带有延迟组的项目调度阻断问题
The Project Scheduling Interdiction Problem with Delay Groups
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中文总结 AI 辅助
本文针对大型项目的相关延误问题，提出带有延迟组的项目调度阻断问题（PSIP-DG），证明其为NP-hard，开发了贪心等启发式算法，实验显示这些算法高效且解质量良好。
中文摘要 AI 辅助
大型项目常因相关干扰而延误：当共享输入（如共同供应商、专业团队或支撑平台）性能下降时，所有依赖活动会同时放缓。本文引入延迟组来捕捉此类干扰：延迟组是一组活动，其延误源于共同原因，由不确定性集合共同描述。我们的模型从阻断者视角出发，在k个组的预算约束下，选择要阻断的组以最大化项目总工期。阻断者可从特定于组的不确定性集合中选择延误，延长每个被阻断组内活动的持续时间，未被阻断的活动则保持名义持续时间。我们研究了由此产生的带有延迟组的项目调度阻断问题（PSIP-DG）的复杂性，该问题对调度进行了最坏情况压力测试。对于一般多面体不确定性集合，即使是具有连续背包约束的单个延迟组，该问题也具有计算难解性（NP-hard）。对于预算不确定性集合，我们证明了当被阻断组的所有活动都延误，以及当每组仅一个活动可延误时，该问题均为NP-hard，并对前者情况得出了1-1/e+ε的不可近似性界限。我们进一步开发了一种具有k近似保证的贪心启发式算法，以及两种基于结构的启发式算法，其初始化和邻域来自可处理的特殊情况。对包含5000个活动的网络进行的实验表明，这些启发式算法在运行时间显著更短的情况下，达到了精确求解器的解质量，在某些情况下还找到了严格更优的解。
英文摘要
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.
