Resolving major societal challenges, such as stagnated economic growth or wasted resources, heavily relies on successful project delivery. However, projects are notoriously hard to deliver successfully, partly due to their interconnected nature which makes them prone to cascading failures. We deploy a model of cascading failure to temporal network data obtained from an engineering project, where tasks constituting the entire project and inter-dependencies between tasks correspond to time-stamped nodes and edges, respectively. We numerically evaluate the performance of six strategies to mitigate cascading failures. It is assumed that increased time between a pair of inter-connected tasks acts as a buffer, preventing a failure to propagate from one task to another. We show that, in a majority of cases that we explored, temporal properties of the activities (i.e., start and end date of each task in the project) are more relevant than their structural properties (i.e., out-degree and the size of the out-component of the task) to preventing large-scale cascading failures. Our results suggest potential importance of changing timings of tasks, apart from the static structure of the same network of tasks, for containing project failure.
Project-based processes are central in resolving major societal challenges 1 , from accelerating economic growth (e.g., delivering infrastructure projects 2,3 ) to fostering public resilience (e.g., mobilising resources in response to a natural hazard 4,5 ). As an example, World Bank data from 2009 indicate that 22% of the world's gross domestic products, which is equivalent to approximately $48 trillion, relies almost entirely on project-based delivery mechanisms. 6 Successfully delivering projects is a non-trivial task, partly due to the interdependent nature of tasks composing a project. 7 A 2004 report by PricewaterhouseCoopers concluded that out of 10,640 projects reviewed in 30 countries and across a variety of industries, with a total value of approximately €5 billion, only 254 were successfully delivered. 8 A 2011 report concluded that out of 1,417 IT projects reviewed, 236 projects experienced cost overruns of at least 200% and the delivery of these projects was delayed by almost 70% in time. 9 Similar findings have also been reported elsewhere. 10,11 Because project scales are predicted to increase in the future (e.g., 1.5-2.5% annual growth in value over the past century 12 ), the implications of project failure are expected to increase even further.
Research into understanding project failure can be broadly classified into two distinct, yet complementary, strands. 13 Several studies focus on mapping the sociological factors that contribute to project failure (e.g., importance of leadership 14,15 and corporate environment 16 ). However, this strand of work is generally associated with a multitude of biases such as recollection bias (i.e., information bias in which recalled information is inaccurate) and self-report bias (i.e., behavioural bias in which participants over-report positive results), which challenges the integration of their findings to develop mitigation strategies against project failure. 13 A second approach relies on computational methods 17,18 that model the conditions of project failure, from lacking a ‘healthy’ organisational culture 19 to the propensity of wastefully repeating certain tasks. 20 In computational approaches, a project is typically viewed as a directed acyclic graph and often called activity network 21 , in which time-stamped nodes represent scheduled tasks (Figure 1). Directed edges between two nodes model functional dependencies between the two tasks. For example, a directed edge from node 𝑖 to node 𝑗 indicates that task 𝑖 must be completed before task 𝑗 begins. Because tasks are time-stamped, an activity network can be regarded as a temporal network. [22][23][24] Early work on project failure focused on a particular failure scenariodelay propagation. 25,26 Under this scenario, a delay in the completion of a single task can propagate throughout the activity network, eventually delaying the entire project. A similar scenario has been examined in the context of delay propagation in airport networks. [27][28][29] Subsequent work on project failure has focussed on an alternative failure scenario in which changes in task specifications can trigger substantial rework in subsequent, downstream tasks and similarly affect the delivery of the overall project. In this case, a relatively minor change in the specifications of a single task can propagate across an entire project, severely affecting the overall project performance. [30][31][32] These scenarios of project failure, in which a delay or a change in the task specification that occurs in a single task propagate across the overall project, seem to be an exemplary type of a cascading failure on activity networks. By cascading failure we refer to iterative processes in which a single failure leads to subsequent failures, which can potentially lead to a system-wide failure 33,34 . Past studies attributed a diverse set of system-wide failures to cascading failures, including financial systemic risk 35,36 , the spread of misinformation 37,38 , and power blackouts 39,40 . Along this line, our recent studies tackled long-lasting project-management challenges using network analysis (e.g., assessing potential of conflict between sub-contractors) 41 and associated certain project features with heightened vulnerability to cascading failures 42 . However, both studies did not aim to provide specific mitigation strategies with which to contain failure cascades, which is the main focus of the present study.
Robustness against cascading failures in networks can be engineered via structural or temporal mitigation schemes. Structural mitigation can be deployed when the structure of the network can be changed. For example, in power grids, one can modify the network structure to discourage the onset of large-scale cascades e.g., by introducing network modules or purposefully fragmenting the network before a cascade happens. 43,44 However, some network systems that are susceptible to cascading failures may not accommodate structural
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