WAENO WORKSHOP

Fortum Fuzzy Decision Tree

Fortum Fuzzy Decision Tree

Alternatives considered in the Fuzzy RO Decision Tree:

1. Grate Boiler2. Crushing and cofiring of Biofuel-NA23. No investment4. CCGT Fr9E5. CCGT 2*Fr9Fa6. Old Boilers Changed to Gas No investment 7. Old Boilers Changed to Gas CCGT Fr9E8. Old Boilers Changed to Gas CCGT 2*Fr9Fa9. Repowering

Triangular Fuzzy Numbers

jjjjjjjj

iijj

aCFCFCFCFa

monthiyearjCFa

12*...max;12*...min

,,

121121

12

1

Trapezoidal Fuzzy Numbers

jj12j7jj6j1jj

j12j2j1

12

7ssjj

6

1ssjj

b12*CF...CFmax;12*CF...CFmina

CF....CFCFand,2*CFb

yearj,2*CFa

Fuzzification ProcessFortum Fuzzy Decision Tree

Investment Cost

n

jj

n

jj nx

n

CostInvestmentxx

11

1

21

1,

1min

Risk IndexTriangular Fuzzy Number:

FofvaluemeanticPossibilisFMFMFUA

OptimisticlosetochancesMorePesimisticwintochancesMoreIf

ishesDisAaverseRisk

losetochancesMoretimpormoresideLowerloverRisk

wintochancesMoretimpormoresideUpper

If

StrengthesA

FofUtilityFUIndexRiskAAaFU

)(),(1

00

min10

tan0

tan0

1

,6

*

Trapezoidal Fuzzy Number:

IdemAba

FU ,6

*2

Fortum Fuzzy Decision Tree

Inputs:• Discount Rate {r: 0 <= r <= 10 %}• Risk Free Interest Rate {rf :0 <= rf <= 6 %}• Risk Aversion {A: 0 <= A <= 10}• Price Scenario {P: P = 1, 2, 3}Outputs• FROV and FuzzyCF• U(FROV)• Project Index (1st position)• Deferral Time• M(FROV) and M(FuzzyCF)

Inputs vary according to an uniform distribution Analysis for triangular and trapezoidal fuzzy number

Sensitivity AnalysisFortum Fuzzy Decision Tree

Discount RateFortum Fuzzy Decision Tree

• Both types give the same optimal projects• The discount rate where the decision changes is similar, 2.16 % and 2.05 %• Optimal deferral time constant • Rf = 3 %, A = 5.5 Price Scenario = 2

Discount Rate – Trapezoidal – Project 5Fortum Fuzzy Decision Tree

Fortum Fuzzy Decision TreeDiscount Rate – Trapezoidal – Project 1

Discount Rate – Triangular – Project 5Fortum Fuzzy Decision Tree

Fortum Fuzzy Decision TreeDiscount Rate – Triangular – Project 1

Fortum Fuzzy Decision TreeDiscount Rate – Trapez - Triang – Project 5

Fortum Fuzzy Decision TreeDiscount Rate – Trapez - Triang – Project 1

Fortum Fuzzy Decision TreePrice Scenario

• Both types give the same optimal projects• Optimal deferral time constant • Rf = 3 %, A = 5.5 r = 5 %

Fortum Fuzzy Decision TreePrice Scenario

Fortum Fuzzy Decision TreeRisk Free Interst Rate

• Both types give the same optimal project• Optimal deferral time constant • A = 5.5 r = 5 % Price scenario 2

Fortum Fuzzy Decision TreeRisk Free Interst Rate - Trapezoidal

Fortum Fuzzy Decision TreeRisk Free Interst Rate - Triangular

Fortum Fuzzy Decision TreeRisk Free Interest Rate – Triang – Trapez

Fortum Fuzzy Decision TreeRisk Index

• Both types give the same optimal projects• The risk index where the decision changes is similar, 3.84 and 3.45• Optimal deferral time constant • Rf = 3 %, r = 5 % Price Scenario = 2

Fortum Fuzzy Decision TreeRisk Index – Trapezoidal – Project 5 - 1

Fortum Fuzzy Decision TreeRisk Index – Triangular – Project 5 - 1