The Project Scheduling Interdiction Problem with Delay Groups

Large-scale projects are frequently delayed by correlated disruptions: when a shared input such as a common supplier, a specialized team, or a supporting platform degrades, all dependent activities are slowed down simultaneously. This paper introduces delay groups to capture such disruptions: a delay group is a set of activities whose delays stem from a common cause, described jointly by an uncertainty set. Our model takes the perspective of an interdictor that, subject to a budget of $k$ groups, selects which groups to disrupt so as to maximize the project makespan. The interdictor can extend activity durations within each disrupted group by delays from a group-specific uncertainty set, while non-disrupted activities keep their nominal duration. We study the complexity of the resulting Project Scheduling Interdiction Problem with Delay Groups (PSIP-DG), which provides a worst-case stress test of the schedule. The problem is computationally intractable ($N\!P$-hard) for general polyhedral uncertainty sets, even for a single delay group with a continuous knapsack constraint. For budgeted uncertainty sets, we prove $N\!P$-hardness both when all activities of a disrupted group are delayed and when only one activity per group may be delayed, and derive an inapproximability bound of $1-1/e+ε$ for the former case. We further develop a greedy heuristic with approximation guarantee $k$ and two structure-based heuristics with initializations and neighborhoods from tractable special cases. Experiments on $5{,}000$-activity networks show that the heuristics match the solution quality of an exact solver at substantially lower running times, in some cases finding strictly better solutions.