Laboratory of Industrial & Energy Economics School of Chemical Engineering National Technical University of Athens George MAVROTAS Olena PECHAK 8 th Multi-criteria Meeting (HELORS) 8-10 December 2011, Eretria, Greece Dealing with uncertainty in project portfolio selection: Combining MCDA, Mathematical Programming and Monte Carlo simulation: a trichotomic approach
8 th Multi-criteria Meeting (HELORS) 8-10 December 2011, Eretria, Greece. Dealing with uncertainty in project portfolio selection: Combining MCDA, Mathematical Programming and Monte Carlo simulation: a trichotomic approach. George MAVROTAS Olena PECHAK. Contents. - PowerPoint PPT Presentation
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Laboratory of Industrial & Energy EconomicsSchool of Chemical EngineeringNational Technical University of Athens
George MAVROTASOlena PECHAK
8th Multi-criteria Meeting (HELORS)8-10 December 2011, Eretria, Greece
Dealing with uncertainty in project portfolio selection: Combining MCDA, Mathematical Programming and
Monte Carlo simulation: a trichotomic approach
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Contents
The project portfolio selection problem Methodology
Case study Results and discussion Conclusions & Future research
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Methodology
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
MCDA problematiques = What kind of problems we can address
4 problematiques (B. Roy) Description – Understanding of the MCDA problem Selection of the most preferred alternative Ranking of the alternatives Sorting of the alternatives in categories
Belton – Stewart (2002) Selection of a subset under constraints (Portfolio)
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Description of the simple case of project selection (without constraints)
MCDA
Ranking
Selection of the first n-projects
Ranking
1η
2η
3η
4η
…
20η
…
55η
Top 20
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Environmental uncertaintyWeights of criteriaTotal budget…
We assume stochastic nature of the uncertainty (probabilities, distributions)
Monte Carlo simulation
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Monte Carlo simulation & Optimization
A B
M
CA B
param1
param2
paramN
value1(i)
value2(i)
value3(i)
Solution of MP model
i =1…n
Project portfolio 1
Project portfolio 2
Project portfolio 3
Project portfolio n
. . .
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Project allocation in sets
Trichotomic allocation of projects
green set
Projects selected in all optimal portfolios
red set
Projects not selected in none optimal portfolio
grey set
Projects selected in some optimal
portfolios
In each iteration we obtain an optimal portfolioEach project can be present (Xj=1) or not (Xj=0) in the optimal portfolio
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Project allocation in sets
x1 x2 x3 x4 … xn
1 1 0 0 1 … 1
2 0 0 1 1 … 1
3 0 0 0 1 … 0
… … … … … … …
1000 1 0 0 1 … 1
Itera
tion
s
Projects
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Remarks from phase 1
Usually there is no dominating portfolio1000 iterations about 1000 different portfolios
Trichotomic approach provides useful informationGreen set they are in under any circumstancesRed set they are out under any circumstancesGrey set we are not sure, we need more info
Exploit information from phase 1 and go to phase 2Only the grey set
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
The model of phase 2
Fix the values of green and red projects
Use as objective function coefficients the frequencies (fj) of the projects from the 1st phase
j
j
X 1 ( )
X 0 ( )
j gs green set
j rs red set
j= max Xn
jj
Z f
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Results from phase 2
Two cases: No stochastic parameters in the constraints
One single run Final selection: the unique optimal portfolio
Stochastic parameters in the constraints Monte Carlo simulation – Optimization (1000 runs) Final selection: the dominating optimal portfolio
The portfolio with the highest frequency in 2nd phase If there is no clear winner comparison among the first two project-
wise comparison total budget adjustments
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Illustration of the method
Set of projects
Multiple criteria
Multiple constraints
Uncertainty
red set
greyset
green set
Notselected
selected
1st phase 2nd phase
MCDAMC simulation
MathProg
1st phase infoMC simulation
MathProg
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Case study
Input dataShakhsi-Niaei, M., Torabi, S.A., Iranmanesh, S.H. (2011) A comprehensive framework
for project selection problem under uncertainty and real-world constraints Computers and Industrial Engineering 61, 226-237.
40 projects for telecommunication company, classified in 3 groups: Basic - 2,7,9,12,13,14,17,22,23,26,28,37,38,39 Applied - 1,3,4,6,10,11,16,18,20,21,24,25,27,30,31,32,33,35,36 Developing - 5,8,15,19,29,34,40
Constraints Available total budget (we allow a 15% excess) Limits by project type (at most 20% Basic, 70% Applied, 40% Developing)
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Case studyThe projects are evaluated by 5 criteria: Cost: Total project cost including all expenses required for project completion. Proposed methodology: Degree of being step-by-step, well planned, scientifically-proven,
disciplined, and proper for organization current status in the proposed methodology. The abilities of personnel: Work experience of project team related to concerned project. Scientific and actual capability: Scientific degree and educational certificates of project’s
team. Technical capability: Ability of providing technical facilities and infrastructures.
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Project’s dataPro
ject
s’ d
ata
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Results of the model – phase 1
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Results
Phase 1 No clear dominating portfolio We may introduce threshold for green and red projects
1% projects are green if freq > 99% and red if freq < 1% Results
Green set - 7 projects (5, 8, 15, 19, 29, 34, 40) Red set - 3 projects (2, 9, 17) Grey set - 30 projects
Phase 2 Still no clearly dominating portfolio, but 2 combinations are most
preferred The difference between 2 most frequent portfolios --> 1 project.
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
Results
Results for 1000 iterations of seed 1513.
(we test 15 different seeds 15 MC experiments no significant difference)
Frequency 1 and 2 are the frequencies of top 2 portfolios.
Phase 1 Phase 2
ThresholdGREE
N RED GREYFrequency
1Frequency
2Time, sec
0 6 0 34 226 190 352
0.5 % 7 1 32 226 190 355
1% 7 3 30 226 190 367
2% 7 3 30 226 190 371
5% 8 3 29 226 190 399
10% 10 5 25 229 191 364
The most frequent portfolios differ only by 1 project 16 or 24 (only one of two may be in): Both are in the group of “applied” projects Have similar characteristics (in some criteria 24 performs weaker)
Final decision still to be made by a person according to the main goals.
min max min max min max min max min maxProject 16 374 486 2 6 4 8 1 3 2 6Project 24 385 416 1 4 1 4 1 5 3 5
8th MCDA meeting HELORS, Eretria, 8-10 December 2011
The naïve approach: Consider the expected values
Expected values no uncertainty
Although the result may be almost the same…… we have more fruitful information than considering just the expected values We know which are the sure projects (green
and red) We can identify the “borderline projects” We know the probability of the preferred