A Theoretical Framework for Instance Complexity of the Resource-Constrained Project Scheduling Problem
针对资源受限项目调度问题，提出一个独立于求解算法的理论框架，通过整合优先关系、资源约束和活动时长来解释实例的难易程度，实验表明该框架能有效区分易解与难解实例。
The resource-constrained project scheduling problem (RCPSP) addresses the problem of constructing a schedule with minimum makespan for a set of activities, subject to precedence and resource constraints. Recent research introduced a data set with small instances that cannot be solved by the state-of-the-art algorithms, revealing a gap in our understanding of instance complexity. We propose a new theoretical framework for the instance complexity for the RCPSP, consecutively incorporating precedence constraints, resource constraints, and activity durations. Our approach contributes to the existing knowledge base in two ways. First, it is independent from solution algorithms, which enables generalisable conclusions. Second, the theoretical perspective enables a deeper understanding of the drivers of instance complexity. We evaluate the performance of our approach with a series of computational experiments. These show that our framework is a strong discriminator between easy and hard instances and explains a large fraction of CPU times of optimal solution algorithms.