3 summer 1 2013 34.12 4 autumn 1 2013 24.37 5 winter 1 2014 19.89 6 spring 1 2014 25.58 Table 1: Example D parameter values (first 6 values). 2 Solving the problem Once we have the instance in an optimInstance object, it can be solved and the solution imported (see source code). Results checking is also possible as this information is also stored: We can embed calculations within the text, for example the value of the objective function (68595), or we can print pretty LATEX tables with the optimal values, as the ones in Tables 2 and 3, or any other analysis and representation (see Figure 2). See the .Rnw source file to see the code. i t value RTE 2013 45.65 PV 2013 57.65 PV 2014 1.78 Table 2: Optimal values for x i j n t value RTE winter 1 2014 2.31 RTE winter 1 2015 4.27 RTE winter 1 2016 8.96 RTE winter 1 2017 7.92 RTE winter 2 2014 1.76 RTE winter 2 2015 5.21 Table 3: Optimal values for y (first 6 values) 3 Conclusion This document can be compiled at any time, by any researcher. Note that if any value is changed, for example in the script that contain the parameters ("../data/model2Instance2.R"), the whole report is updated automatically (including tables, equations and charts). If we use simulation during the re- search, we can simply fix the seed to allow the verification of the results by third parties. Different reports for different stakeholders can be produced using a common structure and tailoring the outputs. 2 0 10 20 30 2013 2014 2015 2016 2017 Year kW Technology RTE PV Optimal production plans (Autumn) Figure 2: Output data representation. 3 Gold Standard Computational Management Science 2016 9/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw documentclass [ a4paper ]{ a r t i c l e } usepackage {Sweave} t i t l e { Comprehensive Example f o r ``An I n t e g r a t e d Framework f o r the R e p r e s e n t a t i o n and S o l u t i o n of S t o c h a s t i c Energy Optimization Problems ' '} author { Emilio L . Cano} <<i n t r o , echo=FALSE , r e s u l t s=hide>>= ## System r e q u i r e m e n t s ## − The R s o f t w a r e and the packages loaded below ## − A l i c e n c e d GAMS i n s t a l l a t i o n . I f GAMS d i r e c t o r y ## i s other than ”˜/ app/gams23 . 9 ” , change the l i n e ## ' igdx (”˜/ app/gams23 . 9 ”) ' ## − A LaTeX d i s t r i b u t i o n f o r the c u r r e n t system ## Load needed packages l i b r a r y ( k n i t r ) l i b r a r y ( optimr ) l i b r a r y ( gdxrrw ) l i b r a r y ( x t a b l e ) l i b r a r y ( ggplot2 ) l i b r a r y ( g r i d ) ## T e l l gdxrrw where GAMS i s i n s t a l l e d igdx (”˜/ app/gams23 . 9 ”) ## Run s c r i p t s with data ## D e t e r m i n i s t i c model Computational Management Science 2016 10/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) source ( ”. / data /model1SMS .R ”) ## S t o c h a s t i c e x t e n s i o n source ( ”. / data /model2SMS .R ”) ## I n s t a n c e with 100 s c e n a r i o s source ( ”. / data / model2Instance2 .R ”) @ begin {document} SweaveOpts{ concordance=TRUE} m a k e t i t l e s e c t i o n { I n t r o d u c t i o n } This document i s an example on how to use t e x t s f {R} as an i n t e g r a t e d environment f o r o p t i m i z a t i o n . I t i s assumed that the t e x t s f { optimr } package i s Here we can i n c l u d e any s t a t i s t i c a l a n a l y s i s , f o r example a time s e r i e s a n a l y s i s to f o r e c a s t the f u t u r e energy p r i c e s , s a v i n g the v a l u e s as parameters . We can a l s o show g r a p h i c a l r e p r e s e n t a t i o n s of the parameter values , as i n Figure ˜ r e f { f begin { f i g u r e }[ htp ] begin { c e n t e r } <<examplepar , f i g=TRUE, echo=FALSE , width=10>>= ## Demand dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”D”) d t o P l o t $ i d <− 1:20 pD <− ggplot ( data = dtoPlot , aes ( x = id , y = value , group=n , c o l=n )) pD <− pD + geom path () pD <− pD + s c a l e x d i s c r e t e (name = ”” , breaks = seq (1 ,21 , by =5) , l a b e l s = 2013:2 pD <− pD + g g t i t l e ( ”Energy demand ”) Computational Management Science 2016 11/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) pD <− pD + s c a l e y c o n t i n u o u s (name =”Demand l e v e l (kW) ”) pD <− pD + theme ( legend . p o s i t i o n = ”none ”) pD <− pD + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1) , ## Investment c o s t dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”CI ”) pCI <− ggplot ( data = dtoPlot , aes ( x = t , y = value , group=n , c o l=n )) pCI <− pCI + geom path () pCI <− pCI + f a c e t g r i d ( i ˜ . ) pCI <− pCI + s c a l e x c o n t i n u o u s (name = ””) pCI <− pCI + g g t i t l e ( ”Investment c o s t ”) pCI <− pCI + s c a l e y c o n t i n u o u s (name =”EUR/kW”) pCI <− pCI + theme ( legend . p o s i t i o n = ”none ”) pCI <− pCI + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1 ## Operation c o s t dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”CO”) d t o P l o t $ i d <− 1:20 pCO <− ggplot ( data = dtoPlot , aes ( x = id , y = value , group=n , c o l=n )) pCO <− pCO + geom path () pCO <− pCO + f a c e t g r i d ( i ˜ . ) pCO <− pCO + s c a l e x d i s c r e t e (name = ”” , breaks = seq (1 ,21 , by =5) , l a b e l s = 2013 pCO <− pCO + g g t i t l e ( ”Energy p r i c e ”) pCO <− pCO + s c a l e y c o n t i n u o u s (name =”EUR/kWh”) pCO <− pCO + g u i d e s ( c o l o r = g u i d e c o l o u r b a r ( t i t l e = ”S c e na ri o ”) ) pCO <− pCO + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1 g r i d . newpage () v p A l l <− viewport ( l a y o u t = g r i d . l a y o u t (2 , 3 , widths = c (1/3 , 1/3 , 1/3) , Computational Management Science 2016 12/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) h e i g h t s = c ( 0 . 1 , 0 . 9 ) ) ) vpT <− viewport ( l a y o u t . pos . c o l = 1:3 , l a y o u t . pos . row = 1 , name = ” t i t l e ”) vpD <− viewport ( l a y o u t . pos . c o l = 1 , l a y o u t . pos . row = 2 , name = ”D”) vpCI <− viewport ( l a y o u t . pos . c o l = 2 , l a y o u t . pos . row = 2 , name = ”CI ”) vpCO <− viewport ( l a y o u t . pos . c o l = 3 , l a y o u t . pos . row = 2 , name = ”CO”) s p l o t <− vpTree ( vpAll , v p L i s t (vpT , vpD , vpCI , vpCO )) pushViewport ( s p l o t ) seekViewport ( ” t i t l e ”) g r i d . t e x t (”100 s c e n a r i o s s i m u l a t i o n ”, gp = gpar ( cex =2)) seekViewport ( ”D”) p r i n t (pD, newpage = FALSE) seekViewport ( ”CI ”) p r i n t ( pCI , newpage = FALSE) seekViewport ( ”CO”) p r i n t (pCO, newpage = FALSE) @ c a p t i o n { Parameter v a l u e s f o r the s t o c h a s t i c parameters .} l a b e l { f i g : examplepar } end{ c e n t e r } end{ f i g u r e } <<echo=FALSE , r e s u l t s=tex>>= x t a b l e ( head ( i n s t a n c e P a r s ( model2Instance2 , ”D”) ) , l a b e l = ”tab : exampletable ”, c a p t i o n = ”Example $D$ parameter v a l u e s ( f i r s t 6 v a l u e s ) . ”) @ The e q u a t i o n s or any item of the model can be p r i n t e d a u t o m a t i c a l l y from the Computational Management Science 2016 13/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) t e x t s f {model2SMS} o b j e c t . For example , the f o l l o w i n g command f e t c h e s the o b j e c t i v e f u n c t i o n : <<r e s u l t s=tex>>= cat ( ”$$ ”, getEq ( model2SMS , 6 , ”tex ”, only = ”rExpr ”) , ”$$ ”) @ s e c t i o n { S o l v i n g the problem } Once we have the i n s t a n c e i n an t e x t t t { optimInstance } object , i t can be s o l v e d <<sol , echo=FALSE , r e s u l t s=hide>>= wProblem ( model2Instance2 , f i l e n a m e = ”. / data / model2Instance2 . gms ”, format = ”gams ”, s o l v e r = ”LP ”) r e s <− gams ( ”. / data / model2Instance2 . gms −−o u t f i l e =./ data / model2Instance2 . gdx ”) data ( gamsOut ) i f ( r e s == 0){ importGams ( model2Instance2 ) <− ”. / data / model2Instance2 . gdx ” message ( ”Optimization okn ”, ” tModel Status : ”, as . c h a r a c t e r ( s u bs e t ( gamsModelStatusCode , i d == model2Instance2@result$model , desc , drop = TRUE) ) , ” n t S o l v e r Status : ”, as . c h a r a c t e r ( s u bs e t ( gamsSolverStatusCode , i d == m o d e l 2 I n s t a n c e 2 @ r e s u l t $ s o l v e , desc , drop = TRUE) ) ) } e l s e { warning ( ”Check the l i s t i n g f i l e , something was wrong : ”, s ub s e t ( gamsOutCode , i d == res , desc , drop = TRUE)) Computational Management Science 2016 14/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) } @ We can embed c a l c u l a t i o n s w i t h i n the text , f o r example the v a l u e of the o b j e c t i v e f u n c t i o n ( Sexpr { round ( m o d e l 2 I n s t a n c e 2 @ r e s u l t $ o b j )}) , or we can p r i n t LaTeX˜ t a b l e s with the optimal values , as the ones i n Tables r e f { tab : x} and r e other a n a l y s i s and r e p r e s e n t a t i o n ( see Figure ˜ r e f { f i g : r e s } ) . See the t e x t t t {.R <<r e s u l t s=tex , echo=FALSE>>= p r i n t ( x t a b l e ( i n s t a n c e V a r s ( model2Instance2 , ”x ”) , ”Optimal v a l u e s f o r $x$ ”, ”tab : x ”) , i n c l u d e . rownames = FALSE) p r i n t ( x t a b l e ( head ( i n s t a n c e V a r s ( model2Instance2 , ”y ”) ) , ”Optimal v a l u e s f o r $y$ ( f i r s t 6 v a l u e s ) ”, ”tab : y ”) , i n c l u d e . rownames = FALSE) @ begin { f i g u r e }[ htp ] begin { c e n t e r } <<bar , echo=FALSE , f i g=TRUE>>= d f 2 p l o t <− s ub s e t ( i n s t a n c e V a r s ( model2Instance2 , ”y ”) , j == ”autumn ”) d f 2 p l o t <− aggregate ( v a l u e ˜ i + t , data = df2plot , FUN = mean) d f 2 p l o t $ t <− as . i n t e g e r ( as . c h a r a c t e r ( d f 2 p l o t $ t )) p <− ggplot ( df2plot , aes ( x=t )) p <− p + geom area ( aes ( y=value , f i l l =i )) p <− p + l a b s ( t i t l e = ”Optimal production p l a n s (Autumn ) ”, x = ”Year ”, y = ”kW”) p <− p + s c a l e f i l l d i s c r e t e ( ”Technology ”) p r i n t ( p ) @ Computational Management Science 2016 15/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) end{ c e n t e r } c a p t i o n {Output data r e p r e s e n t a t i o n . l a b e l { f i g : r e s }} end{ f i g u r e } s e c t i o n { Conclusion } This document can be compiled at any time , by any r e s e a r c h e r . Note that i f any v a l u e i s changed , f o r example i n the s c r i p t that c o n t a i n the parameters ( t e x t t t { ”. . / data / model2Instance2 .R”} ) , the whole r e p o r t i s updated a u t o m a t i c a l l ( i n c l u d i n g t a b l e s , e q u a t i o n s and c h a r t s ) . I f we use s i m u l a t i o n during the research , we can simply f i x the seed to a l l o w the v e r i f i c a t i o n of the r e s u l t s by t h i r d p a r t i e s . D i f f e r e n t r e p o r t s f o r d i f f e r e n end{document} Computational Management Science 2016 16/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Workflow Computational Management Science 2016 17/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 18/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage models Rolling horizon In Cano EL, Moguerza JM, Ermolieva T and Ermoliev Y (2014). “Energy efficiency and risk management in public buildings: Strategic model for robust planning.” Computational Management Science, 11, pp. 25-44 Moving random time horizons In Cano EL, Moguerza JM, Ermolieva T and Ermoliev Y (under review). “A strategic decision support system framework for energy-efficient technology investments.” TOP. Computational Management Science 2016 19/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Fsto(x∗sto) = 68, 595 EUR. Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Fsto(x∗sto) = 68, 595 EUR. VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Infeasible 56/100 Fsto(x∗sto) = 68, 595 EUR. VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Infeasible 56/100 Fsto(x∗sto) = 68, 595 EUR. Robust, optimal against all VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Multi-stage model Complete model with risk In Cano EL, Moguerza JM and Alonso-Ayuso A (2016). “A multi-stage stochastic optimization model for energy systems planning and risk management.” Energy and Buildings, 110, pp. 49–56. Reproducible data and code In Cano EL, Moguerza JM and Alonso-Ayuso A (2015). “Optimization instances for deterministic and stochastic problems on energy efficient investments planning at the building level.” Data in Brief, 5, pp. 805–809. Computational Management Science 2016 21/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Multi-stage model with risk management Different objectives: min cost, emissions, or energy use Risk measure CVaR [Rockafellar and Uryasev (2000)] Weighted objective function Computational Management Science 2016 22/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Computational Management Science 2016 23/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Computational Management Science 2016 23/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 24/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Computational Management Science 2016 25/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Further Research Two-stage vs Multi-stage applicability New models for energy storage systems Productize package. Extend to further formats Explore new reproducible research paths (R Markdown, interactive visualisation, . . . ) Computational Management Science 2016 25/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Further Research Two-stage vs Multi-stage applicability New models for energy storage systems Productize package. Extend to further formats Explore new reproducible research paths (R Markdown, interactive visualisation, . . . ) Links Publications: http://emilio.lcano.com/content/en/ publicaciones.html optimr package: https://github.com/emilopezcano/optimr Computational Management Science 2016 25/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions DSS Mission Joseph Kallrath (2012). Algebraic Modeling Systems, Springer. Chapter 12: A Practioner’s Wish List Towards Algebraic Modeling Systems “The automatic generation of a model’s documentation in LATEX would be very helpful for mathematicians, physicists, astronomers, and other communities publishing in LATEX.” Computational Management Science 2016 26/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Acknowledgements We acknowledge projects: OPTIMOS3 (MTM2012-36163-C06-06) GROMA (MTM2015-63710-P) PPI (RTC-2015-3580-7) UNIKO (RTC-2015-3521-7) and the Young Scientists Summer Program (YSSP) at the International Institute of Applied Systems Analysis (IIASA). Computational Management Science 2016 27/28
DSS framework CMS 2016 Emilio L. Cano An Integrated Framework Stochastic Models Conclusions Discussion Thanks ! emilio.lopez@urjc.es @emilopezcano http://emilio.lcano.com Computational Management Science 2016 28/28

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Energy-efficient technology investments using a decision support system framework

  • 1.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Energy-efficient technology investments using a decision support system framework Emilio L. Cano1 Javier M. Moguerza1 Tatiana Ermolieva2 Yurii Yermoliev2 1Rey Juan Carlos University 2International Institute for Applied Systems Analysis (IIASA) Salamanca, May 31 - June 2 2016 Computational Management Science 2016 1/28
  • 2.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 2/28
  • 3.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 3/28
  • 4.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Algorithms Model Symbolic model Variables, relations Underlying theory Methodology, technique Uncertainty modelling Data Deterministic data Uncertain data - Stochastic processes Data analysis Solution Data treatment Analysis Visualization DSS Interpretation Computational Management Science 2016 4/28
  • 5.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Algorithms Model Symbolic model Variables, relations Underlying theory Methodology, technique Uncertainty modelling Data Deterministic data Uncertain data - Stochastic processes Data analysis Solution Data treatment Analysis Visualization DSS Stakeholders Dialog Interpretation Computational Management Science 2016 4/28
  • 6.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Decision Support Systems Computational Management Science 2016 4/28
  • 7.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Computational Management Science 2016 5/28
  • 8.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Computational Management Science 2016 5/28
  • 9.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Copy-paste Inconsistencies Errors Out-of-date non-reproducible Painful changes Computational Management Science 2016 5/28
  • 10.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Black box Compiled software for specific solutions Changes require re-programming Not reproducible Computational Management Science 2016 5/28
  • 11.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Framework Requirements Statistical software Data visualization Mathematical modeling Solver input generation Call to the solver Output documentation Framework Reproducible Research & Literate Programming omptimr R package & Algebraic Modeling Languages (AMLs) “The goal of RR is to tie specific instructions to data analysis and experimental data [and modeling] so that results can be recreated, better understood and verified” “LP: a document that is a combination of content and data analysis code [and models]” Computational Management Science 2016 5/28
  • 12.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions R as an Integrated Environment Advantages Open Source Reproducible Research and Literate Programming capabilities. Integrated framework for SMS, data, equations and solvers. Data Analysis (pre- and post-), graphics and reporting. Computational Management Science 2016 6/28
  • 13.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions optimr Package Computational Management Science 2016 7/28
  • 14.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions optimr Package Computational Management Science 2016 7/28
  • 15.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions optimr Package getEq(model1SMS, 4, format = "gams") ## [1] "eqDemand(j,t) ..nt Sum((i), y(i,j,t)) =e= D(j,t) n;n" Computational Management Science 2016 7/28
  • 16.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Solution and Analysis wProblem(mod1Instance, "mod1.gms", "gams", "lp") library(gdxrrw) igdx(" /Programs/gams") gams("mod1.gms") importGams(mod1Instance) <- "outSolDeterministic1.gdx" 0 50 100 150 200 0 50 100 150 200 scenario1scenario2 1 2 Period Units a 0 1 Available units profile1 profile2 profile3 profile4 0 50 100 150 200 0 50 100 150 200 0 50 100 150 200 Node3Node4Node5 time2 time3 time4 time5 time2 time3 time4 time5 time2 time3 time4 time5 time2 time3 time4 time5 t Supply(kWh) i PV Electricity generation Computational Management Science 2016 8/28
  • 17.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Integration Sweave("comprehensiveExample.Rnw") library(tools) texi2pdf("comprehensiveExample.tex") Computational Management Science 2016 9/28
  • 18.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Integration Sweave("comprehensiveExample.Rnw") library(tools) texi2pdf("comprehensiveExample.tex") Comprehensive Example for “An Integrated Framework for the Representation and Solution of Stochastic Energy Optimization Problems” Emilio L. Cano January 6, 2014 1 Introduction This document is an example on how to use R as an integrated environment for optimization. It is assumed that the optimr package is installed. Here we can include any statistical analysis, for example a time series analysis to forecast the future energy prices, saving the values as parameters. We can also show graphical representations of the parameter values, as in Figure 1, or tables with data, e.g. Table 1. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Figure 1: Parameter values for the stochastic parameters. The equations or any item of the model can be printed automatically from the model2SMS object. For example, the following command fetches the objec- tive function: > cat("$$", getEq(model2SMS, 6, "tex", only = "rExpr"), "$$") n∈N Pn · t∈T   i∈I CI t i,n · xt i + i∈I,j∈J COt i,j,n · DTt j · yt i,j,n   1 j n t value 1 winter 1 2013 17.06 2 spring 1 2013 21.93 3 summer 1 2013 34.12 4 autumn 1 2013 24.37 5 winter 1 2014 19.89 6 spring 1 2014 25.58 Table 1: Example D parameter values (first 6 values). 2 Solving the problem Once we have the instance in an optimInstance object, it can be solved and the solution imported (see source code). Results checking is also possible as this information is also stored: We can embed calculations within the text, for example the value of the objective function (68595), or we can print pretty LATEX tables with the optimal values, as the ones in Tables 2 and 3, or any other analysis and representation (see Figure 2). See the .Rnw source file to see the code. i t value RTE 2013 45.65 PV 2013 57.65 PV 2014 1.78 Table 2: Optimal values for x i j n t value RTE winter 1 2014 2.31 RTE winter 1 2015 4.27 RTE winter 1 2016 8.96 RTE winter 1 2017 7.92 RTE winter 2 2014 1.76 RTE winter 2 2015 5.21 Table 3: Optimal values for y (first 6 values) 3 Conclusion This document can be compiled at any time, by any researcher. Note that if any value is changed, for example in the script that contain the parameters ("../data/model2Instance2.R"), the whole report is updated automatically (including tables, equations and charts). If we use simulation during the re- search, we can simply fix the seed to allow the verification of the results by third parties. Different reports for different stakeholders can be produced using a common structure and tailoring the outputs. 2 0 10 20 30 2013 2014 2015 2016 2017 Year kW Technology RTE PV Optimal production plans (Autumn) Figure 2: Output data representation. 3 Gold Standard Computational Management Science 2016 9/28
  • 19.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw documentclass [ a4paper ]{ a r t i c l e } usepackage {Sweave} t i t l e { Comprehensive Example f o r ``An I n t e g r a t e d Framework f o r the R e p r e s e n t a t i o n and S o l u t i o n of S t o c h a s t i c Energy Optimization Problems ' '} author { Emilio L . Cano} <<i n t r o , echo=FALSE , r e s u l t s=hide>>= ## System r e q u i r e m e n t s ## − The R s o f t w a r e and the packages loaded below ## − A l i c e n c e d GAMS i n s t a l l a t i o n . I f GAMS d i r e c t o r y ## i s other than ”˜/ app/gams23 . 9 ” , change the l i n e ## ' igdx (”˜/ app/gams23 . 9 ”) ' ## − A LaTeX d i s t r i b u t i o n f o r the c u r r e n t system ## Load needed packages l i b r a r y ( k n i t r ) l i b r a r y ( optimr ) l i b r a r y ( gdxrrw ) l i b r a r y ( x t a b l e ) l i b r a r y ( ggplot2 ) l i b r a r y ( g r i d ) ## T e l l gdxrrw where GAMS i s i n s t a l l e d igdx (”˜/ app/gams23 . 9 ”) ## Run s c r i p t s with data ## D e t e r m i n i s t i c model Computational Management Science 2016 10/28
  • 20.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) source ( ”. / data /model1SMS .R ”) ## S t o c h a s t i c e x t e n s i o n source ( ”. / data /model2SMS .R ”) ## I n s t a n c e with 100 s c e n a r i o s source ( ”. / data / model2Instance2 .R ”) @ begin {document} SweaveOpts{ concordance=TRUE} m a k e t i t l e s e c t i o n { I n t r o d u c t i o n } This document i s an example on how to use t e x t s f {R} as an i n t e g r a t e d environment f o r o p t i m i z a t i o n . I t i s assumed that the t e x t s f { optimr } package i s Here we can i n c l u d e any s t a t i s t i c a l a n a l y s i s , f o r example a time s e r i e s a n a l y s i s to f o r e c a s t the f u t u r e energy p r i c e s , s a v i n g the v a l u e s as parameters . We can a l s o show g r a p h i c a l r e p r e s e n t a t i o n s of the parameter values , as i n Figure ˜ r e f { f begin { f i g u r e }[ htp ] begin { c e n t e r } <<examplepar , f i g=TRUE, echo=FALSE , width=10>>= ## Demand dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”D”) d t o P l o t $ i d <− 1:20 pD <− ggplot ( data = dtoPlot , aes ( x = id , y = value , group=n , c o l=n )) pD <− pD + geom path () pD <− pD + s c a l e x d i s c r e t e (name = ”” , breaks = seq (1 ,21 , by =5) , l a b e l s = 2013:2 pD <− pD + g g t i t l e ( ”Energy demand ”) Computational Management Science 2016 11/28
  • 21.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) pD <− pD + s c a l e y c o n t i n u o u s (name =”Demand l e v e l (kW) ”) pD <− pD + theme ( legend . p o s i t i o n = ”none ”) pD <− pD + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1) , ## Investment c o s t dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”CI ”) pCI <− ggplot ( data = dtoPlot , aes ( x = t , y = value , group=n , c o l=n )) pCI <− pCI + geom path () pCI <− pCI + f a c e t g r i d ( i ˜ . ) pCI <− pCI + s c a l e x c o n t i n u o u s (name = ””) pCI <− pCI + g g t i t l e ( ”Investment c o s t ”) pCI <− pCI + s c a l e y c o n t i n u o u s (name =”EUR/kW”) pCI <− pCI + theme ( legend . p o s i t i o n = ”none ”) pCI <− pCI + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1 ## Operation c o s t dtoPlot <− i n s t a n c e P a r s ( model2Instance2 , ”CO”) d t o P l o t $ i d <− 1:20 pCO <− ggplot ( data = dtoPlot , aes ( x = id , y = value , group=n , c o l=n )) pCO <− pCO + geom path () pCO <− pCO + f a c e t g r i d ( i ˜ . ) pCO <− pCO + s c a l e x d i s c r e t e (name = ”” , breaks = seq (1 ,21 , by =5) , l a b e l s = 2013 pCO <− pCO + g g t i t l e ( ”Energy p r i c e ”) pCO <− pCO + s c a l e y c o n t i n u o u s (name =”EUR/kWh”) pCO <− pCO + g u i d e s ( c o l o r = g u i d e c o l o u r b a r ( t i t l e = ”S c e na ri o ”) ) pCO <− pCO + stat summary ( fun . y=mean , c o l o u r =”darkred ”, geom=”l i n e ”, aes ( group =1 g r i d . newpage () v p A l l <− viewport ( l a y o u t = g r i d . l a y o u t (2 , 3 , widths = c (1/3 , 1/3 , 1/3) , Computational Management Science 2016 12/28
  • 22.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) h e i g h t s = c ( 0 . 1 , 0 . 9 ) ) ) vpT <− viewport ( l a y o u t . pos . c o l = 1:3 , l a y o u t . pos . row = 1 , name = ” t i t l e ”) vpD <− viewport ( l a y o u t . pos . c o l = 1 , l a y o u t . pos . row = 2 , name = ”D”) vpCI <− viewport ( l a y o u t . pos . c o l = 2 , l a y o u t . pos . row = 2 , name = ”CI ”) vpCO <− viewport ( l a y o u t . pos . c o l = 3 , l a y o u t . pos . row = 2 , name = ”CO”) s p l o t <− vpTree ( vpAll , v p L i s t (vpT , vpD , vpCI , vpCO )) pushViewport ( s p l o t ) seekViewport ( ” t i t l e ”) g r i d . t e x t (”100 s c e n a r i o s s i m u l a t i o n ”, gp = gpar ( cex =2)) seekViewport ( ”D”) p r i n t (pD, newpage = FALSE) seekViewport ( ”CI ”) p r i n t ( pCI , newpage = FALSE) seekViewport ( ”CO”) p r i n t (pCO, newpage = FALSE) @ c a p t i o n { Parameter v a l u e s f o r the s t o c h a s t i c parameters .} l a b e l { f i g : examplepar } end{ c e n t e r } end{ f i g u r e } <<echo=FALSE , r e s u l t s=tex>>= x t a b l e ( head ( i n s t a n c e P a r s ( model2Instance2 , ”D”) ) , l a b e l = ”tab : exampletable ”, c a p t i o n = ”Example $D$ parameter v a l u e s ( f i r s t 6 v a l u e s ) . ”) @ The e q u a t i o n s or any item of the model can be p r i n t e d a u t o m a t i c a l l y from the Computational Management Science 2016 13/28
  • 23.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) t e x t s f {model2SMS} o b j e c t . For example , the f o l l o w i n g command f e t c h e s the o b j e c t i v e f u n c t i o n : <<r e s u l t s=tex>>= cat ( ”$$ ”, getEq ( model2SMS , 6 , ”tex ”, only = ”rExpr ”) , ”$$ ”) @ s e c t i o n { S o l v i n g the problem } Once we have the i n s t a n c e i n an t e x t t t { optimInstance } object , i t can be s o l v e d <<sol , echo=FALSE , r e s u l t s=hide>>= wProblem ( model2Instance2 , f i l e n a m e = ”. / data / model2Instance2 . gms ”, format = ”gams ”, s o l v e r = ”LP ”) r e s <− gams ( ”. / data / model2Instance2 . gms −−o u t f i l e =./ data / model2Instance2 . gdx ”) data ( gamsOut ) i f ( r e s == 0){ importGams ( model2Instance2 ) <− ”. / data / model2Instance2 . gdx ” message ( ”Optimization okn ”, ” tModel Status : ”, as . c h a r a c t e r ( s u bs e t ( gamsModelStatusCode , i d == model2Instance2@result$model , desc , drop = TRUE) ) , ” n t S o l v e r Status : ”, as . c h a r a c t e r ( s u bs e t ( gamsSolverStatusCode , i d == m o d e l 2 I n s t a n c e 2 @ r e s u l t $ s o l v e , desc , drop = TRUE) ) ) } e l s e { warning ( ”Check the l i s t i n g f i l e , something was wrong : ”, s ub s e t ( gamsOutCode , i d == res , desc , drop = TRUE)) Computational Management Science 2016 14/28
  • 24.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) } @ We can embed c a l c u l a t i o n s w i t h i n the text , f o r example the v a l u e of the o b j e c t i v e f u n c t i o n ( Sexpr { round ( m o d e l 2 I n s t a n c e 2 @ r e s u l t $ o b j )}) , or we can p r i n t LaTeX˜ t a b l e s with the optimal values , as the ones i n Tables r e f { tab : x} and r e other a n a l y s i s and r e p r e s e n t a t i o n ( see Figure ˜ r e f { f i g : r e s } ) . See the t e x t t t {.R <<r e s u l t s=tex , echo=FALSE>>= p r i n t ( x t a b l e ( i n s t a n c e V a r s ( model2Instance2 , ”x ”) , ”Optimal v a l u e s f o r $x$ ”, ”tab : x ”) , i n c l u d e . rownames = FALSE) p r i n t ( x t a b l e ( head ( i n s t a n c e V a r s ( model2Instance2 , ”y ”) ) , ”Optimal v a l u e s f o r $y$ ( f i r s t 6 v a l u e s ) ”, ”tab : y ”) , i n c l u d e . rownames = FALSE) @ begin { f i g u r e }[ htp ] begin { c e n t e r } <<bar , echo=FALSE , f i g=TRUE>>= d f 2 p l o t <− s ub s e t ( i n s t a n c e V a r s ( model2Instance2 , ”y ”) , j == ”autumn ”) d f 2 p l o t <− aggregate ( v a l u e ˜ i + t , data = df2plot , FUN = mean) d f 2 p l o t $ t <− as . i n t e g e r ( as . c h a r a c t e r ( d f 2 p l o t $ t )) p <− ggplot ( df2plot , aes ( x=t )) p <− p + geom area ( aes ( y=value , f i l l =i )) p <− p + l a b s ( t i t l e = ”Optimal production p l a n s (Autumn ) ”, x = ”Year ”, y = ”kW”) p <− p + s c a l e f i l l d i s c r e t e ( ”Technology ”) p r i n t ( p ) @ Computational Management Science 2016 15/28
  • 25.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions comprehensiveExample.Rnw (cont.) end{ c e n t e r } c a p t i o n {Output data r e p r e s e n t a t i o n . l a b e l { f i g : r e s }} end{ f i g u r e } s e c t i o n { Conclusion } This document can be compiled at any time , by any r e s e a r c h e r . Note that i f any v a l u e i s changed , f o r example i n the s c r i p t that c o n t a i n the parameters ( t e x t t t { ”. . / data / model2Instance2 .R”} ) , the whole r e p o r t i s updated a u t o m a t i c a l l ( i n c l u d i n g t a b l e s , e q u a t i o n s and c h a r t s ) . I f we use s i m u l a t i o n during the research , we can simply f i x the seed to a l l o w the v e r i f i c a t i o n of the r e s u l t s by t h i r d p a r t i e s . D i f f e r e n t r e p o r t s f o r d i f f e r e n end{document} Computational Management Science 2016 16/28
  • 26.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Workflow Computational Management Science 2016 17/28
  • 27.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 18/28
  • 28.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage models Rolling horizon In Cano EL, Moguerza JM, Ermolieva T and Ermoliev Y (2014). “Energy efficiency and risk management in public buildings: Strategic model for robust planning.” Computational Management Science, 11, pp. 25-44 Moving random time horizons In Cano EL, Moguerza JM, Ermolieva T and Ermoliev Y (under review). “A strategic decision support system framework for energy-efficient technology investments.” TOP. Computational Management Science 2016 19/28
  • 29.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Computational Management Science 2016 20/28
  • 30.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Computational Management Science 2016 20/28
  • 31.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Fsto(x∗sto) = 68, 595 EUR. Computational Management Science 2016 20/28
  • 32.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Fsto(x∗sto) = 68, 595 EUR. VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
  • 33.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Infeasible 56/100 Fsto(x∗sto) = 68, 595 EUR. VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
  • 34.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage instance Five periods, two technologies (CHP, PV), only electricity. 100 scenarios simulation 20 40 60 80 2013 2014 2015 2016 Demandlevel(kW) Energy demand 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 0 500 1000 1500 2000 2500 CHPPVRTE 2013 2014 2015 2016 2017 EUR/kW Investment cost 0.1 0.2 0.3 0.1 0.2 0.3 CHPRTE 2013 2014 2015 2016 EUR/kWh 25 50 75 100 Scenario Energy price Fdet (x∗det ) = 66, 920 EUR. Infeasible 56/100 Fsto(x∗sto) = 68, 595 EUR. Robust, optimal against all VSS = Fsto(x∗det ) − Fsto(x∗sto) = ∞ Computational Management Science 2016 20/28
  • 35.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Multi-stage model Complete model with risk In Cano EL, Moguerza JM and Alonso-Ayuso A (2016). “A multi-stage stochastic optimization model for energy systems planning and risk management.” Energy and Buildings, 110, pp. 49–56. Reproducible data and code In Cano EL, Moguerza JM and Alonso-Ayuso A (2015). “Optimization instances for deterministic and stochastic problems on energy efficient investments planning at the building level.” Data in Brief, 5, pp. 805–809. Computational Management Science 2016 21/28
  • 36.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Multi-stage model with risk management Different objectives: min cost, emissions, or energy use Risk measure CVaR [Rockafellar and Uryasev (2000)] Weighted objective function Computational Management Science 2016 22/28
  • 37.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Computational Management Science 2016 23/28
  • 38.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Computational Management Science 2016 23/28
  • 39.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
  • 40.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
  • 41.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Two-stage vs. Multi-stage Dynamic two-stage First-stage decisions: strategic Second-stage decisions: operational Solution: trajectory, recalculated at each step Multi-stage First-stage decisions: before branching 2nd -, . . . , nth-stage decisions: after branching Solution: strategy, recalculated at each step Computational Management Science 2016 23/28
  • 42.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Outline 1 An Integrated Framework 2 Stochastic Models 3 Conclusions Computational Management Science 2016 24/28
  • 43.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Computational Management Science 2016 25/28
  • 44.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Further Research Two-stage vs Multi-stage applicability New models for energy storage systems Productize package. Extend to further formats Explore new reproducible research paths (R Markdown, interactive visualisation, . . . ) Computational Management Science 2016 25/28
  • 45.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Conclusions Results Reproducible Research methods in Optimization The stakeholders dialog viewpoint for DSSs The optimr library Comprehensive example demonstrating the framework Further Research Two-stage vs Multi-stage applicability New models for energy storage systems Productize package. Extend to further formats Explore new reproducible research paths (R Markdown, interactive visualisation, . . . ) Links Publications: http://emilio.lcano.com/content/en/ publicaciones.html optimr package: https://github.com/emilopezcano/optimr Computational Management Science 2016 25/28
  • 46.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions DSS Mission Joseph Kallrath (2012). Algebraic Modeling Systems, Springer. Chapter 12: A Practioner’s Wish List Towards Algebraic Modeling Systems “The automatic generation of a model’s documentation in LATEX would be very helpful for mathematicians, physicists, astronomers, and other communities publishing in LATEX.” Computational Management Science 2016 26/28
  • 47.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Acknowledgements We acknowledge projects: OPTIMOS3 (MTM2012-36163-C06-06) GROMA (MTM2015-63710-P) PPI (RTC-2015-3580-7) UNIKO (RTC-2015-3521-7) and the Young Scientists Summer Program (YSSP) at the International Institute of Applied Systems Analysis (IIASA). Computational Management Science 2016 27/28
  • 48.
    DSS framework CMS 2016 EmilioL. Cano An Integrated Framework Stochastic Models Conclusions Discussion Thanks ! emilio.lopez@urjc.es @emilopezcano http://emilio.lcano.com Computational Management Science 2016 28/28