Presentation

Project Portfolio SelectionA PPS Model

HeuristicExperiments

DSS prototypeConclusion

A GRASP-based heuristic for a Project PortfolioSelection Problem

Cleber Mira, Pedro Feijao, Maria Angelica Souza, ArnaldoMoura, Joao Meidanis, Gabriel Lima, Rafael Schmitz, Renato

P. Bossolan, Italo T. Freitas

November 28, 2012

Cleber Mira, Pedro Feijao, Maria Angelica Souza, Arnaldo Moura, Joao Meidanis, Gabriel Lima, Rafael Schmitz, Renato P. Bossolan, Italo T. FreitasA GRASP-based heuristic for a Project Portfolio Selection Problem

Overview

1 Project Portfolio SelectionProblem Input

2 A PPS ModelDecision VariablesObjective functionConstraints

3 HeuristicGRASP Metaheuristc

4 ExperimentsResults

5 DSS prototype

6 Conclusionconclusion

Problem Input

Project Portfolio Selection Problem

PPS Problem

Given a set of projects, construct a portfolio, i.e. a selection andscheduling of a subset of the projects scheduled over a period oftime, such that it maximizes a given objective function, accordingto a combination of criteria, and given a limited amount ofresources.

Problem Input

Planning Horizon, Resources and Projects

Input data

1 Planning horizon: sequence of t = 1, . . . , T months.

2 Yearly available resources.

3 A set of i = 1, . . . , I projects

Problem Input

Input data

Problem Input

Input data

Problem Input

Project parameters

Project i parameters

1 Manually selected initial month p(i)

2 Duration of a project i: d(i)

3 Amount of risk the project controls: Ri

4 Mandatory classification: indicates whether i must start atp(i)

5 A sequence of costs that describes the amount of resources ineeds at each month along its duration. ci,k denotes project icost at the k-th month from its start time.

6 A resource classification into two categories: operationalexpenditures (OPEX) or capital expenditures (CAPEX).

Problem Input

Project parameters

Problem Input

Project parameters

Problem Input

Project parameters

Problem Input

Project parameters

Problem Input

Project parameters

Problem Input

Example

Problem Input

Provide a greedy heuristic for a real world PPS problem found inthe power generation industry that achieve better results thanmanually generated solutions.

Decision VariablesObjective functionConstraints

Decision Variables

Decision variables

Variables xit indicate whether project i was chosen to start atperiod t, where i = 1, . . . , I, t = 1, . . . , T , as:

{1 if project i starts at month t0 otherwise

Controlled Risk Contribution

Contribution

The sum of a project controlled risk from the end of its life timeup 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 finishesoutside the PH.

Objective function

Cumulative Controlled Risk

The sum of contributions from all projects at each month of thePH, 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.

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 firstmonth of the PH.

Constraints

Eventual scheduling∑Tt=1 xit ≤ 1, i = 1, . . . , I

Mandatory projects

xi,p(i) = 1, where i is mandatory

Constraints

Eventual scheduling∑Tt=1 xit ≤ 1, i = 1, . . . , I

Mandatory projects

xi,p(i) = 1, where i is mandatory

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 atthe month j.W (m, q): resources of category q available at the year m.

GRASP Metaheuristc

Multi-start metaheuristic based on a greed strategy that generatesgood quality solutions for many combinatorial optimizationproblems.

Algorithm

Repeat two phases:

1 construction of a feasible solution.

2 search for a locally optimal solution by checking for bettersolutions in the neighborhood of the previously constructedsolution.

After reaching several locally optimal solutions, then the bestsolution is chosen.

GRASP Metaheuristc

Multi-start metaheuristic based on a greed strategy that generatesgood quality solutions for many combinatorial optimizationproblems.

Algorithm

Repeat two phases:

1 construction of a feasible solution.

2 search for a locally optimal solution by checking for bettersolutions in the neighborhood of the previously constructedsolution.

After reaching several locally optimal solutions, then the bestsolution is chosen.

GRASP Metaheuristc

Benefit function

The amount of controlled risk gained by unit of cost, weighted bythe number of months when the controlled risk is effectively usedis:

b(i, t) =(2T − t− d(i) + 1)Ri

1 +T∑

for 1 ≤ t ≤ T + 1.

Projects not included in the portfolio

t can assume the value T + 1 for allowing the assignment of avalue outside the PH.

GRASP Metaheuristc

Benefit function

The amount of controlled risk gained by unit of cost, weighted bythe number of months when the controlled risk is effectively usedis:

b(i, t) =(2T − t− d(i) + 1)Ri

1 +T∑

for 1 ≤ t ≤ T + 1.

Projects not included in the portfolio

t can assume the value T + 1 for allowing the assignment of avalue outside the PH.

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 do5: 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 then7: Make P = P ∪ {(i, t)}.8: end if9: end while

10: return Portfolio P.

Results

Experiment strategy

1 Generate input instances from an original real-world instance.

2 Set the kRGH paramenter k to 5 and execute the procedure20 times for each input instance.

3 Measure parameters that indicate the solution quality.

4 Summarize the results according to the input instancecategories.

Results

Generating Input Instances

Input instances

Obfuscated real-world instance used as seed.

Automatically generated by modifying the seed instance usinga disturbance factor (DF).

50 instances for each DF: 5%, 10%, 20%, and 30%.

Results

Measured Parameters

Measured parameters

1 Manual portfolio objective function (IOF) value

2 Optimized solution objective function (OOF) value

3 Running time (Time)

Results

Measured Parameters

Measured parameters

Results

Measured Parameters

Measured parameters

Results

Optimized versus Manual Solutions

DF IOF/UB OOF/UB OOF/IOF Time (s)

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

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

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

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

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

Results

Box-and-whiskers plot of OOF/IOF

0 5 10 20 30

Optimized to Initial OF values ratio by Disturbance Factor

Disturbance Factor

Summary

OOF/IOF median valuearound 1.057.

DF of 30% does not havea significative impact.

OOF no more than 7%distant from the optimumand around 5% betterthan manually generatedsolutions.

DSS Prototype

Technologies

1 Python/Django

2 PostgreSQL

3 JQuery

4 MVC architecture

DSS Prototype

Technologies

1 Python/Django

2 PostgreSQL

3 JQuery

4 MVC architecture

DSS Prototype

Technologies

1 Python/Django

2 PostgreSQL

3 JQuery

4 MVC architecture

DSS Prototype

Technologies

1 Python/Django

2 PostgreSQL

3 JQuery

4 MVC architecture

Features

Importing and exporting of portfolios, project and portfolio CRUDoperations.

Features

Portfolio optimization

Features

Portfolio comparison – charts that facilitate comparing two or moreportfolios.

Features

Charts and tables presenting values, such as, monthly and yearlytotal costs, total risks, and cumulative controlled risks.

conclusion

Conclusion

We modeled a PPS problem and proposed the kRGH heuristcfor solving it.

We performed experiments that confirmed that solutionsproduced by the heuristic are better than manuallyconstructed solutions.

We developed a DSS prototype that implements the heuristicand includes several features that allows decision makers tomodify an existing portfolio and to recompute new solutions.

conclusion

Conclusion

conclusion

Conclusion

conclusion

Contact

Thank you!

Cleber Mira, [email protected] Bioinformatics

Presentation

Technology

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