The Project Scheduling Interdiction Problem with Delay Groups

2026-08-27

AI Summary

本文通过引入延迟组来处理大型项目中由共享输入导致的关联中断问题，并研究了在预算限制下最大化项目工期的调度干扰问题。

Abstract

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.

Problem

• Project Scheduling
• Interdiction Problem
• Delay Groups
• Disruptions
• Uncertainty Set

Innovation

• delay groups
• project scheduling interdiction problem
• uncertainty sets
• heuristics
• computational complexity