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Projects are characterised by activity networks with a critical path, a sequence of activities from start to end, that must be finished on time to complete the project on time. Watching over the critical path is the project manager’s strategy to ensure timely project completion. This intense focus on a single path contrasts the broader complex structure of the activity network, and is due to our poor understanding on how that structure influences this critical path. Here, we use a generative model and detailed data from 77 real world projects (+ $10 bn total budget) to demonstrate how this network structure forces us to look beyond the critical path. We introduce a duplication-split model of project schedules that yields (i) identical power-law in- and-out degree distributions and (ii) a vanishing fraction of critical path activities with schedule size. These predictions are corroborated in real projects. We demonstrate that the incidence of delayed activities in real projects is consistent with the expectation from percolation theory in complex networks. We conclude that delay propagation in project schedules is a network property and it is not confined to the critical path.”
We breakdown complex projects into activities and their logical dependencies. We estimate the project finish time based on the activity durations and relations. However, adverse events trigger delay cascades shifting the finish time. Here I derive a tropical algebraic equation for the finish time of activity networks, encapsulating the principle of linear superposition of exogenous perturbations in the tropical sense. From the tropical algebraic equation I derive the finish time distribution with explicit reference to the distribution of exogenous delays and the network topology and geometry.
Understanding the role of individual nodes is a key challenge in the study of spreading processes on networks. In this work we propose a novel metric, the reachabilityheterogeneity (RH), to quantify the contribution of each node to the robustness of the network against a spreading process. We then introduce a dataset consisting of four large engineering projects described by their activity networks, including records of the performance of each activity, i.e., whether it was timely delivered or delayed; such data, describing the spreading of performance fuctuations across activities, can be used as a reliable ground truth for the study of spreading phenomena on networks. We test the validity of the RH metric on these project networks, and discover that nodes scoring low in RH tend to consistently perform better. We also compare RH and seven other node metrics, showing that the former is highly interdependent with activity performance. Given the context agnostic nature of RH, our results, based on real world data, signify the role that network structure plays with respect to overall project performance.
Spreading on networks Project managementNode vulnerabilityDelay spreadingProject performanceDynamical processes on networksNetwork heterogeneity
Engineering projects are notoriously hard to complete on-time, with project delays often theorised to propagate across interdependent activities. Here, we use a novel dataset consisting of activity networks from 14 diverse, large-scale engineering projects to uncover network properties that impact timely project completion. We provide empirical evidence of perturbation cascades, where perturbations in the delivery of a single activity can impact the delivery of up to 4 activities downstream, leading to large perturbation cascades. We further show that perturbation clustering significantly affects project overall delays. Finally, we find that poorly performing projects have their highest perturbations in high reach nodes, which can lead to largest cascades, while well performing projects have perturbations in low reach nodes, resulting in localised cascades. Altogether, these findings pave the way for a network-science framework that can materially enhance the delivery of large-scale engineering projects.
Activity networks Network science Spreading processes Cascades Project performance
Successful on-time delivery of projects is a key enabler in resolving major societal challenges, such as wasted resources and stagnated economic growth. However, projects are notoriously hard to deliver successfully, partly due to their interconnected and temporal complexity which makes them prone to cascading failures. Here, we develop a cascading failure model and test it on a temporal activity network, extracted from a large-scale engineering project. We evaluate the effectiveness of six mitigation strategies, in terms of the impact of task failure cascading throughout the project. In contrast to theoretical arguments, our results indicate that in the majority of cases, the temporal properties of the activities are more relevant than their structural properties in preventing large-scale cascading failures. In practice, these findings could stimulate new pathways for designing and scheduling projects that naturally limit the extent of cascading failures.
Project risk Cascading failures Mitigation strategies Complex networks
Back in 1983, in the inaugural issue of Civil Engineering and Environmental Systems, editors in- chief Colin B. Brown and John Munro opened their editorial by stating that ‘The complexity of civil engineering practices has greatly increased over the last 30 years’, concluding that ‘this places on the engineer the onus of communicating efficiently with other professionals’. This observation has become increasingly prominent, with the built environment now being composed of a wide range of systems, interacting together across different scales and at almost real-time. With this Special Issue, we sought to take this observation towards one possible direction by addressing two interrelated questions: (1) should civil engineers play a role in understanding how organisations operate, and (2) is complex systems perspective a viable way for doing so, compared to other more established perspectives.
Invited Editorial Complex Projects Systems Engineering
Activity network analysis is a widely used tool for managing project risk. Traditionally, this type of analysis is used to evaluate task criticality by assuming linear cause-and-effect phenomena, where the size of a local failure (e.g., task delay) dictates its possible global impact (e.g., project delay). Motivated by the question of whether activity networks are subject to nonlinear cause-and-effect phenomena, a computational framework is developed and applied to real-world project data to evaluate project systemic risk. Specifically, project systemic risk is viewed as the result of a cascading process which unravels across an activity network, where the failure of a single task can consequently affect its immediate, down-stream task(s). As a result, we demonstrate that local failures are capable of triggering failure cascades of intermittent sizes. In turn, a modest local disruption can fuel exceedingly large, systemic failures. In addition, the probability for this to happen is much higher than anticipated. A systematic examination of why this is the case is subsequently performed with results attributing the emergence of large-scale failures to topological and temporal features of activity networks. Finally, local mitigation is assessed in terms of containing these failures cascades–results illustrate that this form of mitigation is both ineffective and insufficient. Given the ubiquity of our findings, our work has the potential of deepening our current theoretical understanding on the causal mechanisms responsible for large-scale project failures.
Risk management Project failure Complex networks Systemic risk Modeling

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