A Theoretical Framework for Instance Complexity of the Resource-Constrained Project Scheduling Problem

• 成果类型: Article; Early Access
• 署名作者: Van Eynde, Rob; Vanhoucke, Mario
• 署名单位: Ghent University; Vlerick Business School; University of London; University College London
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2021.1237
• 发表日期: 2022
• 关键词: modular decomposition; generation

摘要

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.