energy-efficient technology investments using a decision support system framework

DSS framework

CMS 2016

Emilio L. Cano

An IntegratedFramework

StochasticModels

Conclusions

Energy-efficient technology investments using a decisionsupport system framework

Emilio L. Cano1 Javier M. Moguerza1

Tatiana Ermolieva2 Yurii Yermoliev2

1Rey Juan Carlos University2International 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


StochasticModels

Conclusions

Outline

1 An Integrated Framework

2 Stochastic Models

3 Conclusions


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Outline


2 Stochastic Models

3 Conclusions


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Decision Support Systems

Algorithms

ModelSymbolic modelVariables, relations

Underlying theoryMethodology, technique

Uncertainty modelling

DataDeterministic dataUncertain data -Stochastic processes

Data analysis

SolutionData treatmentAnalysisVisualization

DSS

Interpretation


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions


Algorithms

ModelSymbolic modelVariables, relations

Underlying theoryMethodology, technique

Uncertainty modelling

DataDeterministic dataUncertain data -Stochastic processes

Data analysis

SolutionData treatmentAnalysisVisualization

DSS

Stakeholders Dialog

Interpretation


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions



DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

DSS Framework

Requirements

Statistical softwareData visualizationMathematical modelingSolver input generationCall to the solverOutput 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 andexperimental 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]”


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

DSS Framework

Requirements


Copy-paste

Inconsistencies

Errors

Out-of-date

non-reproducible

Painful changes

Framework







DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

DSS Framework

Requirements


Black box

Compiled software for specificsolutions

Changes require re-programming

Not reproducible

Framework







DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

DSS Framework

Requirements


Framework







DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

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.


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

optimr Package

getEq(model1SMS, 4, format = "gams")

## [1] "eqDemand(j,t) ..\n\t Sum((i), y(i,j,t)) =e= D(j,t) \n;\n"


DSS framework

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Emilio L. Cano


StochasticModels

Conclusions

Solution and Analysis

wProblem(mod1Instance, "mod1.gms", "gams", "lp")

library(gdxrrw)

igdx(" /Programs/gams")

gams("mod1.gms")

importGams(mod1Instance) <- "outSolDeterministic1.gdx"

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DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

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 foroptimization. It is assumed that the optimr package is installed.

Here we can include any statistical analysis, for example a time series analysisto forecast the future energy prices, saving the values as parameters. We canalso show graphical representations of the parameter values, as in Figure 1, ortables with data, e.g. Table 1.

100 scenarios simulation

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Figure 1: Parameter values for the stochastic parameters.

The equations or any item of the model can be printed automatically fromthe model2SMS object. For example, the following command fetches the objec-tive function:

> cat("$$", getEq(model2SMS, 6, "tex", only = "rExpr"), "$$")

∑

n∈NPn ·

∑

t∈T

∑

i∈ICI ti,n · x t

i +∑

i∈I,j∈JCO t

i,j,n ·DT tj · yt

i,j,n

1

j n t value1 winter 1 2013 17.062 spring 1 2013 21.933 summer 1 2013 34.124 autumn 1 2013 24.375 winter 1 2014 19.896 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 andthe solution imported (see source code). Results checking is also possible as thisinformation is also stored:

We can embed calculations within the text, for example the value of theobjective function (68595), or we can print pretty LATEX tables with the optimalvalues, 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 valueRTE 2013 45.65PV 2013 57.65PV 2014 1.78

Table 2: Optimal values for x

i j n t valueRTE winter 1 2014 2.31RTE winter 1 2015 4.27RTE winter 1 2016 8.96RTE winter 1 2017 7.92RTE winter 2 2014 1.76RTE 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 ifany 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 bythird parties. Different reports for different stakeholders can be produced usinga common structure and tailoring the outputs.

2

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RTE

PV

Optimal production plans (Autumn)

Figure 2: Output data representation.

3

Gold Standard


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Emilio L. Cano


StochasticModels

Conclusions

comprehensiveExample.Rnw

\ documentc l a s s [ a4paper ]{ a r t i c l e }\ usepackage {Sweave}

\ t i t l e {Comprehens ive Example f o r``An I n t e g r a t e d Framework f o r theRep r e s e n t a t i o n and So l u t i o n o f S t o c h a s t i cEnergy Opt im i z a t i on Problems ' '}\ autho r { Em i l i o L . Cano}

<< i n t r o , echo=FALSE , r e s u l t s=hide>>=## System r equ i r emen t s## − The R so f twa r e and the packages l oaded 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 o th e r than ”˜/ app/gams23 . 9 ” , change the l i n e## ' i g d x ( ”˜/ 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 packagesl i b r a r y ( k n i t r )l i b r a r y ( opt imr )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 ( ggp l o t2 )l i b r a r y ( g r i d )

## Te l l gdxrrw where GAMS i s i n s t a l l e di gdx ( ”˜/ app/gams23 . 9 ”)

## Run s c r i p t s w i th data## De t e rm i n i s t i c model


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Emilio L. Cano


StochasticModels

Conclusions

comprehensiveExample.Rnw (cont.)

s ou r c e ( ”. / data /model1SMS .R”)## S t o c h a s t i c e x t e n s i o nsou r c e ( ”. / data /model2SMS .R”)## In s t a n c e wi th 100 s c e n a r i o ss ou r c e ( ”. / data /mode l2 In s t ance2 .R”)@

\ beg in {document}\SweaveOpts{ concordance=TRUE}

\mak 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 denv i ronment f o r o p t im i z a t i o n . I t i s assumed tha t the \ t e x t s f { opt imr } package i s i n s t a l l e d .

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 t ime s e r i e s a n a l y s i sto f o r e c a s t the f u t u r e ene rgy p r i c e s , s a v i n g the v a l u e s as pa ramete r s . We cana 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 o f the paramete r va l u e s , as i n F i gu r e ˜\ r e f { f i g : examplepar } , o r t a b l e s w i th data , e . g . Table ˜\ r e f { tab : e xamp l e t ab l e } .

\ beg in { f i g u r e } [ htp ]\ beg in { c e n t e r }<<examplepar , f i g=TRUE, echo=FALSE , width=10>>=## Demandd toP l o t <− i n s t a n c ePa r s ( mode l2 Ins tance2 , ”D”)d t oP l o t $ i d <− 1 :20pD <− ggp l o t ( data = dtoPlot , ae s ( x = id , y = va lue , 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 = ”” , b r eak s = seq (1 ,21 , by=5) , l a b e l s = 2013 :2017)pD <− pD + g g t i t l e ( ”Energy demand ”)


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StochasticModels

Conclusions


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 ( l eg end . p o s i t i o n = ”none ”)pD <− pD + stat summary ( fun . y=mean , c o l o u r =”da rk r ed ” , geom=”l i n e ” , aes ( group=1) , s i z e =1)

## Inve s tment c o s td toP l o t <− i n s t a n c ePa r s ( mode l2 Ins tance2 , ”CI ”)pCI <− ggp l o t ( data = dtoPlot , ae s ( x = t , y = va lue , 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 ( ” Inve s tment 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 ( l egend . p o s i t i o n = ”none ”)pCI <− pCI + stat summary ( fun . y=mean , c o l o u r =”da rk r ed ” , geom=”l i n e ” , aes ( group=1) , s i z e =1)

## Opera t i on co s td toP l o t <− i n s t a n c ePa r s ( mode l2 Ins tance2 , ”CO”)d t oP l o t $ i d <− 1 :20pCO <− ggp l o t ( data = dtoPlot , ae s ( x = id , y = va lue , 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 = ”” , b r eak s = seq (1 ,21 , by=5) , l a b e l s = 2013 :2017)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 + gu i d e s ( c o l o r = gu i d e c o l o u r b a r ( t i t l e = ”Sc ena r i o ”) )pCO <− pCO + stat summary ( fun . y=mean , c o l o u r =”da rk r ed ” , geom=”l i n e ” , aes ( group=1) , s i z e =1)

g r i d . newpage ( )v pA l l <− v i ewpo r t ( l a y o u t = g r i d . l a y o u t (2 , 3 ,

w id th s = c (1/3 , 1/3 , 1/3) ,


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions


h e i g h t s = c ( 0 . 1 , 0 . 9 ) ) )vpT <− v i ewpo r t ( 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 <− v i ewpo r t ( l a y o u t . pos . c o l = 1 , l a y o u t . pos . row = 2 , name = ”D”)vpCI <− v i ewpo r t ( l a y o u t . pos . c o l = 2 , l a y o u t . pos . row = 2 , name = ”CI ”)vpCO <− v i ewpo r t ( 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 ( vpA l l , v p L i s t ( vpT , vpD , vpCI , vpCO) )pushViewport ( s p l o t )s e ekV i ewpo r t ( ” t i t l e ”)g r i d . t e x t (”100 s c e n a r i o s s imu l a t i o n ” , gp = gpar ( cex=2))s eekV i ewpo r t ( ”D”)p r i n t (pD , newpage = FALSE)seekV i ewpo r t ( ”CI ”)p r i n t ( pCI , newpage = FALSE)seekV i ewpo r t ( ”CO”)p r i n t (pCO, newpage = FALSE)@

\ c ap 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 pa ramete r s .}\ 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 ePa r s ( mode l2 Ins tance2 , ”D”) ) ,

l a b e l = ”tab : e xamp l e t ab l e ” ,c ap t i o n = ”Example $D$ paramete r v a l u e s ( f i r s t 6 v a l u e s ) . ”)

@

The equa t i o n s or any i tem o f the model can be p r i n t e d a u t oma t i c a l l y from the


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StochasticModels

Conclusions


\ 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 theo 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 ( ”$$ ” , getEq (model2SMS , 6 , ”t e x ” , on l y = ”rExpr ”) , ”$$ ”)@

\ s e c t i o n { So 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 { op t im In s t an c e } ob j e c t , i t can be s o l v e d and the s o l u t i o n impor ted ( s e e s ou r c e code ) . R e s u l t s check i ng i s a l s o p o s s i b l e as t h i s i n f o rma t i o n i s a l s o s t o r e d :

<<s o l , echo=FALSE , r e s u l t s=hide>>=wProblem ( mode l2 Ins tance2 ,

f i l e n ame = ”. / data /mode l2 In s t ance2 . gms ”,fo rmat = ”gams ”,s o l v e r = ”LP ”)

r e s <− gams ( ”. / data /mode l2 In s t ance2 . gms −−o u t f i l e =./ data /mode l2 In s t ance2 . gdx ”)data ( gamsOut )i f ( r e s == 0){

importGams ( mode l 2 In s t ance2 ) <− ”. / data /mode l2 In s t ance2 . gdx ”message ( ”Opt im i z a t i on ok\n ”,

”\ tModel S ta tu s : ” ,as . c h a r a c t e r ( s ub s e t ( gamsModelStatusCode ,

i d == mode l2 In s t ance2@re su l t $mode l , desc , drop = TRUE) ) ,”\ n\ t S o l v e r S ta tu s : ” ,as . c h a r a c t e r ( s ub s e t ( gamsSo lverStatusCode ,

i d == mode 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 {

warn ing ( ”Check the l i s t i n g f i l e , someth ing was wrong : ” ,s ub s e t ( gamsOutCode , i d == res , desc , drop = TRUE) )


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CMS 2016

Emilio L. Cano


StochasticModels

Conclusions


}@

We can embed c a l c u l a t i o n s w i t h i n the t ex t , f o r example the v a l u e o f theo b j e c t i v e f u n c t i o n (\ Sexpr { round ( mode l 2 I n s t a n c e 2@ r e s u l t $ ob j )} ) , o r we can p r i n t p r e t t y\LaTeX˜ t a b l e s w i th the op t ima l va l u e s , as the ones i n Tab le s \ r e f { tab : x} and \ r e f { tab : y } , o r anyo th e r a n a l y s i s and r e p r e s e n t a t i o n ( s e e F i gu r e ˜\ r e f { f i g : r e s } ) . See the \ t e x t t t { .Rnw} s ou r c e f i l e to s e e the code .

<< 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 eVa r s ( mode l2 Ins tance2 , ”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 eVa r s ( mode l2 Ins tance2 , ”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)

@

\ beg in { f i g u r e } [ htp ]\ beg in { 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 eVa r s ( mode l2 Ins tance2 , ”y ”) , j == ”autumn ”)d f 2 p l o t <− agg r ega t e ( v a l u e ˜ i + t , data = d f2p l o t , 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 <− ggp l o t ( d f 2p l o t , ae s ( x=t ) )p <− p + geom area ( aes ( y=va lue , f i l l =i ) )p <− p + l a b s ( t i t l e = ”Optimal p r oduc t i o n 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 )@


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StochasticModels

Conclusions


\end{ c e n t e r }\ c ap 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 {Conc l u s i on }This document can be comp i l ed at any time , by any r e s e a r c h e r . Note tha t i f anyv a l u e i s changed , f o r example i n the s c r i p t t ha t c on t a i n the pa ramete r s(\ t e x t t t { ”. . / data /mode l2 In s t ance2 .R”} ) , the whole r e p o r t i s updated a u t oma t i c a l l y( i n c l u d i n g t a b l e s , e qua t i o n s and c h a r t s ) .I f we use s imu l a t i o n du r i ng the r e s e a r ch , we can s imp l y f i x the seed to a l l owthe v e r i f i c a t i o n o f 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 t s t a k e h o l d e r s can be produced u s i n g a common s t r u c t u r e and t a i l o r i n g the ou tpu t s .

\end{document}


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Workflow


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Outline


2 Stochastic Models

3 Conclusions


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Two-stage models

Rolling horizon

In Cano EL, Moguerza JM, Ermolieva T and Ermoliev Y(2014). “Energy efficiency and risk management in publicbuildings: 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 (underreview). “A strategic decision support system framework forenergy-efficient technology investments.” TOP.


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Emilio L. Cano


StochasticModels

Conclusions

Two-stage instance

Five periods, two technologies (CHP, PV), only electricity.


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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) =∞


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Two-stage instance



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Infeasible 56/100Fsto(x

∗sto) = 68, 595 EUR.



∗sto) =∞


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Emilio L. Cano


StochasticModels

Conclusions

Two-stage instance



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Infeasible 56/100




∗sto) =∞


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Emilio L. Cano


StochasticModels

Conclusions

Two-stage instance



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100Scenario

Energy price

Fdet(x∗det) = 66, 920 EUR. Infeasible 56/100




∗sto) =∞


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Two-stage instance



20

40

60

80

2013 2014 2015 2016

Dem

and

leve

l (kW

)

Energy demand

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

0

500

1000

1500

2000

2500

CH

PP

VR

TE

2013 2014 2015 2016 2017

EU

R/k

W

Investment cost

0.1

0.2

0.3

0.1

0.2

0.3

CH

PR

TE

2013 2014 2015 2016

EU

R/k

Wh

25

50

75

100Scenario

Energy price

Fdet(x∗det) = 66, 920 EUR. Infeasible 56/100

Fsto(x∗sto) = 68, 595 EUR. Robust, optimal against all


∗sto) =∞


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Multi-stage model

Complete model with risk

In Cano EL, Moguerza JM and Alonso-Ayuso A (2016). “Amulti-stage stochastic optimization model for energy systemsplanning 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 stochasticproblems on energy efficient investments planning at thebuilding level.” Data in Brief, 5, pp. 805–809.


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

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


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

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


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Outline


2 Stochastic Models

3 Conclusions


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Conclusions

Results

Reproducible Research methods in OptimizationThe stakeholders dialog viewpoint for DSSsThe optimr libraryComprehensive example demonstrating the framework

Further Research

Two-stage vs Multi-stage applicabilityNew models for energy storage systemsProductize package. Extend to further formatsExplore 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


http://emilio.lcano.com/content/en/publicaciones.html

http://emilio.lcano.com/content/en/publicaciones.html

https://github.com/emilopezcano/optimr

DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

DSS Mission

Joseph Kallrath (2012). Algebraic ModelingSystems, Springer. Chapter 12: A Practioner’sWish List Towards Algebraic Modeling Systems

“The automatic generation of a model’s documentation inLATEX would be very helpful for mathematicians, physicists,astronomers, and other communities publishing in LATEX.”


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

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 Instituteof Applied Systems Analysis (IIASA).


DSS framework

CMS 2016

Emilio L. Cano


StochasticModels

Conclusions

Discussion

Thanks !

[email protected]

@emilopezcanohttp://emilio.lcano.com


http://emilio.lcano.com

energy-efficient technology investments using a decision support system framework

Presentations & Public Speaking