Presentation

Project Portfolio Selection
A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
A GRASP-based heuristic for a Project Portfolio
Selection Problem
Cleber Mira, Pedro Feijão, Maria Angélica Souza, Arnaldo
Moura, João Meidanis, Gabriel Lima, Rafael Schmitz, Renato
P. Bossolan, Ítalo T. Freitas
November 28, 2012
Cleber Mira, Pedro Feijão, Maria Angélica Souza, Arnaldo Moura, João Meidanis, Gabriel Lima, Rafael Schmitz, Renato P. BossoA GRASP-based heuristic for a Project Portfolio Selection Prob

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Overview
1 Project Portfolio Selection
Problem Input
2 A PPS Model
Decision Variables
Objective function
Constraints
3 Heuristic
GRASP Metaheuristc
4 Experiments
Results
5 DSS prototype
6 Conclusion
conclusion

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project Portfolio Selection Problem
PPS Problem
Given a set of projects, construct a portfolio, i.e. a selection and
scheduling of a subset of the projects scheduled over a period of
time, such that it maximizes a given objective function, according
to a combination of criteria, and given a limited amount of
resources.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Planning Horizon, Resources and Projects
Input data
1 Planning horizon: sequence of t = 1, . . . , T months.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Input data
2 Yearly available resources.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Input data
2 Yearly available resources.
3 A set of i = 1, . . . , I projects

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
Project i parameters
1 Manually selected initial month p(i)

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
2 Duration of a project i: d(i)

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
3 Amount of risk the project controls: Ri

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
4 Mandatory classiﬁcation: indicates whether i must start at
p(i)

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
p(i)
5 A sequence of costs that describes the amount of resources i
needs at each month along its duration. ci,k denotes project i
cost at the k-th month from its start time.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Project parameters
p(i)
5 A sequence of costs that describes the amount of resources i
needs at each month along its duration. ci,k denotes project i
cost at the k-th month from its start time.
6 A resource classiﬁcation into two categories: operational
expenditures (OPEX) or capital expenditures (CAPEX).

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Example

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Problem Input
Goal
Goal
Provide a greedy heuristic for a real world PPS problem found in
the power generation industry that achieve better results than
manually generated solutions.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Decision Variables
Decision variables
Variables xit indicate whether project i was chosen to start at
period t, where i = 1, . . . , I, t = 1, . . . , T, as:
xit =
1 if project i starts at month t
0 otherwise

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Controlled Risk Contribution
Contribution
The sum of a project controlled risk from the end of its life time
up to 2T months. Formally:
(2T − s(i) − d(i) + 1)Ri
s(i): project i start time.
2T months
We assume 2T months to cover the cases when a project ﬁnishes
outside the PH.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Objective function
Cumulative Controlled Risk
The sum of contributions from all projects at each month of the
PH, that is:
I
i=1
T
t=1
(2T − t − d(i) + 1)Rixit, (1)
Objective Function
Maximize the Cumulative Controlled Risk over the vector X.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Upper Bound
Simple Upper Bound
I
i=1
T
t=1
(2T − d(i))Rixit, (2)
Observation
The upper bound covers the case when all projects start at the ﬁrst
month of the PH.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Constraints
Eventual scheduling
T
t=1 xit ≤ 1, i = 1, . . . , I

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Constraints
Eventual scheduling
T
t=1 xit ≤ 1, i = 1, . . . , I
Mandatory projects
xi,p(i) = 1, where i is mandatory

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Decision Variables
Objective function
Constraints
Constraints
Limited resource per year
12m
j=12(m−1)+1
C(j, q) ≤ W(m, q),
for m = 1, . . . , T/12, and all resource categories q.
C(j, q): total category q cost demanded by all active projects at
the month j.
W(m, q): resources of category q available at the year m.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
GRASP Metaheuristc
GRASP Metaheuristc
GRASP Metaheuristc
Multi-start metaheuristic based on a greed strategy that generates
good quality solutions for many combinatorial optimization
problems.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
GRASP Metaheuristc
GRASP Metaheuristc
GRASP Metaheuristc
Multi-start metaheuristic based on a greed strategy that generates
good quality solutions for many combinatorial optimization
problems.
Algorithm
Repeat two phases:
1 construction of a feasible solution.
2 search for a locally optimal solution by checking for better
solutions in the neighborhood of the previously constructed
solution.
After reaching several locally optimal solutions, then the best
solution is chosen.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
GRASP Metaheuristc
Benefit function
Benefit function
The amount of controlled risk gained by unit of cost, weighted by
the number of months when the controlled risk is effectively used
is:
b(i, t) =
(2T − t − d(i) + 1)Ri
1 +
T
k=1
cik
,
for 1 ≤ t ≤ T + 1.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
GRASP Metaheuristc
Benefit function
Benefit function
The amount of controlled risk gained by unit of cost, weighted by
the number of months when the controlled risk is effectively used
is:
b(i, t) =
(2T − t − d(i) + 1)Ri
1 +
T
k=1
cik
,
for 1 ≤ t ≤ T + 1.
Projects not included in the portfolio
t can assume the value T + 1 for allowing the assignment of a
value outside the PH.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
GRASP Metaheuristc
GRASP-based heuristc: kRGH
1: Initialize an empty portfolio P.
2: Resolve mandatory projects.
3: Construct the list SP of I ×(T +1) project and start time pairs,
sorted by beneﬁt values and start times.
4: while SP is not empty do
5: Get a pair (i, t) randomly chosen from the ﬁrst k pairs at the
top of the SP list and remove it from SP.
6: if i was not already scheduled and P ∪{(i, t)} is feasible then
7: Make P = P ∪ {(i, t)}.
8: end if
9: end while
10: return Portfolio P.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Experiment strategy
Steps
1 Generate input instances from an original real-world instance.
2 Set the kRGH paramenter k to 5 and execute the procedure
20 times for each input instance.
3 Measure parameters that indicate the solution quality.
4 Summarize the results according to the input instance
categories.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Generating Input Instances
Input instances
Obfuscated real-world instance used as seed.
Automatically generated by modifying the seed instance using
a disturbance factor (DF).
50 instances for each DF: 5%, 10%, 20%, and 30%.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Measured Parameters
Measured parameters
1 Manual portfolio objective function (IOF) value

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Measured Parameters
Measured parameters
2 Optimized solution objective function (OOF) value

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Measured Parameters
Measured parameters
2 Optimized solution objective function (OOF) value
3 Running time (Time)

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Optimized versus Manual Solutions
DF IOF/UB OOF/UB OOF/IOF Time (s)
0% 88.44% 93.51% 1.0573 50.21

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
0% 88.44% 93.51% 1.0573 50.21
5% 88.44% 93.48% 1.0570 50.85

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
0% 88.44% 93.51% 1.0573 50.21
5% 88.44% 93.48% 1.0570 50.85
10% 88.46% 93.49% 1.0569 51.26

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
0% 88.44% 93.51% 1.0573 50.21
5% 88.44% 93.48% 1.0570 50.85
10% 88.46% 93.49% 1.0569 51.26
20% 88.44% 93.47% 1.0568 51.00

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
0% 88.44% 93.51% 1.0573 50.21
5% 88.44% 93.48% 1.0570 50.85
10% 88.46% 93.49% 1.0569 51.26
20% 88.44% 93.47% 1.0568 51.00
30% 88.47% 93.50% 1.0569 51.04

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Results
Box-and-whiskers plot of OOF/IOF
0 5 10 20 30
1.0521.0541.0561.0581.0601.062
Optimized to Initial OF values ratio by Disturbance Factor
Disturbance Factor
OptimizedtoInitialRatioValue
Summary
OOF/IOF median value
around 1.057.
DF of 30% does not have
a signiﬁcative impact.
OOF no more than 7%
distant from the optimum
and around 5% better
than manually generated
solutions.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
DSS Prototype
Technologies
1 Python/Django

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
DSS Prototype
Technologies
1 Python/Django
2 PostgreSQL

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
DSS Prototype
Technologies
1 Python/Django
2 PostgreSQL
3 JQuery

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
DSS Prototype
Technologies
1 Python/Django
2 PostgreSQL
3 JQuery
4 MVC architecture

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Features
Importing and exporting of portfolios, project and portfolio CRUD
operations.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Features
Portfolio optimization

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Features
Portfolio comparison – charts that facilitate comparing two or more
portfolios.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
Features
Charts and tables presenting values, such as, monthly and yearly
total costs, total risks, and cumulative controlled risks.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
conclusion
Conclusion
We modeled a PPS problem and proposed the kRGH heuristc
for solving it.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
conclusion
Conclusion
for solving it.
We performed experiments that conﬁrmed that solutions
produced by the heuristic are better than manually
constructed solutions.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
conclusion
Conclusion
for solving it.
We performed experiments that conﬁrmed that solutions
produced by the heuristic are better than manually
constructed solutions.
We developed a DSS prototype that implements the heuristic
and includes several features that allows decision makers to
modify an existing portfolio and to recompute new solutions.

A PPS Model
Heuristic
Experiments
DSS prototype
Conclusion
conclusion
Contact
Thank you!
Cleber Mira, Ph.D.
cleber@scylla.com.br
Scylla Bioinformatics

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