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Vol.:(0123456789)
Energy Systems
https://doi.org/10.1007/s12667-022-00503-w
1 3
ORIGINAL PAPER
Energy project portfolio selection andscheduling
DimitriosTselios1· GrigoriosPapageorgiou1· NikolaosAlamanis1 ·
PandelisIpsilandis1
Received: 15 July 2021 / Accepted: 26 January 2022
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2022
Abstract
In the present work, we formulated an integrated method in order to confront two
problems regarding a project portfolio that contains energy projects and/or proposals
for projects to be implemented in the future. More specifically, the problems are: the
selection of the most beneficial projects and then the their scheduling. Our approach
is based on extending a tested and well-performed Dynamic Programming solution
for project portfolio scheduling in order to serve the selection problem as well. The
approach is utilizing the Incremental Funding Method (IFM). Most of the existing
bibliography is focused on project scheduling problems, although an adequate part
is dedicated to the project portfolio scheduling problem. Moreover, the mainstream
line of thought until recently, considered these two fields of study as relevant but the
majority of the researchers tried to concentrate on only one of them treating them as
two distinct domains. However, contemporary organizations ought to handle simul-
taneously a bundle of project proposals, to select a subset of them due to budget’s
constraints, and then to schedule them in order to maximize their potential profit.
The proposed method extends the IFM concept in order to cover the energy projects
and stands for a tool to select and schedule simultaneously the implementation of
project proposals that give the maximum value to the performing organization. The
outcome of this enhanced method produces quite promising results when tried on a
tailor-made set of benchmark instances.
Keywords Project portfolio· Project selection· Energy projects· Scheduling· IFM
* Nikolaos Alamanis
alam@uth.gr
Dimitrios Tselios
dtselios@uth.gr
Grigorios Papageorgiou
gpapageor@uth.gr
Pandelis Ipsilandis
ipsil@uth.gr
1 University ofThessaly, Geopolis Campus, Larissa41500, Greece
D.Tselios et al.
1 3
1 Introduction
Most of the bibliography is focused on the project scheduling problem and an
adequate part of this work is dedicated to the project portfolio scheduling prob-
lem[10]. Moreover, the mainstream thought until recently considered these two
fields of study as relevant but the majority of the researchers tried to concentrate
on only one of them because they trait them as two distinct domains[8].
However, contemporary organizations ought to handle simultaneously a bundle
of project proposals, to select a subset of them due to budget’s constraints, and
then to schedule their implementation in order to maximize their potential profit.
Most of these new approaches cannot be characterized clearly as all in-one
methods but they are phased methods that solve the two problems in a serial
fashion i.e. each one acts independently. In our opinion, this characteristic does
not give new insights to the problem and it does not guarantee more efficient
solutions[4].
Though the IFM was proposed to address software project deliverables, it can
easily applied to other industries that have characteristics similar to software pro-
jects. Hence, according to IFM, the self-contained energy projects that offer busi-
ness value can be considered as Minimum Marketable Features (MMFs). Usually,
a MMF i.e. an energy project is depended on the development of other prede-
cessor projects. Moreover, some energy projects require the completion of other
projects, which do not provide direct business value. IFM terminology calls them
Architectural Elements (AEs).
The real benefit of a combined solution, i.e. a solution that tries to maximize
the profitability by selecting and scheduling the energy projects simultaneously is
that its setting is closer to real business cases because the project managers have
finite resources and limited budget. Hence, they have to exploit them in a way that
permit them to choose the right project at the right moment[6, 8].
In the present work, we formulated an integrated method in order to confront
two semantic problems regarding a project portfolio e.g. the selection of the most
beneficial projects and their scheduling. Our approach is based on a Dynamic
Programming solution for project portfolio scheduling by extending it in order to
serve and the selection problem as well. This enhanced method has been already
tested and well performed and its outcome gives quite promising results using a
tailor-made set of benchmark instances.
The rest of the paper is organized as follows. In Sect.2 a brief overview of
related work is given. The system model is defined in Sect. 3 and the dynamic
algorithm is presented in Sect. 4, while the experimental results are presented
in Sect.5. Finally, Sect.6 concludes the paper and highlights the future research
directions.
1 3
Energy project portfolio selection andscheduling
2 Related Work
An interesting and thorough research work[12] presents an approach to schedul-
ing multiple projects using two genetic algorithms. Although its results are quite
promising there are two limitations. The first one is that the selected domain of
the projects, product development projects, is very specific and narrow. Moreo-
ver, their work is overloaded with too many well-known details about the struc-
ture of genetic algorithm that do not add much value to the overall contribution
in the practice of project management. In other words, this work seems like a
review paper about genetic algorithms and the presented methods aiming at the
structuring of the project portfolio as a single project. Hence, the project portfolio
scheduling becomes a project scheduling problem. Of course, the authors assert
that their model outperforms other approaches when they tested on instances that
are derived by themselves.
Another research effort [6] studied a special formulation of project portfolio
and tried to give a solution that concurrently selects and schedule the projects of
a portfolio. The derived method is an integer programming method that maxi-
mizes the overall cashflow. Although this approach seems quite effective there are
some concerns about its generalizability because the test sets are adapted to the
specific problem structure.
Some researchers [1] aimed to a very specific and narrow subset of project
portfolios. Most specifically, the studied subset is assumed that has dedicated
resources to specific unique projects. This assumption affects the generalizability
and their solution cannot be utilized from other forms of project portfolios. The
method is an extension of a genetic algorithm approach that has been proposed in
a previous work and it was tested on problem instances derived by the research
team in order to fit to their problem’s specifications. The method uses as objective
function the total weighted tardiness.
Another research work [7] proposes a multi-agent evolutionary algorithm for
the resource constrained project portfolio selection and scheduling problem. The
authors assert that their aim is the selection and scheduling of a project portfolio but
their method is a rather selection method. The specific approach is based on genetic
algorithm and they produce a tailor-made set of instances in order to test it.
Song etal.[8] tried to solve simultaneously the selection and scheduling prob-
lem by using a multi-objective approach. However, their solution is tested on one
only concrete example of a project portfolio. This means that there are some scal-
ability issues and the generalizability is debated. Moreover, the proposed method
does not confront the dynamic nature of the project portfolios.
Villafáñez etal. [11] followed an alternative path to solve the multi-project
scheduling problem. They proposed a very simple heuristic algorithm that arises
some concerns about its effectiveness and value. As most of the researchers in
this field of study they created their own benchmark instances which derived
from other sets in order to fit their problem setting.
Kumar et al. [4] proposed a two phases algorithm that combines a genetic
algorithm and a typical tabu search approach in order to maximizes the profit
D.Tselios et al.
1 3
of a project portfolio that has some unique characteristics about the independ-
encies, exclusiveness, and complementariness. Although this work gives promis-
ing results, there are some issues about generalizability because it was tested on
tailor-made instances and due the assumptions about the specific characteristics
of the project portfolio.
Peréz etal.[5] try to overcome the main drawbacks of the mainstream approaches
to project portfolio selection and planning i.e. the limitations of the project portfolio
structure, its static form and the ignorance of the budget’s constraints. This work uti-
lizes an integer programming solution based on fuzzy constraints and it was tested
using a real project portfolio and a concrete example of an invented one.
A recent work[9] exhibits a method that is based on a DP algorithm in order
to face the project portfolio scheduling problem by using as objective function the
maximization to the NPV e.g. the maximization of the profit. This research effort
utilized an older construction, the Incremental Funding Method (IFM), in order
to conceptualize the project portfolio and it gave very good solutions compared to
other methods, when it was tested on formulated benchmark instances.
However, in real business environment[10] the organizations do not have unlim-
ited resources and funding in order to implement all the projects that are proposed
by several stakeholders. Hence, the project portfolio manager ought to choose the
appropriate projects at the appropriate time in order to obtain the maximum profit-
ability. So, recently a part of the research effort in this field of study is diverted from
pure scheduling to an all-in-one method that selects and schedules the projects of a
portfolio at the same time[6, 8].
Energy projects recent research efforts[13] tried to employed a hybrid multi-cri-
teria method in order to select the most appropriate projects among several green
energy proposals. Other researchers[2] proposed a multi-objective approach to solve
problems with energy storage projects aiming, among other objectives, at schedul-
ing issues. The common characteristic of these efforts is their dependence on meth-
ods and algorithms that are multi criteria driven and employ intelligent approaches.
Hence, a method that aims at both goals, selection and scheduling, should be based
on similar approaches.
An inspiring research effort[3] suggested that project portfolio management can
integrate the sustainability coming from above, a crucial factor of the energy pro-
ject portfolio, with the functional sustainability of the individual energy projects by
enhancing the standardization of the projects’ selection process in line with the long
term objectives.
3 System model
The system model that is briefly presented in this section is an amendment of the
model[10] that has been exploited in recent research works[9] in order to confront
the project portfolio scheduling for portfolios that have a very specific structure i.e.
their projects are ordered in serial way. That structure is easily adapted to energy
project portfolios that have similar characteristics.
1 3
Energy project portfolio selection andscheduling
Let’s hypothesize that at each time unit there is a maximum of negative present
value available for the whole energy portfolio. This is the limit of the available
resources that can be assigned by the energy organization to this specific portfolio at
each time unit. In other words, the organization cannot allow the whole budget at a
short time period because this is not the safest alternative.
According to the initial model’s[10] terminology, two significant ingredients of
each portfolio are the MMF (minimum marketable feature) and AE (architectural
element). The first term is symbolized the project that delivers outcome with added
value to the organization and the latter is symbolized the project that is prerequisite
for a MMF project. All projects, no matter their category, have an assigned maxi-
mum negative present value at each specific time unit. This specification expresses
the smooth load balancing of the budget during the portfolio’s life time.
In order to exploit the above mentioned model we tried to express a typical energy
project in IFM terms. We can consider that each energy project portfolio consists of
two types of projects. The first category includes all projects that are typical energy
projects such as a Solar Power construction project. Thus, we face these projects as
MMFs. The rest projects are auxiliary projects that are prerequisite for the MMs and
we symbolized them AEs.
Other cases of energy and environmental projects that can be considered as
MMFs are Small Hydropower Project, Biogas Power Project, Calcium Carbide Res-
idue Utilization and Solid Waste Power Generation.
The whole concept of an energy project portfolio, that has been expressed using
our model, is easily presented by a concrete example that is illustrated graphically in
Fig.1. The explanation of all symbols in this figure can founded in Table1.
Fig. 1 Concrete example of energy project portfolio
D.Tselios et al.
1 3
The detailed description of the Dynamic Programming approach in finding the
best sequence for the selection and scheduling of projects or project proposals
belonged to a specific portfolio, under the specifications of IFM[10] and the con-
straints imposed by maximum negative present values presented above, can be pre-
sented as follows:
Let’s assume a portfolio that contains n energy projects that be in implemen-
tation and performing stages during a time period of T periods. Each project is
assigned with a cash flow, typically with negative flows during the implementa-
tion years and positive flows during the performing cycle. Without loss of gen-
erality, we can hypothesize that each MMF generates positive cash flow, starting
from the end of the implementation, to the end of the time horizon, while AEs
generate only negative cash flows. Because of resource and other constraints, at
each time unit only one project can be implemented, while precedence relation-
ships are considered. The overall objective is to select and schedule the develop-
ment of the projects in a way that the net present value of the total cash flow for
the portfolio obtains its maximum value.
Hence, we define: D: the execution time (number of the time units) required
for the projects of the portfolio that have been selected S, defined as:
The present value of project
i∈S
when r is the interest rate, its development begins
at time
si
and
cit
its cost at time unit t is defined as:
We can conceive the implementation of the subset of the selected projects S as a
multi-stage scheduling problem consisting of S successive stages of variable dura-
tions, where at each stage, only one project is selected and developed. The feasibility
of a given implementation sequence is constrained by the total budget and the prec-
edence relationships defined in P, where P is the set of precedence relationships.
The energy portfolio could enter each stage at different possible states, deter-
mined from previous decisions, and a decision to be taken as to which project will
(1)
D
=
∑
i∈S
d
i
(2)
PV
isi=
T−s
i
+1
∑
t=1
cit
(1+r)
t
Table 1 Energy Projects
Project ID Project Description
UE
Municipal waste incineration unit
UG
Power generation plant (based on municipal waste incineration)
UF
Municipal solid waste composting
UH
Biomass cogeneration
UI
Methane recovery and utilization
UB
Solar power
UA
Building expertise and municipality–private sector consortiums
UC
Establishment of renewal resources know how and expertise
1 3
Energy project portfolio selection andscheduling
be selected and developed at this stage. The entering state and the decision made,
define the start time
sn
and the duration of stage n, the incremental funding that the
specific decision offers to the energy project portfolio, and determines the state of
the whole system before entering the following stage.
The following definitions provide a brief description of the scheduling process by
altering the approach defined in[10]:
The state of the energy portfolio at the end of stage n is defined as
gn
: the
n-dimension array of all n projects that have been selected and deployed from stage
1 to stage n. Therefore
gn−1
denotes a possible state when entering stage n.
Gn
=
{gn|gn
feasible according to rules set in
P}
, and
G0= {�}
The set of all possible decisions (projects to be selected and implemented) at
stage n when the entering state is
gn−1
is defined as:
U(gn−1)={u(gn−1)|gn=gn−1u(gn−1)
is feasible in
P}
, where:
u(gn−1)
is the deci-
sion variable at stage n, in other words, the project that will be selected and begin
being developed at stage n, and
u∗(gn−1)
is the best decision selection at stage n if
the portfolio enters stage n at state
gn−1
.
Then, the state of the energy portfolio at the end of stage n is defined by the
following:
if the state
gn−1
is given and the selection of the decision variable
un
the calculation
of the start period for stage n is as following:
The contribution of each stage to the total net present value is associated with the
selection made at this stage and depends on the entering state and the decision made
at stage n. So, we define:
where present value is defined in(2)
Also at each stage n, we define the cumulative contribution to the net present
value from all stages
n,n+1, S
by the recursive relationship:
where
gn
has been defined in(3), and
where the choice that maximizes the objective functions is
u∗(gn−1)
. Hence,
(3)
gn=gn−1∪u∗(gn−1)
(4)
s
un
=
∑
u∈gn−1
du+
1
(5)
f
n
(g
n−1
,u(g
n−1
)) = PV
unsu
n
(6)
F
(gn−1,u(gn−1)) =
{f
n
(g
n−1
,u(g
n−1
))+F∗
n+1
(g
n
),i∈S
fS(gS−1
,
u(gS−1))
(7)
F∗
n(
g
n
−1
)=
max
u
∈
U
(
gn−1
)
{
F
n(
g
n
−1,u
)},
(8)
Fn(gn−1
,
u∗(gn−1)) = F∗
n(gn−1)
D.Tselios et al.
1 3
4 The dynamic programming algorithm
The key characteristic of a dynamic programming algorithm is that it is executed
by filling in an array of sub-problems (one for each stage). Then, starting from the
last stage, the sub-problems are solved recursively and their solutions are com-
bined in order to give a solution to the initial problem. The algorithm’s advantage
is that every sub-problem is solved only once and the sub-optimum solutions are
saved avoiding the rework every time the sub-problem is met. Hence, following a
backward pass, starting from the last stage S, at each stage the algorithm finds the
best alternative for each feasible entering state, based on the sub-optimization of the
cumulative effect from the current stage onwards to the last one. Finally, at stage 1,
an optimum solution over all stages is obtained.
A description of this algorithm can be found in a recent work[10]. The optimized
value of the project portfolio is:
The optimum solution can be found starting from stage 1 and moving to stage S,
finding the decisions that contribute to
Vmax
.
5 Experimental results
The whole model and the relevant algorithm was tested on selected instances that
have been formulated with specific structural and financial settings. According to
the structural settings the typical energy project portfolios contain from 5 to 10 pro-
jects, each project ranges from 1 to 2 time units (years). The likelihood probability
of connection existence between two energy projects was set to 0.3. Possible redun-
dancies regarding precedence relationships among the energy projects of the portfo-
lio were eliminated.
According to financial criteria, the cash flows are negative during the develop-
ment of the project portfolio, the development cost is assigned randomly using the
uniform distribution based on previous work[9], the base period revenues are ran-
domly assigned as a fraction of the development cost per period. Moreover, the flow
of revenues is adjusted randomly by selecting from four different patterns: constant
over time, triangular loaded, front loaded and back loaded.
It is easily observed in Table2 that for smaller problems with relatively few pro-
jects and dependencies (up to 5 or 6) all approaches have similar performance. As
the the level of complexity is reduced, even the greedy algorithm is quite effective.
For larger size problems, the increased level of complexity in terms of number of
projects and dependencies shows the dynamic programming approach superior to
the other alternatives.
(9)
Vmax =F∗
1(g
0
)
1 3
Energy project portfolio selection andscheduling
6 Conclusions andfuture work
In this article, we propose an innovative method in order to solve two common
problems which are related to a project portfolio that contains projects or project
proposals with specific structure. The two problems that are jointly consider for
optimization are the selection of the most profitable projects and then their sched-
uling. The proposed approach is an extension of a well performed Dynamic Pro-
gramming solution for project portfolio scheduling, modified it in order to include
the selection problem as well. The proposed method alters the Incremental Fund-
ing Method (IFM) concept in order to handle the generic project portfolios and it
tries to select and schedule at the same time the project proposals that gives the
maximum benefit to the organization. The results of this improved method offers
very promising results when applied to tailor-made problem instances. We have
to underline that our approach has not been tested on real project cases.
Our approach was used to give optimal selection and scheduling of projects
contained in a portfolio regarding the portfolio’s financial performance in terms
of NPV. In complex portfolio settings the presented method has better perfor-
mance than the alternatives. A greater size simulation experiment will give
results that may return performance measurements regarding the computational
time and/ or relationships. Another future direction of the present research is the
application of the method on real cases of energy project portfolio.
Data availability Data will be made available on reasonable request.
Declarations
Conflict of interest On behalf of all authors, the corresponding author states that there is no conflict of
interest.
Table 2 Simulation results Case Nodes Arcs Greedy vs DP Weighted IFM vs DP
1 9 11
−
1.64e%
−
0.78e%
2 10 12 1.10% 1.10%
3 5 4 – –
4 7 6 – –
5 9 10 –0.01% –0.01%
6 10 10 –18.73% –4.98%
7 8 7 –0.70% –0.70%
8 8 9 – –15.22%
9 10 9 –4.15% –
10 6 5 – –
D.Tselios et al.
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