Designing a hybrid system dynamic model for analyzing the impact of strategic alignment on project portfolio selection

Accepted Manuscript

Designing a hybrid system dynamic model for analyzing the impact of strategic alignment on project portfolio selection Seyed Mojtaba Rowzan PII: DOI: Reference:

S1569-190X(18)30147-3 https://doi.org/10.1016/j.simpat.2018.10.001 SIMPAT 1866

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Simulation Modelling Practice and Theory

Please cite this article as: Seyed Mojtaba Rowzan , Designing a hybrid system dynamic model for analyzing the impact of strategic alignment on project portfolio selection, Simulation Modelling Practice and Theory (2018), doi: https://doi.org/10.1016/j.simpat.2018.10.001

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Designing a hybrid system dynamic model for analyzing the impact of strategic alignment on project portfolio selection

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Abstract One of the key challenges in project organizations is the alignment of portfolio management with major corporate strategies. Usually, project-based organizations use shared resources to control and plan the project portfolio. Therefore, the exploitation of shared resources and project planning decisions made in this regard can change the progress of projects and affect the success rate of the projects. In this article, the integration of system dynamics with multi-objective decision making is applied to address project portfolio selection. The project portfolio has been modeled using four basic dimensions including technology, complexity, innovation and time sensitivity. The aim is to plan and control the progress of project portfolio while maximizing the strategic adaptation subject to the changes of the human resources. For this purpose, a two-stage MO-PSO with TOPSIS is proposed for portfolio selection problem that can solve real-world instances of the problem in a reasonable time. The result of the sensitivity analysis indicated that the proposed decision support system (DSS) provides insights into the impact of strategic alignment on project portfolio selection. According to the simulation results, the integrated methodology of this research can assist in choosing the suitable projects to achieve a project’s strategic goals following the organization strategy.

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Keywords: System dynamics, portfolio management, multi-objective optimization, project planning

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1. Introduction

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One of the key challenges in project organizations is the alignment of portfolio management with major corporate strategies (Archer and Ghasemzadeh, 1999a). Achieving this convergence involves examining the portfolio behavior of the company's projects, which will examine the behavior in two ways. The first method is to extract the key factors of success from past experience studies and generalize the results of a method consistent with the strategy. The second method is the use of simulation models that can be used in the virtual environment to influence the policies and test the strategies before execution (Ilati et al., 2014). The simulation models are frequently used to get solutions to the particular problem in a virtual environment before implementing the solution in a real-world setting (Hassannayebi et al., 2016). System dynamics (SD) is an analytical simulation technique used to study the equilibrium level of systems that hold a holistic view mainly used at the strategic level (Lättilä et al., 2010). It was a novel invention introduced in the late 1950s by Jay Forrester, which helped gain insights into problems that were more complex with the growing feedback degree. The SD modeling approach has been used in the past few decades for the analysis and improvement of project performance (Gholizad et al., 2017). The mixed notation of flow and stock has been utilized in this approach to characterize our mental model as a network of cause and effect (Sterman, 2000). The mathematics behind the SD, which lies in differential equation modeling, makes it quite simple to include nonlinear relationships, delay, and information feedback. SD is often employed as a stand-alone approach; however, it may receive support from other methodologies to expand and improve its performance. As an example, SD models typically aggregate agents into a relatively small number of states or compartments in which they are assumed to be homogeneous and well mixed. Thus, they cannot include heterogeneity in individual attributes and in the network structure of their interactions. Instead, differences or diversity can be shown with agent-based simulation (ABS) or discrete-event simulation in which agents are represented explicitly rather than as a single aggregate entity at the potentially higher computational expense (Rahmandad and Sterman, 2008). Therefore, the hybrid of SD and ABS simulation can help to overcome difficulties arising from applying these two methods individually. A case in point is presented by (Wakeland et al., 2007). One of the ways that have been received less attention from researchers and can be applied for much the same reason is the integration of SD with multi-objective/criteria approaches. They help system behavior to be represented more explicitly. See Santos et al. (2001), and Aslam et al. (2014) as the evidence that proves the potential power of SD in project management. Integrated simulation and optimization methods have proved their worth to address a broad range of problems (Hassannayebi et al., 2014, Kuhl and Tolentino-Peña, 2008, Lu et al., 2008, Sajedinejad et al., 2011). Further development is needed to unravel more complicated cases. Project and portfolio management are powerful weapons for developing a business strategy (Shenhar and Dvir, 2007). Project portfolio management (PPM) carries out continuous maintenance of project list by reviewing them in a dynamic selection/rejection process, which effectively translates strategic objectives from business level into operational level policies (PMI, 2008). Although PPM is considered a rational decision-making approach, it is unfortunate that political and path-dependent issues often influence the process that affects its complex and dynamic features (Martinsuo, 2013). Despite several applications of multi-criteria decision making (MCDM) models to project portfolio management, there has been little integration of SD and MCDM (Danesh et al., 2018). 2

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SD and multi-objective decision making (MODM) are two beneficial approaches to strategy development which individually have proven their potential to support project and portfolio management problems. This research verifies the synergistic power of integrating these two approaches to serve as a valuable tool that project managers can use to change the way they think, and eventually, make use of available information more effectively. Most of the growing system dynamic models in the field of project management have already examined the project's behavior as an independent entity, and the reasons for time lag or changes are modeled only for a particular project. This is while project-based organizations use shared resources to control and plan a number of projects in the project portfolio. Therefore, the exploitation of shared resources and decisions made in this regard can change the progress of projects. On the other hand, changing the strategic approach in an organization can affect the view of the executives to the project, because each project, by its very nature, requires a different strategy for optimal implementation. A project-centered project strategy has a significant impact on a project called "strategic adaptation" or "strategic fitness". Another area of innovation is that the proposed model is an interactive decision support system (DSS). The system is designed to be implemented repeatedly and without user intervention during the simulation of reciprocating operations between the implementation of the dynamic system model and solving the decision problem. This means that, upon completion of each project and release of resources, system dynamic analysis results are automatically transmitted to Excel spreadsheets. After the implementation of the optimization model, the model of the dynamic model again completes the decision-making results through simulation. Thus, the model results are closer to reality. The success of a project-based organization in winning a bidding and starting a strategic project can change the organization's priorities and affect ongoing projects. The proposed model, as a DSS, facilitates understanding for managers and helps them to improve their strategic look at the concept of project portfolio management. Finally, as another field of innovation, a two-stage MO-PSO is proposed for portfolio selection problem that can solve real-world instances of the problem in a reasonable time. The remainder of this paper shows the research path used to establish the SD/MODM strategy-building methodology: Section 2 presents an overview of the application of system dynamics in project management. Section 3 introduces converting the project management model into a PPM model, including a MODM framework for project selection. The results of integrating SD and MODM for modeling PPM are presented in Section 4 offers a summary of the PPM model, which discusses the benefits provided by the integrated model, in addition to the benefits gained from the two individual approaches presented in Section 5.

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2. Literature review In this section, most significant contributions in the field of project planning and control are discussed. Over the past few decades, researchers have stressed the inefficiency of classical methods to explain the gap between project performance in reality and their scheduled plans. Table 1 provides a taxonomy of the related literature. Lyneis and Ford (2007a) conducted a comprehensive survey to discuss the application of the system dynamics methodology to project management. Different aspects were addressed, including model structures, research directions, and successful implementations. Meanwhile, system dynamics was introduced as a useful way to compensate this dim view (Abdel-Hamid, 1988, Rodrigues and Bowers, 1996).

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2.1. System dynamic application in project management Nowadays, the application of SD simulation in project management has been successfully verified in several well-developed models. The first portfolio management model, introduced in 1974, stressed major problems such as the perception gap, underestimation of project boundaries, and devising decisions based on inaccurate data (Roberts, 1974). Then, the inauguration of the rework cycle in 1993 helped to illustrate the actual behavior of the system (Cooper, 1993). Further development was applied to the model based on what project managers do to overcome the negative effects of delivery slippage—employing more people, utilizing overtime, and finding ways to do the work faster (Sterman, 2000). Then, control loops and their side effects in the forms of ripples and knock-on effects were added to the model. For a full review see Lyneis and Ford (2007b). Love et al. (2002) proposed an SD model to investigate the dynamics of change management policies in construction projects. Results of applying the proposed system dynamics methodology in a real case study prove that it can afford valuable insights into how changes and their interactions affect the project performance. Lee (2006) proposed a reliabilityoriented time buffering method within an SD model that purposes to minimize the disruptive effects of errors and changes during the initial phases of an infrastructure project. The outcomes confirmed that the rate of rework was minimized and the quality of the management process was significantly increased. Lee et al. (2006) designed a novel web-based framework that combines the system dynamics methodology and network-based techniques. The system dynamics was used as a simulation engine to plan strategically and the network-based techniques were used as a tool for the operational management. Lebcir and Choudrie (2011) analyzed the effects of the project complexity elements on the project completion time through a system dynamics approach. In this context, the methodology addressed the project complexity and operations as well as their impacts on the time performance. The outcomes indicated that the project complexity was affected by different factors, including the project uncertainty, the novelty, interconnectivity, and size of the project infrastructure. Yaghootkar and Gil (2012) presented a method based on the system dynamics simulation technique in order to analyze the project management process in resource-constrained multiproject environments. The problem was how to share skillful resources among several parallel schedule-driven projects. It was shown that a scheduling policy might lead to a decrease in the profitability and create deviations in the planned project milestones. The workforce productivity was also analyzed. Zhang et al. (2014) addressed the sustainability of construction projects. To this end, an SD model was developed to verify the stability of construction projects in terms of their feasibility and sustainability during the life cycle of the project. The outcomes of implementing the model in a case study demonstrated the efficiency of the proposed model. Yang and Yeh (2014) recognized the system dynamics as an effective method to control the external risks of projects. The system dynamics modeling enables the project manager to study the cause and effect relationship between risks factors to reduce the negative effects of delays and disruptions. Lopes et al. (2015) proposed a system dynamics model for the risk assessment of software development projects. Risk factors were identified during the development of software and their interactions were analyzed in a dynamic and non-linear setting. Khan et al. (2015) developed a novel system dynamics model to manage collaboration problems in construction enterprises. The results of implementation show that the system dynamics approach provides a better understanding of the dynamics of the information flow through collaborative technologies and leads to enhanced productivity. 4

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Rashedi and Hegazy (2015) developed a system dynamics model to examine the effects of various strategic policies on budgeting, infrastructure development and the sustainability of projects. The outcomes demonstrated that the decision support framework could assess the efficiency of various project planning solutions. Wang et al. (2017) implemented an SD model for dynamic project alignment at a tactical level under uncertain condition. The designed model enables the assessment of corrective actions based on the dynamic behavior of the project components. The designed system supports decision makers in preparing reactive strategies against disruptions during the project execution phase. The outcomes demonstrated the importance of setting appropriate thresholds for corrective actions to evade performance fluctuations and resource wastes.

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2.2. Multi-objective Project portfolio selection models In this subsection, the most significant contributions in multi-objective project portfolio selection are discussed. Ringuest and Graves (1989) presented a linear multi-objective optimization model for selection of R&D projects. The mathematical model was based on the goal programming formulation. Doerner et al. (2006) proposed a multi-objective version of the ant colony optimization (ACO) with preprocessing techniques for multi-objective project portfolio selection problem. Iamratanakul et al. (2008) provided a critical review of existing approaches and methodologies for project portfolio selection. It was concluded that despite the rigorous mathematical programming approaches for project portfolio selection, they cannot be applied solely to the real-world situation due to the existence of variable and dynamic factors in the project. Thus, the future research would be direct toward the combination of mathematical modeling techniques and simulation models to develop more effective methodologies. Liu and Wang (2011) presented a constraint programming (CP) techniques for integrated project portfolio selection and resource-constrained project scheduling problem under timedependent resource availability. The aim was to maximize the total profit of R&D and construction projects with respect to budget constraint. Khalili-Damghani et al. (2012b) developed a hybrid approach for multi-objective and multiperiod project selection problem. The methodology is upon the TOPSIS and an epsilonconstraint method. Shakhsi–Niaei et al. (2014) proposed a hybrid genetic algorithm (GA) and differential evolution algorithm (DEA) for project portfolio selection with a limited budget. The model takes into accounts the interaction effects between selected projects. The efficiency of the proposed algorithm was verified through a case study with up to 500 projects. Mavrotas et al. (2015) conducted a research to analyze the robustness of the solutions generated by the for multi-objective optimization methods for project portfolio selection problem. Perez and Gomez (2016) designed and implemented fuzzy nonlinear mathematical optimization models for integrated project portfolio selection and scheduling problem. Wu et al. (2018) presented a fuzzy multi-objective optimization model for project portfolio selection problem. The problem was solved by a Non-Dominated Sorting Genetic (NSGA-II) algorithm to maximize total benefit and installed capacity. 2.3. Integrated approaches Archer and Ghasemzadeh (1999b) proposed a hybrid approach for project portfolio selection based on a trade-off between the quantitative and qualitative measures of interest. Dey (2006) 5

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addressed the integrated project evaluation and selection problem using multiple-attribute decision-making (MCDM) method. Amiri (2010) applied the integrated AHP and fuzzy TOPSIS for oil project selection. Alvanchi et al. (2011) addressed the system dynamics modeling approach of construction operations aiming at analyzing the mutual effects on the system performance. For this purpose, an integrated model of the discrete event simulation (DES) and system dynamics was proposed. The efficiency of the integrated simulation modeling framework proposed was verified through a real-world construction project. Khanzadi et al. (2012) conducted a research to analyze various aspects affecting the concession period of a project. They presented a fuzzy logic-based system dynamics approach consisted of the intertwined structure of different uncertain factors affecting a build-operatetransfer (BOT) project. Moradi et al. (2015) contributed to the field by presenting a combined simulation modeling approach to analyzing operational factors disturbing the performance of construction projects. In this regard, integrated SD and DES models were developed. This novel methodology has several practical implications. The major one is that within the proposed methodology, the project manager has the capability of modeling detailed and holistic aspects of a complex project and analyzing various interrelated variables influencing construction operations. Boateng et al. (2016) proposed a combination of the Analytical Network Process (ANP) and a system dynamic framework for managing the complications of risk factors in the megainfrastructure project design and construction. Empirical results of simulation experiments indicated that when compared to existing risk management approaches, the system dynamic model shows improvements in the effective management of risks. Debnath et al. (2017) presented an integrated MCDM model based on DEMATEL for project portfolio selection and project scheduling. Chien and Huynh (2018) implemented an integrated approach for R&D project portfolio selection and project scheduling problems. The problem was solved using a multi-objective genetic algorithm (GA). Kumar et al. (2018) proposed a hybrid meta-heuristic algorithm for project portfolio selection and project scheduling problems. The methodology involves the hybridization of teaching learning-based optimization (TLBO) and tabu search (TS) to cope with the large-size instances of the problem.

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Table 1. A taxonomy of the related literature

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Solution approach

Objective type

Objective function

Resource limitations

Interaction between projects

(Dinesh Kumar et al., 2007)

LP

Singleobjective

Costs

Human & material

No

(Kumar et al., 2008)

Mixed-integer linear program (MILP)

Singleobjective

Profit

Material

No

(Hu et al., 2008)

Goal programming (GP)

Multiobjective

Benefits/costs

Human & material

Yes

(Tkáč and Lyócsa, 2010)

Dynamic stochastic programming (DSP)

Singleobjective

Profit

Material

No

(Wang et al., 2014)

Analytic network process (ANP)

Multicriteria

Profit/quality/cycle time

Human & material

Yes

(Costantino et al., 2015)

Artificial neural network (ANN)

Singleobjective

Strategic

Human

No

(Kalashnikov et al., 2017)

Mixed-integer quadratic program (MIQCP)

Multiobjective

Benefits/difficulty

Human & material

Yes

(Yan and Ji, 2017)

Uncertain programming models

Multiobjective

Maximize the expected returns and minimize the sine cross-entropy

Budget

No

(Aviso et al., 2017)

Robust optimization

Multiobjective

System robustness and technical performance level

Budget

No

(Liu et al., 2018)

Dynamic differential evolution algorithm

Singleobjective

Cumulative risk

Budget

No

This study

0-1 Integer linear programming (ILP) and SD

Multiobjective

Strategic fitness, risk, and duration

Human

Yes

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References

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One of the purposes of this paper is to demonstrate the capabilities of the system dynamics approach to selecting projects in dynamic situations. According to the literature review, the selection of projects is usually done through MCDM methods. In this research, the results of choosing different strategies for selecting a project are also examined. To the best of the current researchers’ knowledge, there is little research done in the field of the integrated SD and multi-objective optimization approach to project portfolio selection. Introducing the concept of the project strategy in the simulation process is another innovation of this model compared to the past models of project management. The practical application of this concept created a method for assessing the extent to which the organization's strategy was aligned with the operational level of the project strategy. The use of project management parameters such as project strategy, culture, structure, processes, tools, and techniques to measure how the project's strategy is streamlined in the operational layers is also a concept that its initial formulation is introduced in this study. However, in this study, only a linear relationship was identified as an integration of the organization's strategy into the project's strategy.

3. Methodology

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The final model of this article went through the following steps: 1) the SD model of project management was reproduced based on a thorough literature review; 2) the model was extended into a PPM format, which included implementation of selection/rejection variables as a solution to the multi-objective project selection problems; 3) A structure was determined that could link these two sub-models together. The definition of some important variable for SD model are given in Table 3. The model of Fig. 1 consists of two reinforcing cycles, which cause the delay and its effect on the schedule pressure in both of the two loops. It is worth noting that schedule pressure is not the same for different projects in terms of equal delay times and follows the conditions governing that project. This is related to the various dimensions of the project strategy. In this modeling, the project strategy is modeled according to four aspects of technology, innovation, pace, and complexity. As a result, the effect of the delay on the schedule pressure is determined by the pace variable in the strategy vector. In time-sensitive projects, the delay in the project will further increase schedule pressure. However, increasing schedule pressure causes an increase in error rates, resulting in greater need for rework, and the rework will again increase the delay in the project. Similarly, an increase in schedule pressure is one of the factors that reduces the number of effective workforces, resulting in less work, which will increase the delay. This delay increase in different situations is compensable in several ways. One of these methods is to do more in fixed time as overtime. In other cases, managers try to increase the effective workforce by attracting more manpower. Demand for manpower increases in several ways; (1) new work that must be done as a result of rework, while individuals are busy with their daily duties; (ii) pressure to reduce the duration of the current tasks, so that the project is finished at the due date. Ultimately, the indirect impact of working pressure on losing current staff (which in the past led to an increase in latency in a reinforcing loop) increases the need for new recruits. Although the increase in the new force will compensate for the arrears with a little delay and with less intensity. The causal loop B- outlined in Fig. 1 illustrates these cases.

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Fig. 1. The core casual diagram of the SD model

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Fig. 2 illustrates how to influence the factors affecting manpower by displaying three levels of variables: Exhaustion, New Workforce, and Experienced Workforce. Under the influence of the schedule pressure variable, the error rate increases by decreasing the accuracy (due to increased work speed and due to staff fatigue). The effect of staff morale and its relationship with the rate of error and the rate of withdrawal of human resources is also presented in this figure. As previously explained, recruitment is one of the factors contributing to the increase in effective workforce. On the other hand, the effect of the withdrawal of manpower on the effective reduction of the labor force is more meaningful. The key point is the time it takes to transform a labor-intensive workforce into an experienced workforce. The variable recruitment rate is calculated by considering the difference in the requirements of the projects and the number of available manpower. Since the proposed model is faced with a project portfolio, the human resources required during the simulation period is not constant, and the number of manpower changes dynamically with the completion of each project or the start of a new project. The “work-to-be-done” variable holds the amount of work that is ready to be begun based on the project daily plan as one main stock variable in modeling project management. The key flow, which is controlled by the “progress” variable, takes the planned work and changes them into the “work done” variable as fast as the available manpower and productivity rate allows. Part of the completed job extracted from the state of “work is done” and moved back to be reworked. This is done using the “Error-Generation-Rate,” which depends on some auxiliary variables such as work pressure, fatigue, experience, and congestion plus communication difficulties. Fig. 2 shows the control diagram of the project control processes. Briefly, the description of the project control flow is that the delay and, work pressure and the work speed define the aspects of the project strategy which in turn affects the increase in over-work, fatigue, error rate, morale, and productivity. At the top of the figure, the flow diagram of the fatigue is shown and at the bottom, the human resource absorption process is shown. The inexperienced labor force also becomes an 9

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experienced human resource in a given time period, which must be calculated in terms of productivity.

Fig. 2. Flow control diagram of the project control processes pace-level

nov-level

com-level

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tech-level

NTCP project Pace facet of project strategy project strategy

strategy fitnesss sf

strategic adaptation

NTCP management style

Strategic Orientation

Fig. 3. Flow control diagram of the project strategic alignment

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The array type variables are applied to convert this model into a PPM model. SD modeling commonly uses these variables when addressing different agents regarding their attributes. This can create an opportunity to show projects of separate agents, but it can also show how the projects are interconnected. The array variables are shown in Fig. 4 with double line symbols. The “Project Selection” is a zero-one array that influences the progress by enabling the selected projects in this model. In the process of project control, failure to achieve project goals at a given time is commonplace and in some cases inevitable. This delay is justified in dynamic models with a rework cycle. In this way, it's always necessary to redo some of the work done because of the lack of quality. This is illustrated in Fig. 4, which represents the main flow diagram of the Dynamic Project Management Model. The “work to be done” variable is defined according to the project plan. The "scheduled work" is converted to the variable "work done" with the variable progress rate. The progress rate is determined by two factors of effective productivity and effort applied. The part of the work that enters the rework is calculated using a variable called “Error Generation Rate”.

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Fig. 4. Project Management Model converted into PPM Model

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Each project needs a full breakthrough in order to have a navigational strategy that matches its own characteristics. In the project portfolio selection problem, due to the need to adopt a steady strategy to measure the degree of alignment of projects, a single strategy is in the lead of all portfolio projects. In order to establish a consistency between the organization's strategy and the project's coordinates, project managers will work towards defining a moderated strategy between the organization's strategy and the ongoing project. Project strategies are actually modifying the organization's strategy according to the features that are available in the definition of the project. For example, if an organization's technology strategy is in the high technology field and a running project is high-tech, then the project's strategy is in line with the organization's strategy. Otherwise, if the feature in the project is lowtech, then the project strategy is considered between high technology and low technology. To do this, we need to define the organization's flexibility factor (Table 2).

Symbol

Table 2. The definition of the symbols for the strategic project alignment model Definition 11

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α 𝑎 𝑏 𝑎 ∗ 𝛼 + 𝑏 ∗ (1 − 𝛼)

Flexibility against project features The desired degree of organization's strategy The degree of the desired attribute in the project definition Degree of the desired feature in the project strategy Table 3. The definition of some important variable for SD model

Variable name

Definition

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Variable to (FOR(i=1..10| calculate IF('Stage-Gate Decisions'[i]=0,0, Schedule schedule (IF('Percentage complete'[i]<1, pressure pressure due to GRAPH((delay[i]/Duration[i])*'Pace facet of project strategy'[i],0,.5, delay {0,.1,.2,.35,.5,.7,1}),0))))) Sending a signal from a dynamic stage gate model when it INTEGRATE(PULSE(1,STARTTIME,3<>)+chng/1<>) pulse comes to decisions about events in Excel Indicator variable to chng ARRSUM(IF('Percentage complete'=1 AND chngstt<>1,1,0)) signify the end of a project 1-FOR(i=1..10|( Variable to IF(sf[i,1]<>0,sf[i,1],1) strategy calculate *IF(sf[i,2]<>0,sf[i,2],1) fitness strategic fitness *IF(sf[i,3]<>0,sf[i,3],1) value *IF(sf[i,4]<>0,sf[i,4],1) )^.25) (MIN(AFMDP,1)*('Experienced workforce'*.6/('Experienced Variable to workforce'+'New workforce')+ calculate 'New workforce'*.4/('Experienced workforce'+'New workforce'))* Productivity productivity (1-'Congestion and communication difficulties')*'Multiplier to index for human productivity due to Morale' resources )^(1/3)

4. Mathematical model

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The decision to work on a new project depends on its expected commercial value, its strategic fitness, and its risk factor. Even though a new project is affected by rest of the projects in the portfolio, it can also have its own effect on them; it can even be accepted and incorporated into an existing portfolio at the expense of holding another project and removing it from the project list (Cooper et al., 1999). There are many models that have been developed to support the project portfolio selection in theory and practice, in which the process is influenced by multiple and often conflicting or competing objectives as in the cases reported by Araúzo et al. (2010a), Laslo (2010), and Khalili-Damghani et al. (2012a). Since there is rarely a unique solution to a MODM problem, decision makers have to choose a solution from a set of non-dominated solutions that 12

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Symbol 𝑖 𝐸𝐶𝑉𝑖 𝑆𝐹𝑖 𝑅𝐹𝑖 𝐷𝑖 𝑀

Definition index of projects, i=1,2,..,n Expected commercial value of project i Strategic fitness for project i Risk Factor in project i Duration of project i Maximum available human resource

The decision variable of the model is expressed as:

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1 𝑖𝑓 𝑝𝑟𝑜𝑗𝑒𝑐𝑡 𝑖 𝑖𝑠 𝑠𝑒𝑙𝑒𝑐𝑡𝑒𝑑 𝑓𝑜𝑟 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑚𝑒𝑛𝑡 𝑦𝑖 = { 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

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are technically called Pareto Optimal Solutions. MODM models are formed by a vector of decision variables and objective functions subject to constraints. The MODM project selection model in this study is combined with the preceding SD model. First, the notations and parameters are defined as follows:

Based on the aforementioned definitions, a multi-objective zero-one integer programming model for project portfolio selection is formulated as follows: 𝑛

Objective 1: Max 𝐶 = ∑

𝑦𝑖 ∗ 𝐸𝐶𝑉𝑖

𝑖=1

𝑦𝑖 ∗ 𝑆𝐹𝑖

𝑖=1 𝑛

Objective 3: Min 𝑅 = ∑

𝑦𝑖 ∗ 𝑅𝑉𝑖

𝑖=1

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𝑠𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜: 𝑛

∑

𝑦𝑖 ∗ 𝐻𝑖 ≤ 𝑀

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𝑖=1

𝑦𝑖 ∈ {0,1}

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𝑛

Objective 2: Max 𝑆 = ∑

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According to the equation (1), the total ECV of the portfolio is maximized as the first objective; then, equation (2) is defined regarding the maximum possible value of total strategic fitness. To meet the needs for minimizing total risk, equation (3) was added, and equation (4) imposes the resource constraint limitation.

5. Simulation and optimization methodology Fig. 5 illustrates the details of the proposed simulation methodology. Powersim Studio (2005) Version 6.00 is used to reproduce the PM model. A heuristic code is developed in Visual Basic Application for Excel using the PSO-TOPSIS algorithm to find a Pareto Optimal solution to the MODM model problem.

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Fig. 5. Simulation methodology block diagram

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In each iteration of the PSO algorithm, particles are moved in accordance with the velocity vector. This vector of velocity is affected by the inertia weight of the particle against the change of position. The particles move dynamically based on the best position in which the particle is located and the best position in the whole solution space. Finally, after several iterations, the optimal solution is obtained in the case of particle population convergence. But in multiobjective optimization models, given that an optimal response is not usually obtained, each goal can determine local optimal solutions. To solve this problem, a two-stage algorithm is proposed.

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Initialization: Get the input parameters of the MO-PSO

Stage 1

Preference setup: Gather the user preferences about objectives and criteria

Weight adjustment: Adjusting the preference weights

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The stopping criteria is satisfied?

Stage 2

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Ranking: Perform preference ordering by similarity to ideal solution using TOPSIS

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Solution generation: Generate non-dominated solution using MO-PSO and store them in database

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Finalization: Output the compromise solutions

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Fig. 6. The two-stage MO-PSO for portfolio selection problem

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In the first step, a number of local optimal solutions are generated independently based on each of the objective functions. In the second stage, a number of optimal local solutions are selected from the Pareto front. Then, the TOPSIS algorithm extracts an optimal solution as the final response. The SD simulation results were applied as the basis for the optimization process. These results that were optimized and included the active workforce number, and a new available project list with a list of attributes based on the updated prerequisite dependencies. Similarly, the SD side of the simulation runs according to the reevaluated project list. The code will be executed upon the activation of one worksheet change event: First, we considered an auxiliary variable in the SD model, which experienced a value change at each major milestone. Then we dedicated a sheet in one MS Excel workbook file which is referenced with the VBA code in the worksheet change event and is linked to that auxiliary variable using a data-set connection. The SD simulation process triggered the available event both at the seasonal re-evaluation plan (for example every 3 months) and when one project is completed and has to be closed.

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6. Result and discussion

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This section presents the data and the validation results of the proposed project portfolio selection model. To define a program of several projects, it is assumed that a high-tech project or innovation, or both, is initially defined in the organization, which naturally cannot be a component of competitive sensitivity and is of a non-competitive nature, but can be defined on the basis of an arbitrary complexity. Then, looking for specific goals, typically determined as a percentage of progress, can be a source of defining projects that are at a lower level of technology and innovation but are more competitive. Following these projects, the organization defines projects to make full use of its original design by making minor changes to its previous products, but on a fully competitive, time-sensitive market. The data of the projects used in a portfolio selection model is provided in Table 4. As illustrated in Table 4, Project 1 is a prerequisite for Project 2, and when it starts, Project 1 has reached 75% of its execution, and the project 2 will be the project's pre-requisite. As shown in this table, projects 1, 2, and 3, have a higher level of technology than each other and a lower level of competition, respectively.

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Table 4. The data of the projects in a portfolio selection model Project Number 1 2 3 4 5 6 7 Project prerequisite 1 1 2 4 4 5 7 Precedence condition 0 75% 50% 0 100% 50% 0 Project makespan (day) 300 200 150 300 400 350 300 Man-hours 4000 3000 1000 1500 3000 2000 1500 Technology level 3 2 1 3 2 2 3 Innovation level 2 1 1 3 2 1 3 Level of complexity 2 2 1 2 1 1 3 Time sensitivity 1 2 3 1 2 2 1 Business Expected Value (US$ Billion) 1.9 1.44 2.5 2.1 3.3 3 2.76 Required human resources 7 7 7 9 6 7 8

8 7 100% 200 3000 3 2 2 1 2.8 5

9 8 50% 150 3000 1 2 2 2 3.2 7

10 8 50% 100 2000 1 2 3 2 1.67 7

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For the monitoring of a specific resource vs. the proposed timeline of a project, project managers use the S-shaped curve diagram. It helps to understand the percentage of completion at specific stages of the project. Figure 3b shows the rate of daily resource allocation plan for one labor-intensive project. Fig. 7 represents the cumulated amount of man-days which depicts its Sshaped curve and shows the progress and growth of that project.

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Fig. 7. Single project progress report using S-Curve

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In order to check the system behavior in a complex environment, we considered a portfolio of nine projects (P1, P2, …, P9). Each project was defined by expected commercial value, strategic fitness, risk factor, and the expected time to be completed (duration). Prerequisite relationships indicated the expected start-up time of a project. The diamond-shaped symbols in the upper left area of Fig. 8 under the progress bar of Project 1 show the milestones in which the next eight project can start after needed lag time.

(b)

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(a)

Fig. 8. Project Interactions in the Gantt Chart Diagram

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We set the simulation time to four years to estimate when all the projects in the portfolio would be completed. A timeline graph was applied to show the S-Curve reports of all the projects. Fig. 9 demonstrates two long intervals for holding project 1. Instead, all dependent projects ended before the first project as the simulation shows.

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Fig. 9. Project Portfolio Progress Report with Project Selection Effects

7. Validation

In order to assess the appropriateness of the model presented, model validation and sensitivity analysis have been conducted respectively.

7.1 Model Validation

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This section provides the results to validate the model. Srivannaboon and Milosevic (2006) describe how to rank in accordance with the strategy of following the conceptual model mentioned as the third aspect of his research. For this purpose, the Euclidean distance takes the role of translation into a degree of project alignment. Two types of questionnaires have been set up to perform these calculations: first, project executives were asked to prioritize management, and then senior managers also rated the importance of prioritizing projects. Ultimately, the Euclidean distance has shown these two scores for nonconformity. At the end of the report, there is an interesting reference to the project, which, despite the identification of 90% alignment with the organization's strategy, resulted in a failure due to the fact that at the end of the project, the customer was looking for more in the product due to the change in demand. They conclude that to avoid these cases, it is essential to set up a periodic review align the components of project management with the implementation of the project. In all cases where the simulation results were previously reported, the revision has not played a role in changing the project portfolio. While in reality, the portfolio program is undergoing a periodic review. The results presented in Table 5 show how the portfolio program, under the first strategy, various revisions of the year, six months and three months will bring different results. Although there is a poor match between the layers of strategy, culture, structure, processes, and tools and techniques. Table 5. An overview of the effect of changing time intervals in the project portfolio revision

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Poor limitation

Strong Limitation

1

2

3

4

5

6

7

8

9

10

39 40 39 39

154 154 154 12

100 101 100 7

0 0 0 0

0 0 0 0

103 103 103 38

0 0 0 0

60 60 60 54

225 225 225 41

154 154 154 34

Nothing 12 6 3

243 326 611 514

302 330 427 217

331 458 470 291

0 da 0 0 0

7 17 15 19

18 12 14 13

0 0 0 0

99 101 104 102

575 466 253 462

255 208 170 210

Nothing 12 6 3

486 623 564 678

412 394 438 369

507 480 471 381

0 0 0 0

7 5 6 12

191 172 138 47

21 24 20 0

167 164 163 126

670 639 708 580

372 372 339 258

Delays (days)

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Projects Revision intervals Nothing 12 6 3

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As shown in Table 6, the reduction of review periods will improve the status of the project portfolio. However, in some circumstances, in addition to reducing delay in some projects, with an increase in the number of revision periods, or a reduction in review time, we see an increase in delay and this will make it impossible to explicitly remark on the improvement of the project portfolio. However, due to the inclusion of time sensitivities at different levels, we can weigh the amount of delay in each project according to the sensitivity defined by the project for that project, so instead of the number of delay days for each project, the weighted delay ratio is adjusted to the project makespan. Finally, the sum of the calculated results for each portfolio will be considered as a measure to evaluate the improvement of the delay. Obviously, the lower the number is, the project portfolio is more suitable in terms of total delay time. These calculations have been made in Table 6, suggesting that the shortening of the review period had a positive effect on the reduction of delays. Improvement of the total delay in the project portfolio is used as a precision in predicting model behavior for the final stage of validation of the model.

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Table 6. Weighted delay values for the project portfolio in different conditions

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Project no. Review Period

6 3

Nothing Poor limitation

12 6 3

Nothing Strong Limitation

12 6 3

4

5

6

7

8

9

Total delay ratio

10

Weighted delay=time interval/(delay*time sensitivity) 0.13

1.54

2.00

0.00 0.00 0.59 0.00

0.30

3.00

3.08

10.64

0.13

1.54

2.02

0.00 0.00 0.59 0.00

0.30

3.00

3.08

10.64

0.13

1.54

2.00

0.00 0.00 0.59 0.00

0.30

3.00

3.08

10.64

0.13

0.12

0.14

0.00 0.00 0.22 0.00

0.27

0.55

0.68

2.10

0.50

7.67

5.10

23.85

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Infinite

3

0.81

3.02

6.62

Delay(day) 0.00 0.04 0.10 0.00

1.09

3.30

9.16

0.00 0.09 0.07 0.00

0.51

6.21

4.16

24.58

2.04

4.27

9.40

0.00 0.08 0.08 0.00

0.52

3.37

3.40

23.16

1.71

2.17

5.82

0.00 0.10 0.07 0.00

0.51

6.16

4.20

20.74

1.62

Delay(day) 4.12 10.14 0.00 0.04 1.09 0.07

0.84

8.93

7.44

34.28

2.08

3.94

9.60

0.82

8.52

7.44

33.48

1.88

4.38

9.42

0.00 0.03 0.79 0.07

0.82

9.44

6.78

33.60

2.26

3.69

7.62

0.00 0.06 0.27 0.00

0.63

7.73

5.16

27.42

0.00 0.03 0.98 0.08

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7.2. Sensitivity analysis

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Resource status

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In this section, a sensitivity analysis is conducted for important parameters of the system. For this purpose, a panel is designed for simulation experiments in Powersim Studio software (Fig. 10). Prior to simulation experiments, some points should be noted. According to Patanakul and Shenhar (2012b), customer intimacy, product time-to-market, and product superiority are considered as key strategies in aligning the organization's strategy with the portfolio of projects. In order to quantify these specifications and make it possible to compare different types of organization's strategy in terms of technology, innovation, complexity, and speed, a grading system is proposed. In this grading system, a weight is allocated to each of the dimensions mentioned above in accordance with Table 7. In this way, these dimensions are distinguished from one another, and the degree to which each project's compliance strategy is measured by the organization's strategy. For this purpose, in each dimension, for each approach the weights are assigned as follows:  

Technology: Very High (4), High (3), Medium (2), Low (1) Complexity: Arrays (3), System (2), Functional (1) 20

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 

Innovation: Revolutionary (3), Production Line (2), Corrective (1) Time Sensitivity: Critical (4), Accurate (3), Competitive (2), Normal (1)

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The goal of quantifying the strategy is to create a method that can be used to measure the degree of alignment of strategies with the objectives of the projects. The magnitude of these values indicates a higher competitive advantage in each dimension. Scaling is based on the previous experience of the organization.

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Fig. 10. A view of sensitivity analysis panel designed for simulation experiments

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Table 7. Grading dimensions of three types of organizational strategy Technology 3 1 2

Complexity 2 2 2

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Organization's strategy Product superiority Product time-to-market Customer intimacy

Innovation 2 1 3

Time sensitivity 1 3 1

Different scenarios have been considered in order to fully examine the dimensions of the strategy selection for a specific portfolio of projects. These scenarios overlap to meet the possible conditions. These scenarios can be distinguished in two dimensions: 1) resource constraints and 2) the degree of strategic alignment.

7.2.1. Resource constraint 21

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Simulations are performed once under the assumption of unlimited resources and again under limited resources. The resource constraint is that the amount of resources available at startup is less than required, but the type of policy defined for resource absorption can compensate for resource shortages during the simulation. The recruitment policy in this simulation is based on prediction-based assimilation. Thus, if there are currently 14 people as human resources and 20 personnel in the next two months, then 6 new staff will be recruited with a two-month training period. Although during the preparation period, these resources are allocated to projects, the new human resources are less productive, their production volumes are less than the more experienced ones. At the same time, the pressures caused by delays cause a certain percentage of human resources to leave the organization monthly, and therefore existing resources will be constantly changing. Obviously, the more resources are limited, the greater the delay in the projects and the higher the ratio of the number of stopped projects to the number of running projects.

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7.2.2. The degree of strategic alignment

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  

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

The degree of effectiveness of a modified strategy from the organization's strategy and project's net strategy. The degree of cultural impact of the project from the project's net strategy and modified strategy. The degree of effectiveness of organizing the project's net strategy and project culture. The degree of process impacts from the project's net strategy and project structure. The degree of effectiveness of the tools and techniques of the project's net strategy and modalities for the project.

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

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According to the strategic project management model for each project, five levels of strategy, culture, organization, processes, and tools and techniques are defined. The simulation rule is based on the fact that each individual project, individually and independently, needs to have its own unique strategy, which is defined in four levels of technology, innovation, complexity, and sensitivity dimensions. But the organization-level strategy is fixed for all projects. The existence of this strategy leads to the definition of a project strategy that has moderated dimensions between the organization's strategy and the specific strategy of the project. The ability of each organization to adapt its master strategy to a project strategy depends on the following factors:

In this study, for ease of implementation of the model, three levels of flexibility are considered for the organization. Accordingly, the organization is adapted to one of three weak, moderate and strong levels: this degree of matching is the equivalent of the parameter α in Table 2. This parameter is considered for each of the five factors at all three levels of 0.4, 0.6 and 0.8, respectively. Given the above description, the simulation results under different conditions are as follows: a) Unlimited resource

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In the case of unlimited resource, simulation results are specified in Fig. 11. In this graph, the planning and completion of projects are displayed. Also, the more complete results are shown in three weak, moderate and strong adoption levels in Table 8. As shown in this table, despite the availability of sufficient resources, the projects have a considerable delay, which is due to the effect of productivity. Of course, in some strategies, such as the first one, more effort is being made to compensate for delays by overtime or recruitment. But, it is expected that this delay will increase with a decrease in resource levels.

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Fig. 11. project portfolio plan in case of unlimited resource

Table 8. Simulation results in case of unlimited resource Poor adaptation Project number First to Market

D

1

2

3

4

5

6

7

8

9

10

39

154

100

0

0

103

0

60

225

154

23

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Costumer intimate

E

40%

19%

19%

53%

39%

19%

40%

40%

39%

39%

D

0

143

52

0

0

55

0

19

185

122

E

57%

32%

32%

71%

57%

32%

54%

57%

57%

57%

D

0

126

54

0

0

54

0

5

174

125

E

39%

19%

19%

53%

39%

19%

40%

39%

39%

39%

1

2

3

4

5

6

D

0

56

0

0

0

0

E

39%

25%

25%

45%

39%

25%

D

0

161

42

E

66%

48%

48%

D

0

143

51

E

39%

25%

25%

1

2

3

76

Medium adaptation Project number

Costumer intimate

8

9

10

0

23

58

55

34%

40%

39%

39%

0

0

41

0

11

176

108

71%

67%

47%

53%

67%

67%

67%

0

0

49

0

2

174

123

45%

39%

25%

34%

39%

39%

39%

4

5

6

7

8

9

10

35

0

0

21

0

3

46

48

M

Leader

D

0

E

39%

31%

32%

38%

39%

31%

28%

39%

39%

39%

D

0

193

52

0

7

42

0

2

184

105

CE

Project number

ED

Strong adaptation

Costumer intimate

AC

PT

First to Market

Leader

7

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First to Market

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Leader

E

77%

67%

67%

71%

78%

67%

53%

77%

78%

78%

D

0

148

34

0

0

30

0

3

154

104

E

39%

32%

32%

38%

39%

31%

28%

39%

39%

39%

b) Limited resource with an adequate level In the case of the limited resource with adequate level, simulation results are specified in Fig. 12. In this graph, the planning and completion of projects are displayed. Also, the more complete results are shown in three weak, moderate and strong adoption levels in Table 9. 24

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Fig. 12. S-curve and portfolio plan in case of adequate resource constraint

Poor adaptation

1

2

3

4

5

6

7

8

9

10

D

250

294

320

0

13

12

0

100

581

262

E

40%

19%

19%

56%

40%

19%

44%

40%

39%

39%

D

317

383

389

0

60

58

0

141

602

326

E

57%

32%

32%

74%

57%

32%

58%

57%

57%

57%

D

259

304

323

0

23

12

0

104

604

276

E

40%

19%

19%

56%

40%

19%

44%

40%

39%

39%

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Project number

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Table 9. Simulation result in case of adequate resource constraint

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First to Market

Costumer intimate

Leader

25

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Medium adaptation Project number

1

2

3

4

5

6

7

8

9

10

D

243

302

331

0

7

18

0

99

575

255

E

40%

25%

25%

47%

40%

25%

38%

40%

39%

39%

D

341

439

445

0

73

99

0

158

765

348

E

67%

48%

48%

74%

67%

48%

58%

67%

67%

67%

D

250

311

333

0

17

18

0

100

600

270

E

40%

25%

25%

47%

40%

25%

38%

40%

39%

39%

1

2

3

D

241

315

463

E

40%

32%

32%

D

363

498

499

E

78%

67%

67%

D

245

323

E

40%

32%

Costumer intimate

Leader

4

5

6

7

8

9

10

0

17

146

0

76

383

254

38%

40%

32%

28%

40%

39%

39%

0

88

135

0

162

807

369

M

Project number

74%

78%

67%

58%

78%

78%

78%

343

0

12

22

0

93

612

265

32%

40%

40%

32%

32%

40%

39%

39%

PT

Leader

ED

First to Market

Costumer intimate

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Strong adaptation

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First to Market

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According to the simulation results, as expected, the amount of delays has been increased by decreasing the available resources. It is also seen in the project progress graph that for project number 9, faces two interruptions. the resulting interruptions have dramatically delayed the project. It is expected that there will be more delays and more delays in the projects by reducing resource levels. In the next section, this issue is addressed by simulation results.

a) Limited resource with an insufficient level

In the case of the limited resource with insufficient level, simulation results are specified in Fig. 13. In this graph, the planning and completion of projects are displayed. Also, the more complete results are shown in three weak, moderate and strong adoption levels in Table 10.

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Fig. 13. S-curve of the project portfolio in case of limited and inappropriate level of resources

Table 10. Simulation results in case of limited and inappropriate level of resources

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Poor adaptation

1

2

3

4

5

6

7

8

9

10

D

623

395

480

0

5

172

25

165

637

372

E

40%

19%

19%

56%

40%

19%

44%

40%

39%

39%

Costumer intimate

D

700

467

542

0

43

218

23

211

745

435

E

57%

32%

32%

74%

57%

32%

58%

57%

57%

57%

Leader

D

500

505

618

0

6

173

23

165

526

373

AC

Project number

First to Market

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E

40%

19%

19%

56%

40%

19%

44%

40%

39%

39%

1

2

3

4

5

6

7

8

9

10

D

616

403

480

0

6

180

23

166

518

372

E

40%

25%

25%

47%

40%

25%

38%

40%

39%

39%

D

734

520

600

0

62

259

E

67%

48%

48%

74%

67%

D

495

512

673

0

E

40%

25%

25%

47%

1

2

3

D

486

412

507

E

40%

32%

32%

D

770

582

668

E

78%

67%

D

623

E

40%

Medium adaptation Project number

Costumer intimate

23

236

730

469

48%

58%

67%

67%

67%

5

178

22

162

419

372

40%

25%

38%

40%

39%

39%

Project number

4

5

6

7

8

9

10

0

7

191

21

167

670

372

40%

40%

32%

32%

40%

39%

39%

0

85

308

21

263

777

507

67%

74%

78%

67%

58%

78%

78%

78%

426

492

0

5

188

21

163

533

371

32%

32%

40%

40%

32%

32%

40%

39%

39%

ED

CE

PT

Leader

M

First to Market

Costumer intimate

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Leader

Strong adaptation

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First to Market

8. Conclusion

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Today, project-based companies have a growing need to create integrated and integrated portfolio management systems based on the overall strategy of the organization. Project portfolio selection is a vital and dynamic decision, and simultaneous scheduling of current and new projects has created special challenges for these organizations. One of the biggest challenges is to ensure that the organization's projects are consistent with the company's corporate governance strategy. This is also true of resources that can guide the company in the desired direction because the human resources devoted to each project are scarce. In this context, the optimal selection and allocation of limited resources to a number of projects is considered a strategic decision. In this study, different scenarios have been considered to fully examine the dimensions 28

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of the strategy selection for a specific portfolio of projects through an integrated system dynamics model. According to the research outcomes, the components of a project portfolio should be quantitatively measurable, ranked and prioritized. In this study, customer intimacy, product timeto-market, and product superiority were considered as key elements in aligning the organization's strategy with the portfolio of projects. A grading system was proposed to compare different types of organization's strategy in terms of technology, innovation, complexity, and pace. In addition, the effects of shared human resource on the overall performance of the project portfolio were analyzed. According to the obtained result, shortening of the review period has a significant effect on the reduction of project delays. The reduction of total delay in the project portfolio was used as a basis for predicting model behavior for validation of the model. The simulation outcomes provide policymakers with a useful means to adopt an effective business strategy. Time to market is an important factor to consider when measuring project success, which can be interpreted in different ways when considering short-, medium-, and longterm tasks, goals or achievements. Projects often exceed their expected timeline according to rework, design change, and productivity. However, these are not the only factors contributing to this problem. On one hand, policymakers need an accurate project management plan to adopt a proper business strategy; on the other hand, their decisions may lead to delay and cause the project to deviate from its path during the project selection process. This study reveals that this aspect of project behavior is predictable and the proposed model can give real insights into strategy development. The integrated methodology of this research can assist in choosing the right projects and strategies needed to achieve a project’s strategic goals. In real circumstances, all available projects are subject to the project selection process. The simulation showed that one or more of these projects are likely to fail after several evaluations designed to determine acceptance and rejection. Project selection decisions are made often on the grounds of short-lived information and decision makers are, therefore, unable to think about the big picture that encompasses the project environment. Having a wider, dynamic perspective of a project in all its life cycle stages can help decision makers better analyze the potential for project success. Thus, if they find one project to be unsuccessful in the simulation, they can eliminate it from entering the available project list. Apart from the standard project management tools and metrics, taking a strategic approach is a way to demonstrate a perspective for team members based on initiation of clear communication and effective collaboration which, helps project managers focus on competitive advantages and customer needs more so than daily planning. The project strategy is, therefore, a guideline that contains both the project perspective and the position it plans to achieve (Patanakul and Shenhar, 2012a). Nonetheless, as evidence confirms, even the most strategically fitted projects can fail (Srivannaboon, 2006). The model developed in this study provides a practical solution which can evaluate strategic fitness as one effective criterion for decision making in a dynamic process based on project interactions. Apart from system dynamics or discrete-event simulation approaches, agent-based simulation modeling techniques are known as effective tools for managing business complexity and discovering new strategic solutions for project portfolio management. An important research effort has been made in this regard, see for example Pajares et al. (2014) and Araúzo et al. (2010b). therefore, future research can be directed toward developing an agent-based simulation for multi-project environments by considering the role of each stakeholder of the projects as well as the overall organization's strategy. 29

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More research is needed to understand the relationship between the degree of alignment of strategies and other factors affecting project progress, such as duplication or productivity. Although some of these relationships were introduced in this study, new hypotheses were presented and confirmed, with more precision and decisiveness, such factors as leadership style, organizational structure, processes, and the extent to which the organization benefited from tools and techniques, especially in the field of information systems. Studying the alignment of the project's strategy and the factors of productivity and re-working, are the candidate subjects for future research. Undoubtedly, the determination of such calculations requires extensive theoretical and empirical studies. On the other hand, the proper understanding of these relationships can be a reciprocal tool to measure the degree of compliance with the strategy at the project level and the organization's strategy. Future research can also examine how new trends like digitalization has an impact on the way that the corporate strategy is defined and how its executed. Following the adoption of a digital strategy, in the end, organizations are seeking to bring about digital transformation in their organization for better corporate alignment. The purpose of digital transformation is to focus on technology, business model, processes in order to create a new value for customers, employees and other dimensions of the organization through the digital pervasiveness of the organization in order to compete in an ever-changing economy. In other words, the digitalization effect of the whole organization is a digital evolution, which not only improves the processes of the organization in a variety of ways but also creates new and innovative ideas for achieving the goals. Organizations, using digital strategies, can facilitate the innovation process, provide their core services digitally, respond quickly to changing dynamic, flexible and dynamic environments, and face this environment with minimal risk, Improve the control of the company and help them better manage the experience and knowledge of our customers. By adopting a digital strategy, the organization expects to improve performance in its various areas e.g. project portfolio management. New communications for evaluating the level of maturity of the project management organization and the implicit knowledge sharing between the project management and project strategy elements of the organization and project strategy were also introduced in this project. In general, the level of maturity of organizational project management and knowledge sharing for different organizations and even the successful implementation of diverse projects is not the same. Therefore, for a project, the level of maturity of organizational project management and the implicit knowledge sharing may lead to higher productivity and lower operating error than another project in the same organization. In this study, the level of maturity of the project management organization and the level of knowledge sharing implies for the whole organization and in fact, in the overall progress of the projects, it is assumed that these parameters can have a different level of productivity and error rates in each project. Therefore, further research is recommended to clarify the scope of this topic.

Funding

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Conflict of interest 30

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The authors declare that they have no conflict of interest.

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