A Theoretical Framework for Instance Complexity of the Resource-Constrained Project Scheduling Problem
Van Eynde, Rob
Van Eynde, Rob
Publication Type
Journal article with impact factor
Editor
Supervisor
Publication Year
2022-11
Journal
Mathematics of Operations Research
Book
Publication Volume
47
Publication Issue
4
Publication Begin page
3156
Publication End page
3183
Publication Number of pages
Collections
Abstract
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.
Research Projects
Organizational Units
Journal Issue
Keywords
4901 Applied Mathematics, 49 Mathematical Sciences