Project allocation model

a process considering the learning effect for resoruce optimization


Universidade Federal de Pernambuco, Management Engineering Department


The problem of allocating projects to project managers arises in companies that simultaneously conduct multiple projects. This study presents an approach to allocating projects to project managers according to organizational restrictions through mathematical programming, considering the learning effect as an important aspect to be considered for resource optimization. Our proposal incorporates the project manager´s past experience by using the learning curve as an efficiency factor that reduces the time a project manager needs to manage similar projects. The framework consists of a set of structured techniques and methods, which are appropriate within the context of project management. A practical application of the proposed model was implemented in a Brazilian electric energy company. The results demonstrated the feasibility of the model and the effectiveness of the project allocation process. Also noteworthy is that the model performs the allocation of multiple projects, thus reducing the number of analyses performed in this process.

Keywords: project manager; project portfolio; project allocation


It is well known that multiple project management (MPM) is a common reality in many organizations. MPM is about managing groups of several concurrent projects (Patanakul & Milosevic, 2009). In the project management context, the process of selecting a project manager impacts significantly on the successful performance of the project (Hadad, Keren, & Laslo, 2013). Also it is well-known that “the selection of the project manager is one of the two or three most important decisions regarding the project” (Meredith & Mantel, 2011). P. Patanakul, Milosevic, and Anderson (2007) affirm that how best to approach assigning projects to project managers is considered to be one of the most important questions in project management.

In the literature, the project manager selection process has been widely studied (Hadad et al., 2013), which denotes the importance of the subject. Some methodologies to choose a project manager have been put forward (Ogunlana, Siddiqui, Yisa, & Olomolaiye, 2002; P. Patanakul, Milosevic, & Anderson, 2007; Rashidi, Jazebi, & Brilakis, 2011; Hadad et al., 2013). Their models are summarized in the next section on Survey of the Literature. Nevertheless these studies, and any other known to the authors of this article, do not consider the learning curve (also denominated the learning effect) that a project manager has acquired through past experience when managing similar projects. Past experience in managing projects is recognized as an important factor when assigning projects (Hölzle, 2010).

The learning curve shows that it is possible to improve the efficiency of staff by performing a given task again (Wu & Sun, 2006) so, in our proposal, we incorporate the project manager´s past experience by using the learning curve as an efficiency factor that reduces the time a project manager needs to manage similar projects. Our model incorporates this aspect on allocating projects in accordance with a project manager’s experience by using mathematical programming.

Another important aspect in companies that operate MPM is when a group of multiple concurrent projects (MGMP) is developed and implemented simultaneously. Since the number of project managers is often fewer than the number of projects, a project manager will indeed be a multiple-project manager, and accumulate the responsibility of managing multiple projects simultaneously (Patanakul & Milosevic, 2009). So, apart from the learning effect, we also incorporate the switchover-time loss, which denotes the loss in a project manager’s capacity when switching from the issues of one project to another (which represents a loss brought about by multitasking)(Patanakul et al., 2007).

When assigning projects to project managers, the workload must also be taken into account, as well as the project manager’s time availability, because it is very common for a project manager to accumulate other roles or functions in the company and simultaneous projects (Kuprenas, Jung, Fakhouri, & Jreij, 2000; Patanakul & Milosevic, 2009).

We developed an optimization model (an integer programming model) to assign projects to project managers, taking into account their availability, workload, multitasking, the switchover-time loss and learning effect. This model proposed was applied in a private company that operates in the Brazilian electric energy sector.

Survey of the Literature

Several studies show that previous experience in managing projects strongly increases a project manager’s performance: past experience with similar projects has been shown to positively affect the timely completion of projects (McFarlan, 1981). Prior project experience is conducive to shorter delays in projects (Broadbent, Weill, & St Clair, 1999). Accumulated project experience is positively related to higher project performance (Iansiti, 2000). Experience has an influence on work performance (Lee-Kelley & Leong, 2003). Experience with project management and expertise is highly significant for 90% (the highest importance) of all companies (Hölzle, 2010).

Thus, the project manager’s past experience must be considered in the project assignment process and it can be formatted as an efficiency factor that represents a reduction in the total time required for project management. In addition, the learning effect resulting from experience in managing similar projects can be added to this factor because such experience is highly beneficial when reorganizing tasks that were poorly structured, as well as when conducting these and other complex tasks (Abdolmohammadi & Wright, 1987).

A learning curve represents the process of acquiring experience as a consequence of having performed similar tasks. As a result of the learning effect, the time required to perform subsequent tasks is decreased, thus showing a relationship between performance and experience (Corominas, Olivella, & Pastor, 2010; Janiak & Rudek, 2008).

The learning effect in project management has been widely used. Some examples include evaluating productivity in the construction industry (Thomas, Mathews, & Ward, 1986), planning development projects (Eden, Williams, & Ackermann, 1998), IT projects that seek to maximize an organization’s productivity gains (Ngwenyama, Guergachi, & McLaren, 2007), projects on implementing new technologies (Plaza, Ngwenyama, & Rohlf, 2010), quality improvement projects (Lapre, Mukherjee, & Van Wassenhove, 2000), aircraft projects (Gholz, 2011) and a large number of other applications (Anzanello & Fogliatto, 2011).Given that project management involves complexity and a life cycle sequence, it seems appropriate to consider the “on the job” learning effect for project managers who have continuously improved their performance by managing similar projects.

In the MGPM context, the resource capacity of a project manager is very scarce. Therefore, multiple assignments (more than one project per project manager) are very common but a new project should be assigned only when a project manager is available. If the resource capacity of project management is not considered as a limitation in the process of assigning projects, this can lead to ineffectual project management (Adler, Mandelbaum, Nguyen, & Schwerer, 1996).Evidence from studies proves that effective maximization takes place when two or three “major” projects are successfully allocated to a manager (Fricke & Shenbar, 2000). Therefore, the availability and workload of a project manager is one important aspect that must be aggregated to the process for assigning projects.

When assigning more than one project to a single project manager, the characteristics about multitasking must be considered. Multitasking means “people switching between multiple contingent tasks” and “switching means redirecting attention from one task to another” (Buser & Peter, 2012). In project management, this phenomenon (called switchover time-loss), has been studied and the method of estimating the additional time required per project in excess of one has been accepted. This information can be consulted in Kapur International and is shown in Table 1. Nevertheless, it is also recommended that each organization should study (based on its historical data) and identify its own switchover time-loss (Patanakul et al., 2007).

Number of Projects Accumulated Switchover Time-Loss (Person Hours Per Week)
1 0
2 6
3 7.5
4 9

Table 1: Switchover time-loss

Several studies show that past experience in managing projects strongly increases a project manager’s performance: past experience with similar projects has been shown to have an effect on timely completion of projects (McFarlan, 1981); prior project experience have been shown to lead to shorter project delays (Broadbent et al., 1999); accumulated project experience is positively related to higher project performance (Iansiti, 2000); “An experienced project manager is one of the keys to project success” and “The Standish Group found that 97% of successful projects were managed by an experienced project manager” (Standish Group, 2001, p. 12). Additional studies show that experience has an influence on work performance (Lee-Kelley & Leong, 2003); and experience with project management and expertise are highly significant for 90% (the highest importance) of all companies (Hölzle, 2010).

The past experience of a project manager must be considered during the process of assigning projects and can be formatted as an efficiency factor that represents a reduction in the total time required for project management. Also, the learning effect brought about by the experience in managing similar projects can be added to this factor since, experience is most beneficial when performing tasks that are poorly structured and complex (Abdolmohammadi & Wright, 1987).

The learning curve represents the process of acquiring more experience as a consequence of having performed similar tasks. As a result of the learning effect, the time required to perform subsequent tasks is decreased, thus showing the relationship between performance and experience (Corominas et al., 2010; Janiak & Rudek, 2008).

The learning effect in project management has been widely used, e.g. in construction productivity (Thomas et al., 1986); planning development projects (Eden et al., 1998); on project construction productivity (Lam, Lee, & Hu, 2001); IT Projects to maximize organizational productivity gains (Ngwenyama et al., 2007); projects that implement new technologies (Plaza et al., 2010); in quality improvement projects (Lapre et al., 2000); aircraft projects (Gholz, 2011); and a large number of other applications in the context of project management (Anzanello & Fogliatto, 2011).

While project management involves complexity and the sequence of a life cycle, it also seems appropriate to consider the learning effect on the job of project managers who have continuously improved their performance as a result of having managed similar projects. This aspect was considered in our project assignment model.

The Model

Based on the review of the literature, we developed a framework for allocating projects that uses nine steps (see Figure 1), which are in this section.

Framework for allocating projects

Figure 1: Framework for allocating projects

The organization must make a diagnosis of the existing project managers for project management activities (workload availability) and bear in mind that project managers often accumulate both project management and functional activities; this information must be obtained for all project managers. Furthermore, the organization must define what the average length of time is for managing each project to which the project manager must commit (based, for example, on historical data).

These data are then used to complete a matrix that shows the average time needed to manage being considered and the time availability of the project managers. This time should be added to the efficiency factor (EF), which can be represented by the following equation:

Equation 1


MH represents the number of hours required to manage the project and is estimated based on historical data from previous similar projects. If the project manager has no previous experience in that particular type of project, then there will be no discount on management hours (MH). The survey of project manager experience in past projects must contain replies to three questions:

  • Q1: Has the project manager managed a similar project?
  • Q2: How many hours of accumulated management does the project manager have in similar projects? This amount of time must be corrected by the factor of accumulation of the learning curve (LC) adopted in each case.
  • Q3: How many similar projects has the project manager previously managed? Values of Q2 and Q3must be normalized because this involves different scales and unit hours.

a and b represent the weight (relative importance) for issues Q2 and Ç3that can be different in different organizations, i.e., they may be equal or different.

LCq3+1 represents the accumulated value to the learning curve for the next project.

Q3 + 1, for example, indicates that the project manager has previously managed two similar projects—the value of n = 3 should be used in the learning curve.

EF represents the value that will result in a discount (a reduction) in the number of hours required to manage the project when it is managed by a manager with relevant experience. The variables in the model were identified as those that lead to a reduction in this time because of prior learning from similar projects. This experience was considered in the model as being the number of projects the project manager has managed (i.e., the project manager has undergone the cycle of managing this type of project several times, thus accumulating experience that results in being more at ease when dealing with this type of project) and the cumulative hours of management in similar projects (i.e., some projects are long, and the project manager may not have undergone different stages of management several times, but the accumulated knowledge corresponds to several smaller projects).

The optimization function is applied. The optimization model (an integer programming model) aims to minimize the total number of hours (H) of management by better distributing projects on considering the effects of the learning curve. The objective function can be presented as:

Equation 2


i = 1,... n where n is the project manager number;

j = 1,.m where m is the project number;

tnm = the number of hours that project manager n needs to manage projects m, as per the defined MH; and

Pij = the decision variable allocation of the project j to project manager i that can be either yes (1) or no (0).

The objective function has the following restrictions:

  • Resource availability constraints:

Equation 3

where: thn represents the total hours that project manager n has available to manage projects.

  • Technical constraints, because each project should be allocated to only one project manager, are as follows:

Equation 6

After having applied the allocation model, add the “switchover time loss” by the project manager. This variable adds the loss in hours due to the accumulation of designs and occurs because of the time needed to adjust to the issues changing from one project to another. Whenever a project manager is allocated to a project, these additional hours should be aggregated to his/her hours. In this study, this time was calculated using the International Kapur Scale (Patanakul et al., 2007):

Equation 7


Sn = the switchover time-loss of PMn,

Yn = the number of projects (when more than one) that PMn will manage, and

Zn = those project managers (PMn) who manage not more than one project (binary variable).

Having added the switchover time loss to the total time for which the project manager will be appointed, an evaluation should be made to determine whether this time exceeds or underuses the available project manager time. It is often likely that there will be a need to redistribute projects, as some project managers will be allocated too many projects. This decision will depend on the management and policy of each company. A presentation of the application of the model in an energy company is provided in the following section below.

An Application of Proposed Model

An application of the proposed model was carried out in a Brazilian electric energy company. It has included the strategic plan of the organization in its portfolio. In the period under study, there were 49 projects to be implemented that were identified/coded as P1, through P49 so as to keep company data confidential. We also compiled a listing of project managers to be appointed and their availability (hours per week) for project management. This consisted of managers who were devoted exclusively to the management of projects and project managers who were also devoted to their functional activities (routines) in the organization; therefore, the time devoted to project management for each project manager is variable. A survey was conducted with every project manager. The project manager’s names also received an identification number, that is, PM1 through PM16 (for the 16 project managers).

The company divided the projects into three groups: urgency, cost, and innovation. Similarly, the project managers were separated into three groups according to: amount of experience, results on previous projects, and negotiation skills. This served projects with greater urgency, cost, and innovation (termed Class 1, Class 2 and Class 3, sorted in that order) to which the most experienced project managers were allocated. The results were organized by decreasing order of negotiation skills (project managers Class 1, Class 2 and Class 3, sorted in this order). Then, the mathematical model was developed and applied to each group so as to distribute projects within each class.

The composition of the project classification was:

  • Class 1: P44; P46, and P47.
  • Class 2: P1, P2, P3, P4, P5, P6, P7,P8, P9, P10, P11, P12, P13, P14, P16, P17,P18, P19, P21, P23, P24, P25, P27, P28 ,P29, P30, P32, P33, P35, P36, P37, P38, P39, P40, P41, P42, P43, P45, P48, and P49.
  • Class 3: P12, P15, P20, P22, P26, P31, and P34.

The composition of the project manager classes was:

  • Class 1: PM2, PM7, and PM8.
  • Class 2: PM1, PM3, PM5, PM6, PM9, PM10, PM12, and PM16.
  • Class 3: PM4, PM11, PM13, PM14, and PM15.

The organization that defined projects of Class 1 (the most complex) required 20 hours of weekly management; eight hours were needed to manage Class 2 (medium complexity) projects; and Class 3 (lowest complexity) projects required the project manager to dedicate four hours weekly to them.

It is not recommended to allocate project managers to projects in the upper classes if they do not have the skills and competencies needed. In this research, the project management officer. (PMO) requested to assign priority projects to the appropriate project manager class so that project managers could develop their skills.

A survey of data from each project manager was conducted to answer: Q1, Q2 and Q3 — the number of similar projects managed. As shown in Table 2 for Class 1, this value was normalized.

CLASS 1 Q1 P44
Q3 Q1 P46
Q3 Q1 P47
PM2 0 0 0 0 0 0 0 0 0
PM7 1 20 1 1 78.68 6 1 35 2
PM8 1 35 2 0 0 0 0 0 0

Table 2: Survey data of the project and project managers

To complete the matrix by applying the equation 1, the learning curve used was of the classical form (Argote & Epple, 1990):

Equation 8


Yi = performance in the ith period/unit,

a = performance in the first period/unit,

xi = cumulative number of periods or units through time i,

b = learning rate, and

i = time subscript.

In our case, Y represents the total time used to manage a project, whereas x represents the number of similar projects. For example, if PM2 managed six projects similar to Class type 1 (20 hours), then the number of hours of accumulated management is 20 * 3.93 (where 3.93 is the factor value of the cumulative learning curve for 6 units with 75% improvement); therefore, PM2 accumulated 78.68 hours of experience in similar projects. Initially, some tests were performed with different factors of improvements; in this case, an improvement of 75% was the best estimate according to the vision of the managers and the PMO. The application is presented in Table 3 for Class 1 projects.

Class 1 PM2 PM7 PM8
P44 20 16.58 14.78
P46 20 11.08 20
P47 20 14.78 20
Project manager’s available time 30 30 30

Table 3: Time for project management with efficiency factor

The application of an integer programming model (the Risk Solver Platform User was used to solve the mathematical problem).

Equation 8

Subject to:

Equation 8

The solution is presented in Table 4 with the optimal total value of 40.65 hours.

Class 1 PM2 PM7 PM8
P44 0 0 1
P46 0 1 0
P47 0 1 0
Number of projects
allocated 0 2 1

Table 4: Result of the allocation function in Class 1

  • Class 2 — As was done for Class 1, equations 2 and 3 were used to solve the allocation, taking the projects and project managers of Class 2 as variables. The results show an optimal value of 256.18 hours for Class 2, the allocation result of which is: PM1— P6, P8, P25, P35, and P49; PM3—P30, P33, P36, P39, and P40; PM5—P16, P17, P23, P43, and P48; PM5—P5, P9, P10, P13, and P18; PM9—P11; PM10—P14, P19, P21, P24, P27, P28, and P29; PM12—P1, P2, P3, P4, and P32; PM16—P7, P37, P38, P41, P42, and P45.
  • Class 3—Using the same method as Classes 1 and 2, the optimal value was 23.38 hours and the allocation result: PM4—P12, P34; PM1—P15, P20, P22, P26, and P31.

For the added switchover time loss, see T able 5 for Class 1, T able 6 for Class 2 and T able 7 for Class 3.

Class 1 PM2 PM7 PM8
Total hours allocated by manager 0 25.87 14.79
Switchover time loss 0.00 7.50 0.00
Total hours allocated 0.00 33.37 14.79
Leftover hours 30.00 -3.37* 15.21

*Negative values mean that the time after application of the project manager “switchover time loss” was extrapolated from the number of hours.

Table 5: Switchover time loss for project manager Class 1

Class 2 PM1 PM3 PM5 PM6 PM9 PM10 PM12 PM16
Total hours allocated by 38.43 34.04 34.63 40.00 5.60 35.13 38.43 29.93
manager Switchover time loss 12.00 12.00 12.00 12.00 6.00 15.00 12.00 13.50
Total hours allocation 50.43 46.04 46.63 52.00 11.60 50.13 50.43 43.43
Leftover hours -10.43 -6.04 -6.63 -12.00 -1.60 -10.13 -10.43 -13.43

Table 6: Switchover time loss for project manager Class 2

Class 3 PM4 PM11 PM13 PM14 PM15
Total hours allocated by 6.82 16.57 0.00 0.00 0.00
Switchover time loss 7.50 12.00 0.00 0.00 0.00
Total hours allocation 8.50 18.00 0.00 0.00 0.00
Leftover hours 1.50 12.00 10.00 40.00 10.00

Table 7: Switchover time loss for project manager Class 3

After applying the model to each class, some final adjustments are made by checking for over-allocations of project managers because the "switchover time loss" is added after the allocation in linear programming. If this occurs, an analysis must be conducted by the PMO team to check for the possibilities of redistributing projects. Another issue to be checked is whether there was a suballocation and whether it is possible to verify or redistribute projects that have been allocated to over-allocated managers to project managers with available hours.

In the application of this study, it is possible to see that most project managers were categorized as Class 2 with a number of projects that exceeded the amount of hours available; a total of 70.68 hours of project managers with super allocation means that this must be evaluated by the PMO and each manager so as to consider if these projects ought to be redistributed.

One way to solve this problem would be to allocate another Class 2 project to each of the project managers with over 10 hours of over allocation (Class 1 managers with hours available; e.g., PM2 remains with 30 hours available, as well as PM8 who still had 9 hours available), since managers of Class 1 have greater expertise and experience, no adverse effects are generated by such reallocation. Even so, there will still be an overallocation to project managers, demonstrating that the company has a deficit of competencies among their project managers.

For Class 3, four projects were allocated to PM11, while PM14 and PM15 were not allocated any projects. It is also evident that project managers in this class will be underallocated, thus enabling them to be assigned to other functions in the company (or even to help other project managers with their projects), thereby gaining the experience they require to be considered fit to contribute in the future, thereby learning skills needed for other classes.

After an analysis of the PMO and project managers, based on the initial assumption that project managers of a higher class can manage projects from the lower classes, we conducted a redistribution of the projects of Class 2 to project managers of Class 1:

  • Projects: P18; P32; P37 and P49 were assigned to PM2;
  • Projects: P24 and P40 were assigned to PM8.

This results in a deficit of -26.22 hours, thus denoting the lack of better trained and more experienced project managers in the company studied.

After the final allocation, the model showed an optimal result of 320.16 hours of project management (per week). This value, when compared to the expected value before optimization (400 hours), implied a weekly savings of almost 80 hours. The management team and project managers felt that the experience curve used in the reduction factor of hours was consistent with the reality experienced in the organization. In their opinion, the model met the goals and matched the skills and experience levels of the project managers with the project categories.


This paper presents an allocation project model using mathematical optimization for distributing projects to project managers, which takes into account the resource restrictions and learning curves. This proposal differs from other models in the existing literature because this model considers previous experience in managing similar projects with an efficiency factor by using learning curves to obtain an optimal result when allocating projects. In addition, this model allocates multiple projects to project managers, thus reducing the number of analyses performed in this process.

The proposed model was applied in an energy company. The project management team examined the results of the model and found the results of the allocation decisions to be coherent, fair, a viable process.

This model enables availability and resource needs to be investigated and also proves to be an excellent tool for internal assessment on training and recruitment when diagnosing the real situation of a company with regard to the indispensable resource of the project manager function.

For future studies the development of a method for preselecting managers, based on the characteristics of the projects and the managers’ competencies is recommended.


This work is part of research funded by the Brazilian Research Council (CNPq).


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Elaine Oliveira, holds a Bachelor’s degree in Production Engineering and holds a Master’s degree and is a PhD student on aspects of Production Engineering. She teaches the discipline of project management for various courses in Engineering and Management at the Federal Institute of Technology of Paraíba (IFPB). During the last eight years, she has been involved in project management activities in a Brazilian power company, including having been a manager of several large projects.

Ana Paula Cabral Seixas Costa, holds a PhD in Management Engineering from the Federal University of Pernambuco. She is an Associate Professor and was Coordinator of the Post-Graduate Programme in Production Management of the Federal University of Pernambuco. Today she is Head of the Department of Production Management. Her special interest lies in Information Systems, mainly on the following topics: information systems, information technology, decision support systems, and multicriteria decision aid.

Luciana Hazin Alencar, PMP, holds a PhD in Management Engineering at the Federal University of Pernambuco. She is Assistant Professor and Coordinator of the MBA in Project Management for the Federal University of Pernambuco. Her special interest lies in project management, procurement, and multicriteria decision aid.

1Elaine Cristina Batista de Oliveira is also associated with Federal Institute of Technology of Paraíba (IFPB)

©2014 Project Management Institute Research and Education Conference



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    By Haffer, Rafal | Haffer, Joanna | Morrow, Donna Lynne This study examined the effects of job crafting on the work meaningfulness and work engagement of project participants of different ranks.