IntroductionPublic infrastructure (e.g., power, transportation, wastewater, and telecommunication) systems play important roles in urban communities (Di Maddaloni and Davis 2018; ElZomor et al. 2018; Demirel et al. 2021). However, infrastructure megaprojects typically exhibit numerous challenges in terms of their spatiotemporal, technological, political, and economical complexities (Flyvbjerg 2014). Such complexities make infrastructure projects more vulnerable to different risks, which subsequently necessitate experienced and competent management (Daniel and Daniel 2019). The latter is particularly important because the inability to manage such risks typically results in poor performance (e.g., cost overruns, schedule deviations, or safety issues) and subsequent challenges to meet stakeholders’ expectations (Di Maddaloni and Davis 2018; Bjorvatn and Wald 2018; Zhang et al. 2022). In addition, managing infrastructure megaprojects is a dynamic and intricate process that requires extensive attention to details and a broad multidisciplinary experience.Infrastructure Project Complexity and Systemic Risk AnalysisThe theory of complexity has been employed in various fields such as mathematics, economics, and astronomy, where complexity is related to the interactions of a large number of elements (Rad et al. 2017). A project’s complexity refers to the nonlinear interactions among its components (Chapman 2016; Ahn et al. 2017); as such, complexity is a fundamental characteristic of infrastructure projects considering their spatiotemporal, structural, and uncertain evolving nature (Mihm et al. 2003; van Marrewijk et al. 2008; Bakhshi et al. 2016; Jarkas 2017). Within infrastructure projects, complexity has been classified into six categories: (1) goal complexity (e.g., uncertainty and diversity of goals); (2) task complexity (e.g., dependence, dynamics, and diversity of tasks); (3) organizational complexity (e.g., cross-organizational interdependence); (4) technological complexity (e.g., the dependence of technological process); (5) information complexity (e.g., information uncertainty); and (6) environmental complexity (e.g., environmental of changing policy or changes in project construction environment) (Luo et al. 2016). Within each of these categories, interdependence exists as a key dimension (De Toni and Pessot 2021).A better understanding of a project’s complexity can reduce its vulnerability to complexity-induced risks (Zhang 2007; Gao et al. 2018) especially because the latter are more relevant to megaprojects (Locatelli et al. 2017). Systemic risks, which pertain to the probability of cascading failures that may lead to a complete system-level collapse, are consequences of such complexity (Liu et al. 2019b; Eisenberg et al. 2020; Goforth et al. 2022). These risks are typically triggered by the complex dynamic interdependence between different project stakeholders.Contractors (i.e., utilized hereafter to denote both the main contractors and their subcontractors) are among the most critical stakeholders in infrastructure projects (Tan et al. 2017; Liu et al. 2019a; Korb and Sacks 2021); subsequently, managing their interdependence-associated risks is key for project performance (Erol et al. 2020). In a large infrastructure project, contractors’ interdependence is best exemplified by the complexity of the technical tasks performed by different contractors from different disciplines (Luo et al. 2016; An et al. 2018), being spatiotemporally interdependent, all working collaboratively in parallel or in series on the same project site, within the same timeframe (Chester and Hendrickson 2005; Jarkas 2017). A disruption of one contractor’s work can thus create a systemic risk scenario (Ezzeldin and El-Dakhakhni 2019; Yassien et al. 2020) that may cascade to affect the entire project (system) performance (Yang et al. 2021; Chen et al. 2022).Systemic Risk Management and Project Key Performance IndicatorsInterdependence-induced risks should be considered through a systemic risk–informed management strategy where triggering events and their cascading effects are identified and controlled (Alzoor et al. 2021). In this respect, risk management can be employed to address and mitigate possible disruptions that may negatively affect project performance. The process of risk management entails first identification of the risks and subsequently utilizing various qualitative and quantitative tools and techniques (Schatteman et al. 2008; Zou et al. 2010; Wang et al. 2016; Zhang and Guan 2018) for risk analysis. The process is concluded through devising response strategies to mitigate the identified risks followed by monitoring the effects of deploying such strategies (Tang et al. 2007; Schatteman et al. 2008).Interdependence quantification is key to managing the associated project systemic risks. In this respect, the interdependence between project contractors was shown to be best analyzed using network analysis techniques (Chinowsky et al. 2011; Garcia et al. 2021; Liu et al. 2022). Network analysis techniques are based on complex network theory (CNT), where a network is made up of nodes and links (Barabási and Pósfai 2016), where the nodes represent the elements among which interdependence is to be quantified and the links represent the extent/nature of such interdependence (Keung and Shen 2013). Within CNT, dynamic networks are utilized to understand the relationships and structure underlying different interactions between elements within the network at different times (Newman et al. 2006).Interdependence between stakeholders (e.g., contractors and/or subcontractors) within a project has been quantified in different ways in the literature. For example, it has been quantified based on the stakeholders’ involvement in the activities network (Zhu and Mostafavi 2017) or based on their resource sharing or contractual relationships (Mok and Shen 2016; On Cheung et al. 2018). Other studies have quantified interdependence based on the knowledge transfer among project stakeholders (Chinowsky et al. 2011; Garcia et al. 2021; Goforth et al. 2022). In the study performed by Qiang et al. (2021), interdependence was quantified using a dynamic network approach, considering the number of collaborations between different stakeholders. Stakeholder conflicts were also employed by Xue et al. (2020) to quantify interdependence by employing a two-mode dynamic network.Evaluating the impacts of the contractors’ interdependence-induced systemic risks on the project performance requires considering the project performance measures. Project key performance indicators (KPIs) have been utilized to gauge different project performance aspects (He et al. 2021). Such indicators may include schedule deviation (SD), cost deviation (CD), or quality index (QI) (Castillo et al. 2018). Systemic risks impacts on project performance have been evaluated based on the specific characteristics of the interdependence network respecting the project teams (Yang et al. 2017). Questionnaires and regression analyses have been utilized to judge the impacts of interdependence-induced risks on program performance (Parolia et al. 2011). Risk mitigation necessitates the development of effective response strategies (Zhang and Guan 2018) by altering specific interdependence characteristics through network reorganization employing optimization techniques with the objective of improving project KPIs (Liu et al. 2017).More recently, Gondia et al. (2022) quantified contractors’ interdependence based on their number of mutual workdays at different project periods by means of a dynamic network. Gondia et al. (2022) reasoned that contactors’ interdependence is a consequence of project tasks’ complexity where contractors from different disciplines work in parallel (i.e., timewise) within the same vicinity (i.e., spacewise) to deliver the project scope. Their study proposed utilizing historical data correlation analyses between project KPIs and interdependence network characteristics to evaluate contractors’ interdependence-induced risks on project performance. Such analyses can be utilized to determine project KPIs based on certain node measures (e.g., weighted degree centrality) (Barabási and Pósfai 2016) within the contractors’ network. Based on the established relationships between project KPIs and the CNT measures, they suggested that the KPIs can be improved by optimizing (reorganizing) the project schedule from which the network was generated. Fig. 1 illustrates the framework proposed by Gondia et al. (2022), which introduced a radical approach to managing systemic risks resulting from contractors’ interdependence.Current Limitations in Project Risk Management PracticesDespite their utility and effectiveness, current software packages are not designed to analyze and quantify contractors’ interdependence. They are typically based on the principles of the critical path method for analyzing the interdependence among project activities (Wickwire and Smith 1974; Lagos and Alarcón 2021) as well as Monte Carlo analysis to perform statistical sampling of the risks affecting the project (Kwak and Ingall 2007; Chen et al. 2021). Such tools consider the interdependence at the project activity level (e.g., using the Gantt chart) by connecting predecessor and successor activities as shown in Fig. 2(a); they can also consider grouping the activities by the contractor which facilitates showing the scope of work within the project as in Fig. 2(b).However, analyzing the contractors’ interdependence using Gantt charts, within industry-standard software packages, includes many details (e.g., the various relations among numerous activities performed by different contractors) that may be cumbersome to comprehend and utilize, especially when used in subsequent analysis (Tomczak and Jaskowski 2020). Building information modeling (BIM) techniques (Liu et al. 2015; Jang et al. 2019) provide powerful visualizations to view the interactions among different contractors working onsite (Rolfsen and Merschbrock 2016; Sigalov and König 2017; Isaac and Shimanovich 2021). However, BIM techniques do not visualize the structure of the hidden and implicit interactions between contractors within the project efficiently, especially when compared with the visuals resulting from CNT analyses.Despite introducing different interdependence quantification criteria (Mok and Shen 2016; Zhu and Mostafavi 2017; On Cheung et al. 2018), quantification of contractors’ interdependence through their associated tasks’ technical complexity is inconsistent across the literature. Attributed to the limitations of available software and the lack of the appropriate interdependence quantification and analysis tools, managing systemic risks resulting from the latter is often not considered (Erol et al. 2020). In addition, although the work of Gondia et al. (2022) presented a promising approach to manage interdependence-induced risks, it faced several limitations that are worth discussing. For example, within their proposed dynamic network approach, when the interdependence characteristics between contractors within a given network (e.g., month) of the project’s life cycle was changed, the interdependence within other networks (e.g., months) was affected as well. Such an issue may cause cascade disruptions within other months if only the interdependence risks within a single month are managed without considering the entire set of project dynamic networks. In other words, improvement of the project performance at one time period (e.g., month) may lead to the degradation of the whole project’s performance throughout its timeline—an issue that has not been addressed by Gondia et al. (2022). In addition, Gondia et al. (2022) did not present the formulation and explanation pertaining to optimizing the project’s networks. Moreover, their framework was only presented conceptually, without demonstrating its full utility (e.g., on a complex project schedule).Scope and ObjectivesThe knowledge gap addressed by the current study pertains to the lack of proactive systemic risk management strategies to mitigate possibly negative consequences of contractors’ interdependence on infrastructure projects’ performance. The study herein aims to fill this knowledge gap through (1) the early identification of the risks and their potential sources; (2) the proactive quantification and evaluation of the impacts of these risks on the project’s performance; and (3) the mitigation of such risks through effective schedule reorganization and management strategies. In fulfillment of this aim, the remainder of the paper is structured into four sections. The “Methodology” section presents the approach developed for interdependence-induced systemic risk management, followed by a demonstration of the utility of the developed methodology considering a complex infrastructure project schedule in the “Application Demonstration” section. The analysis results are subsequently discussed in the “Discussion” section, where relevant managerial insights are summarized and the limitations of the study are highlighted; finally, the conclusions are presented in the “Conclusion” section.MethodologyThe current methodology encompasses three steps to quantify, analyze, and mitigate interdependence-induced systemic risks. The first step is concerned with the quantification of interdependence by employing two types of networks: a dynamic (e.g., monthly) network and a static (i.e., full project) network. Interdependence is quantified in this paper as the number of mutual workdays between contractors to reflect the complexity of their related technical tasks. Nonetheless, different type of interdependence and/or further complexity (e.g., importance of the tasks performed) can be considered using the same approach presented herein through weighted multiplexes (i.e., networks-of-networks) (Divya et al. 2022). The dynamic network is utilized to analyze the interdependence at the different critical stages (e.g., weeks or months) of the project life cycle. On the other hand, the full project network is used to optimize the remaining period of the whole project to mitigate temporal interdependence-induced risks. To demonstrate the differences between the two network types, Fig. 3 shows an example of a dynamic and full project networks for a project with a 4-month duration.The nodes represent the contractors, and the weights of the links represent the extent of their interdependence—the number of the mutual workdays. The percentage of SD is given as per the equation in the figure, which is a function of the weighted degree centrality (WDC), which is the summation of the link weights of a given node within the contractors’ network. Linking network measures (e.g., WDC) to project KPIs is discussed in Step 2 of the methodology.In Month 2, SD is the highest (i.e., 58.6%). If activities, performed by Contractors 1 and 2 start in Month 2 and continue in Month 3, then optimizing Month 2 by changing activities’ locations along the project’s timeline will affect the interdependence in Month 3. As such, the different networks constituting the dynamic network (e.g., months) are interdependent. Prior to the project start, changing one network may affect the interdependence in previous and subsequent networks (i.e., the full project network constitutes the entire project duration). On the other hand, after the project has started, changing one network may only affect subsequent networks (i.e., the full project network considered for the analysis constitutes only the remaining duration of the project).The second step is concerned with the evaluation of the impacts of interdependence-induced systemic risks on project performance and how such impacts can be measured. Therefore, the procedure of linking the historical project KPIs data to different network measures is explained in this step. Finally, the third step discusses the optimization techniques—the computational core of the systemic risk management strategies. A detailed explanation of these steps and how they should be implemented is discussed next.Step 1: Contractors’ Interdependence NetworksDynamic (temporal) networks present contractors’ (i.e., network nodes) interdependence at intermittent (time) periods within the project’s duration. Because such interdependence is based on the number of mutual workdays between the contractors, the network links are undirected because the contractors’ interdependence is typically mutual; the links are also weighted according to the number of mutual workdays to reflect the relative extent of such interdependence. In this respect, the mutual workdays are obtained from the project schedule (Vanhoucke 2013) and subsequently used to create the undirected network’s adjacency matrix—the elements of which indicate whether a pair of nodes is connected or not (Barabási and Pósfai 2016).The network formulation procedure is repeated for all project site locations (two site locations are different when the contractors of one site share no interdependence with contractors in the other site) and time periods (e.g., weeks, months, or quarters) to capture the contractors’ spatiotemporal interdependence characteristics. Site locations and their corresponding contractors are obtained from the project’s management plan. For example, in a project that has two site locations and a schedule of 12 months, the dynamic nature of the project can be expressed through 24 networks, with each network describing interdependence within a given month at one of the project’s site locations.An additional static network (i.e., full project network) covering the whole/remaining project’s duration (depending on whether the project has started or not) is formulated. Such a network is generated for every site location so that the contractors’ interdependence during the full or the remaining project’s life cycle is quantified. Each site location can be dealt with as a separate project, and the impacts of contractors’ interdependence on the whole project are quantified by considering the interdependence impacts from each site location full project network. Because each site location can be treated as a separate project, the analyses described hereinafter assume a project with one site location because they can be replicated for a project with two or more site locations; and then, they can be aggregated to give the overall project performance.CNT implies applying different analyses to explore the topology of the network and the relationships between the nodes. Based on CNT, node-level measures can be calculated to quantify the different characteristics of the nodes within the network. A variety of node-level measures exists that help in understanding the relationships between the nodes within a network. Centralities give valuable insights pertaining to the nodes’ importance based on their connectivity within the network. WDC is an indicator of a node’s ability to affect other nodes within the network; it is the sum of the weights of the links connected to the node (Wang and Huang 2021). Within the current context, the WDC signifies the criticality of the contractor based on the amount of shared interdependence with other contractors. As such, the demonstration presented in this paper focused on WDC to emphasize the contractors’ criticality in terms of shared interdependence. WDC is given by Eq. (1) (Wang and Huang 2021) (1) where n = number of links connected to a given node; and Wi = weight of the link i.Step 2: Contractors’ Interdependence Impact on the Project PerformanceDefining the KPIs to be tied with contractors’ interdependence network measures is a crucial preliminary step toward the explanation of their linkage process. Six KPIs are employed herein, due to their frequent use by project managers, for each network (i.e., each site location and each time period). These are (1) schedule deviation (SD), which represents the ratio of the actual advance minus the scheduled advance to the scheduled advance (Castillo et al. 2018); (2) cost deviation (CD), which is the ratio of the actual cost incurred minus the budgeted cost to the budgeted cost; (3) quality index (QI), which is the ratio of the number of rework orders to work hours (Cox et al. 2003; Castillo et al. 2018); (4) accident frequency (AF), which is the ratio of the recorded accidents to work hours; (5) productivity rate (PR), which is the ratio of the actual labor cost to the budgeted labor cost; and (6) planning effectiveness (PE), which is the ratio of completed activities to scheduled activities (Castillo et al. 2018).Correlating project KPIs to CNT measures (e.g., WDC) requires utilizing historical data from past similar projects. Fig. 4 shows how such correlation can be realized. Employing records of N past projects (instances) with M contractors hired to deliver these projects, such project schedules are converted to interdependence networks (i.e., full project networks as per Step 1), yielding N different networks (one per project). The impacts of contractors’ WDC values, obtained from the networks on any of the project’s KPIs (e.g., SD), can be investigated using the data set of N rows and M+1 columns as per Fig. 4.In the figure, for each instance (i.e., network/project), the data set includes the WDC values of all contractors in the network as well as the associated project KPI of interest (e.g., SD). Other network measures, such as betweenness and closeness centralities (Barabási and Pósfai 2016) of each contractor, may be included in the data set, with possibly more than one KPI included as response variables.The number of instances and variables within the data set can guide the analyst in selecting the most appropriate statistical method to use in order to associate the network measures (e.g., contractors’ WDC values) with the target KPI (e.g., SD). These methods range from simple models such as multiple regression analysis (Hair 2014) to sophisticated machine learning models, such as random forests (Hastie et al. 2009). The association between the network measures (i.e., predictors) and KPIs (i.e., responses) yields an equation (Fig. 4) from which the value of a response variable can be predicted. Based on the obtained equations that relate project KPIs from network measures (e.g., WDC herein), the project’s performance can be predicted based on its current interdependence network measures.Step 3: Project’s Systemic Risk Predictions and ManagementManaging complex interdependence-induced project risks requires the utilization of powerful optimization techniques to improve the project’s KPIs; this can be achieved through activity reorganization within the project schedule to minimize negative interdependence-related impacts. Selecting an optimization technique requires careful consideration of the type of problem at hand (e.g., linear or nonlinear, and single-objective or multiobjective) (El-Abbasy et al. 2020) and whether it can be approached using mathematical or stochastic procedures. The problem considered herein requires optimizing more than one objective function (i.e., multiobjective optimization of all project KPIs), which are nondifferentiable. Such optimization of the project schedule involves considering numerous activity combinations, achieving exact optimal solutions, which (e.g., through integer programming techniques) would require practically unworkable computations (De et al. 1997).As a stochastic procedure, metaheuristic optimization presents a powerful technique for computing near-optimal solutions to such problems (Elbeltagi et al. 2005; Zhang et al. 2006; Bozorg-Haddad et al. 2017). Within metaheuristic techniques, genetic algorithms have been shown to be very efficient (Owais 2014) and have been utilized to solve challenging multiobjective optimization problems (Yusoff et al. 2011; Rajkumar et al. 2014; Yahui et al. 2020). The nondominated sorting genetic algorithm (NSGA-II) is an example of such techniques where it has been employed to solve multiobjective schedule optimization–related problems (Vanucci et al. 2012; Polat et al. 2015).Because the focus in this study is to optimize the project schedule such that all the KPIs are improved, NSGA-II was selected because it can rapidly sort nondominated solutions and easily calculate the crowding distance to generate a set of Pareto-optimal solutions in a single simulation run. The general concept of the NSGA-II is described in the following six steps (Deb et al. 2002): 1.Generate an initial population of M solutions, each of which is called a chromosome. Each solution is represented by an N-dimensional vector (Xi=[x1,x2,…,xN]), where N is the number of the decision variables, each of which is called a gene.2.Nondominated sorting rearranges the population based on the dominance criteria and assigns them to different fronts (i.e., sets). A solution X1 dominates X2 if X1 is no worse than X2 in terms of all the objective functions’ values and X1 is strictly better than X2 in at least a single objective function value. The solutions that do not dominate each other are assigned to the same front. The solutions in each front dominate all other solutions in the following one. The solutions comprising the first front, which is not dominated by any other front, represent the Pareto-optimal solutions.3.Solutions within the same front are sorted according to the crowding distance. The latter is calculated by sorting the population ascendingly according to the value of each objective function. For each objective function, the solutions with minimum and maximum values are assigned a distance value of infinity. The distance of each remaining solution is calculated as the absolute of the normalized difference in the values of the objective function of the previous and following solutions. This process is repeated for all objective functions where the total crowding distance of a solution is the sum of the individual distances corresponding to each objective function.4.Solutions are chosen as parents through a binary tournament selection using a crowded-comparison operator. This means that for two solutions that do not belong to the same front, the solution in the lower (i.e., better) front is chosen; if they belong to the same front, the solution with the higher crowding distance is chosen. In the current analysis, the genes of the solutions represent the start dates of the activities; therefore, uniform crossover and uniform mutation operators are utilized. The number of genes to be mutated in the solution depends on the mutation rate (μ). The number of offspring and mutated solutions depends on the crossover (γ) and mutation (δ) percentages, respectively.5.Parent, child, and mutated solutions are combined into a single population. This new population is sorted using the nondominated sorting and the crowding distance sorting and the first M solutions are chosen as the new population.6.Steps 4 to 6 are subsequently repeated until the maximum number of iterations is reached.Implementation ProcessTo implement the presented steps, the following sequence should be followed: (1) examine the structure of the original schedule to determine the activities’ durations and floats, resources’ and contractors’ inactive slacks, and underlying sets of constraints; (2) convert the scheduled activities into a network and calculate the WDC value of each node; (3) determine the relationship between the WDC values of the nodes and the KPIs; and (4) use the NSGA-II to rearrange the activities in the case of poor KPIs; the implementation is finalized by returning the solution (i.e., rearranged activities) that corresponds to the optimized KPIs.To generate the dynamic network, the project schedule is segmented based on the site location and the time periods (e.g., month); for the full project network, the whole schedule of each site location is considered. In both cases, the activities must be grouped according to the contractor. Fig. 5 gives an example of the schedule segmentation process, to generate a dynamic network, for a schedule of 20 activities, two site locations (i.e., contractors of one site do not share interdependence with contractors in the other site), two time periods (i.e., months), and four contractors; the schedule is first sorted according to the site location (i.e., either A or B) as in Fig. 5(a), and subsequently divided into two separate schedules, with one schedule for each site as in Fig. 5(b). Each of the two schedules is segmented according to the time period (i.e., the first or second month) resulting in four different schedules as in Fig. 5(c). Finally, the activities in each time period are grouped according to the contractor as in Fig. 5(d).The segmented schedule is then used to generate the dynamic network, and the full schedule, assuming one site location, is used to generate the full project’ network. In the network, the activities’ durations and start/finish dates are used to determine the number of mutual workdays (links) between contractors (nodes) used to establish the network adjacency matrix. The elements of the adjacency matrix represent the weights of the links between the nodes within the network. WDC [Eq. (2)] of each contractor in the network is calculated by summing its corresponding row or column in the adjacency matrix. For each contractor i, WDC is given by Eq. (2), where j refers to other contractors that share interdependence with contractor i and N is the total number of contractors. The value of aij in Eq. (2) corresponds to the element in the ith row and jth column of the adjacency matrix; it represents the number of mutual workdays between contractors i and j(2) Fig. 6 illustrates how to convert the scheduled activities into a network within which Fig. 6(a) shows the original schedule, which is then segmented, as in Fig. 5, according to the site location and time period, as shown in Fig. 6(b). The adjacency matrix is established for each site location and time period; Fig. 6(c) shows the adjacency matrix for Site location 2 and Time period 2 where the elements of the adjacency matrix are the number of mutual workdays between the contractors working at the same site location and the same time period. Fig. 6(d) shows the network corresponding to the adjacency matrix in Fig. 6(c). Figs. 6(e–h) illustrate the utilization of the same concept to generate the full project network for a project with one site location where the full project schedule is considered.Finally, NSGA-II is used to achieve the optimum KPIs by considering the start dates of the activities as the decision variables (i.e., coordinates of the point solution,) where a point solution is a vector of N decision variables for N activities. They determine the locations of the activities along the timeline of the project and consequently the mutual workdays between the contractors and their WDC values. The boundaries of the decision variables are determined herein by the free floats of activities, although other constraints can be used, such as the total float, because an activity cannot be delayed (i.e., rearranged) if it has no free float. Evaluation of the objective functions of a point solution involves converting the schedule into a network, as discussed previously, and calculating the network measures (e.g., WDC). The established relationships from Step 2 are subsequently used to obtain the KPIs’ values, which represent the values of the objective functions. The value of the objective functions corresponding to the optimized solution should be continuously reviewed to determine the effectiveness of the solution in reducing anticipated systemic risks’ effects.Methodology ApplicationHaving described all relevant aspects of the project (i.e., project WBS, schedule, contractors, and duration), the methodology is applied in a step-by-step fashion.Step 1: Contractors’ Interdependence NetworksBecause the span of the project is 26 months, it was assumed that interdependence was quantified on a monthly basis. Therefore, one would have 26 networks, which constitute all dynamic networks that represent the interdependence at different periods within the project’s life cycle. Assuming the project has not yet started, the full project network covers the full project’s duration; this network aggregates the interdependence through the 26 months in one static network. The 26 networks discussed previously are shown in Fig. S2; the full project network and its adjacency matrix are shown in Fig. 7(a) where, unlike standard adjacency matrices with zero diagonals, the values in the matrix diagonal herein show the number of days spent by each contractor working on the project.The WDC, discussed previously, is the most relevant network measure to the discussion herein because it represents the criticality of a specific contractor in terms of how much other contractors depend on him. Fig. 8 shows how the WDC values change for every contractor during the 26 months (i.e., networks); each month in the figure represents a network for which WDC is calculated.Step 2: Contractors’ Interdependence Impact on the Project PerformanceWithin the current demonstration, the WDC was linked to the six KPIs of the project. It is important to recall that establishing the relationships between the network measures and project KPIs depends on historical KPI data . In the absence of actual historical KPI data and to demonstrate the methodology utility, the relationships between the WDC values of the contractors and the KPIs were reasonably assumed using Eq. (3) for each KPI. The constants and coefficients are given in Fig. 9(a) for each KPI and each contractor. The KPIs in Eq. (3) represent the percentages of schedule and cost deviations; accident frequency; and the percentages of loss in productivity, quality, and planning effectiveness (3) where KPI = any considered KPI (e.g., cost deviation); K = constant of the equation corresponding to the considered KPI; WDCX = WDC for contractor x; and Cx = coefficient of WDC of contractor x.Step 3: Project’s Systemic Risk Predictions and ManagementThe KPIs equations discussed in the previous step are essentially the objective functions to be minimized to yield a satisfactory project performance. The full project schedule is to be optimized; therefore, all the scheduled activities were considered. Activities with zero free float were considered in interdependence calculations, but they never changed their position along the project’s timeline; therefore, the activities with a nonzero free float together with their required parameters (i.e., contractor, activity code/name, duration, start date, finish date, and free float) were used as the decision variables, and they are given in Table S1.The schedule was converted into a network, with Saturdays and Sundays considered days off (i.e., excluded from interdependence calculations). Through using Eq. (3), the initial KPIs using the WDC values of the contractors within the full project network were as shown in Fig. 9(b). The initial adjacency matrix and network (i.e., before optimization) are provided in Fig. 7(a).The NSGA-II was then applied to optimize the schedule. The following parameter values were utilized; the number of iterations = 200; the size of the population = 150; the crossover (γ) and mutation (δ) percentages = 70% and 40%, respectively; and the mutation rate (μ)=15%. By applying the NSGA-II process described in Step 3 of the methodology, the optimized arrangement of activities was obtained where the values of the KPIs equations were minimized within the given constraints. The values of the KPIs corresponding to the Pareto-optimal solutions are shown in Figs. 9(b) and 10. The adjacency matrix and network corresponding to Pareto-optimal Solution 4 are shown in Fig. 7(b). Table S2 presents the new start dates of the activities with a nonzero free float corresponding to each Pareto-optimal solution.DiscussionResults OverviewDynamic networks provide valuable information about the criticality and interdependence of contractors during a given period of the project’s duration. The full project network captures the criticality of all the contractors involved during the whole project’s duration. The shapes of the dynamic network (Fig. S2) and the full project network [Fig. 7(a)] provide valuable information because the size of the nodes reflects the relative weighted degree centralities between nodes (i.e., contractors): the larger the size of the node, the larger its WDC. The size of the node reflects the amount of interdependence this contractor shares with other contractors and consequently its criticality in the network; the larger the node, the more critical the contractor is. Node colors reflect the contractors’ discipline where contractors of the same discipline would have the same color. In addition, the line weight of the link between two nodes represents the relative weight of the link when compared with other links within the network.For example, the fifth month of the dynamic network [Fig. 11(a)] involves 10 contractors of different specialties as given by the colors of the nodes. The most critical contractors are FWC and MEC (i.e., their WDC value is 98) and the least critical contractors are COC and SIC (i.e., their WDC values are 20 and 21, respectively) as indicated by the nodes’ sizes. Contractor MEC shares the highest interdependence with FWC (i.e., 21 days) and shares the least interdependence with CAC, COC, and SIC (i.e., 4 days), as indicated by the line weights of the links.Based on the assumed relationships in Step 2 between the full project network and project KPIs, a deteriorated project performance is observed. The percentages of SD and CD were 82.3% and 84.4%, respectively; the AF was 56.8; the losses in PR, QI, and PE were 51.5%, 77.4%, and 59.7%, respectively. The analysis in Step 3 considered minimizing the indicators given by Eq. (3) to achieve enhanced project performance. Fig. 9(b) shows the values of the initial KPIs, whereas Fig. 10 shows those KPIs on a radar chart. The initial activities involved in the optimization process and their possible optimized arrangements are given in Table S2.Each of the obtained Pareto-optimal solutions has trade-offs between one or more KPIs as indicated by their values in Fig. 9(b). The solutions improved the project’s performance (Fig. 10) in terms of all KPIs; however, Solution 1 has the lowest SD value; Solution 2 has the lowest CD value; Solution 3 has the lowest AF value; Solution 4 has the lowest value of the anticipated loss in PR; Solution 5 has the lowest value of the predicted loss in QI; and Solution 6 has the lowest value of the expected loss in PE. From Fig. 10, Solution 4 represents a trade-off between all KPIs; therefore, the network of Solution 4 is provided in Fig. 7(b) together with its adjacency matrix.The activities were rearranged within their free float limits, which means that they do not affect other activities related to them or the full duration of the project, which was deemed satisfactory. Adopting an optimized arrangement of activities changes the structure of the networks comprising the dynamic network; therefore, a new dynamic network needs to be generated based on the optimized arrangement of activities. Subsequently, the network of the fifth month corresponding to the optimized Solution 4 was produced and is shown in Fig. 11(b).Through comparing the networks of Fig. 11, it can be inferred that the most critical contractors, FWC and MEC, remained the same, although their WDC values decreased from 98 to 83. In addition, the least important contractor, COC, also remained the same, with its WDC decreasing from 20 to 17. The diagonals of the adjacency matrices in Fig. 11 show the number of workdays spent by each contractor during the fifth month. It can be observed that SIC was removed from the network (i.e., shifted its tasks to another month), and the number of days spent by CHC and CRC during this month has decreased. In general, the number of mutual workdays between the contractors during this month was reduced for the optimized solution as well as their interdependence. This indicates that the potential for systemic risks during this month has decreased.Managerial InsightsThe preceding section focused on discussing the results of the analyses performed on the project from an analytical perspective. This section presents a different view—from the project manager’s perspective. By inspecting the project’s dynamic network (i.e., months) (Fig. S2), a project manager can expect which months have a high potential for systemic risks. The larger the number of nodes and the weights of the links between them, the larger the potential of interdependence-induced systemic risks during this month; therefore, the project manager should expect the occurrence of disruptions within this month.Generally, from Fig. 8, higher WDC values were detected for contractors over the first 16 months of the project, indicating increased interdependence, and lower values were detected over the rest of the months, indicating decreased interdependence. Hence, Fig. 8 implies that the potential of interdependence-induced systemic risks is very small at the start of the project (i.e., because few contractors are involved), whereas it increases as more contractors become involved, and finally, it starts decreasing (i.e., as fewer contractors become involved) as the project approaches its end date.In addition to the determination of the months with high interdependence, it is important to determine key influential contractors based on their criticality (i.e., how much interdependence is shared with other contractors) within each month. By determining the most critical contractors, the project manager can place more emphasis on their work to ensure no disruptions. Fig. 8 shows the variation of WDC (i.e., for all 14 involved contractors) throughout the project, illustrating how the criticality of the contractor changes during the project. For example, during the fourth month, FWC has a higher WDC (the highest) than MEC, making them the most critical during this month; in the fifth month, FWC and MEC have the same WDC (the highest), and as such, so they both require the same level of attention/considerations; in the sixth month, MEC has a higher WDC (the highest) than FWC, making the former more critical during this month.The full project network and corresponding KPI relationships were used to assess the project performance. Upon result analyses, project performance exhibited deterioration in terms of its six KPIs as shown in Fig. 9(b). To improve the project’s performance, optimized rearrangements of activities were found such that they would result in improved KPIs within the given constraints. The effects of the optimized arrangements on the KPIs are given in Figs. 9(b) and 10. The adopted optimized solution (Table S2) provides the project manager with an alternative optimized schedule to effectively manage systemic risks, and subsequently enhance the overall project’s hyper resilience (to interdependence-induced risks). Based on the new dynamic network corresponding to the identified optimized solution, project managers need to re-evaluate which months have a higher potential for systemic risks and the corresponding critical contractors involved.Opportunities for Future ResearchThe current study provides valuable insights to project managers and practitioners to manage systemic risks attributed to contractors’ interdependence. Notwithstanding the necessary distinction between the generalizability of the presented methodology and the specificity of the demonstration application, it is important to highlight opportunities for future research. First, the demonstration application considered herein focused on only the number of mutual workdays as a measure of contractors’ interdependence. However, the methodology itself is not limited to the same as a measure of interdependence. This is because weighted networks (Divya et al. 2022) can be employed to reflect further complexity including, for example, the importance/criticality of the work performed, beyond merely the mutual workdays. In addition, more factors can be considered by utilizing multiplexes (networks-of-networks) (D’Agostino and Scala 2014) where more than one type of link can be present between any two nodes to reflect different types/sources/qualities of interdependence.Second, the demonstration within the current study formulated the dynamic network by dividing the project into equal window sizes (Salama et.al. 2020) (i.e., months); however, different window sizes (e.g., weeks and months) can be utilized to accurately quantify interdependence within projects as required. Third, the demonstration application considered a medium infrastructure project merely as an example of projects that suffer from poor performance due to systemic risks. The methodology, on the other hand, is developed specifically to handle large complex megaprojects of any type through utilizing CNT and metaheuristic optimization techniques to represent and manage complex interdependence. In this respect, the application of CNT approaches exhibits no restrictions on the network size, whereas large networks (e.g., of millions of nodes) have been analyzed in different applications (Barabási and Pósfai 2016). In addition, metaheuristics are geared to handle complex optimization problems (e.g., NP-hard problems) that cannot be solved using ordinary mathematical optimization techniques (De et al. 1997; Bozorg-Haddad et al. 2017).However, large networks can be difficult to interpret and/or visualize as the corresponding project grows larger. There are two ways to overcome such a problem: (1) when dealing with dynamic networks, the analyst can choose a suitable time window size (Salama et al. 2020) to quantify the interdependence so that the networks are interpretable; and (2) insights gained from the network (e.g., larger nodes indicate higher weighted degree centrality—reflecting relative criticality) can be easily obtained from tabulated values of the network measures, resulting in direct interpretable insights.Fourth, the considered project demonstrated the procedure of linking the network measures (e.g., WDC) to specific project KPIs. Future studies may consider deploying the developed procedure on actual historical project records to gain insights pertaining to the correlation between network measures and project KPIs. Finally, although there are no theoretical limits on the size of the project to be handled using the developed methodology, computational power can become an obstacle in analyzing very large projects. 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