Activity networks determine project performance

Abstract

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.

Figure 1

Duplication-split model. (A) Duplication and split rules acting on an activity (black). (B) Initial conditions where the duplication-split model is applied. (C) Examples of activity networks generated by the duplication-split model for three different values of the duplication probability q. Critical path is highlighted in red.

Figure 2

Degree distributions. Distribution of the number of predecessors (in-degree) and successors (out-degree) across activities in networks generated by the duplication-split model, using (A) q = 0.25 and B) q = 0.5. The dashed line highlights the power law tail predicted by our calculations.

Figure 3

Relative size of the critical path. (A–C) The number of activities c in the critical path relative to the total number of activities n, for activity networks generated by the duplication-split model. The dashed line highlights the power law decay predicted by our calculations. (D) The scaling exponent of the power law decay c ~ n^-α as a function of q (symbols), The dashed line is the theoretical upper-bound.

Figure 4

Empirical data analysed. (A) Distribution of the number of predecessors (in-degree) and successors (out-degree) across activities of a typical construction project. The dashed line highlights a power law fitting the data. (B) The exponents q obtained from the fit to the distribution of the number of predecessors q(in-degree) and successors q(out-degree). Each point represents a project schedule. The dashed line is the equality line. (C) The distribution of estimated duplication rate q across projects. (D) The fraction of activities in the critical path as a function of the number of activities. Different symbols represent a project schedule at different stages of completion. The solid background represents the [20,80]% confidence interval.

Figure 5

Delay incidence. (A) Observed delay incidence in construction projects as a function of p × c, control parameter associated with the critical path. (B) Observed delay incidence in construction projects as a function of p-p_c, the control parameter of percolation theory. p is the fraction of delay transmissions along direct activity-activity relations, c the number of activities in the critical path and p_c is the critical threshold from percolation theory (p_c = 1/ < k >).