Simplifying the Nonlinear Continuous Time-Cost Tradeoff Problem

• Published in: Journal of systems science and complexity 2017-08, Vol.30 (4), p.901-920
• Main Authors: Su, Zhixiong, Qi, Jianxun, Wei, Hanying
• Format: Article
• Language: English
• Subjects: Complex Systems; Control; Critical path; Critical path method; Floats; Mathematics; Mathematics and Statistics; Mathematics of Computing; Operations Research/Decision Theory; Production scheduling; Redundancy; Scheduling; Simplification; Statistics; Systems Theory; Tradeoffs; 关键路径法; 多项式算法; 权衡; 费用; 路径长度; 路径问题; 连续时间; 非线性
• ISSN: 1009-6124; 1559-7067
• DOI: 10.1007/s11424-017-5175-z

Equivalent simplification is an effective method for solving large-scale complex problems. In this paper, the authors simplify a classic project scheduling problem, which is the nonlinear continuous time-cost tradeoff problem （TCTP）. Simplifying TCTP is a simple path problem in a critical path method （CPM） network. The authors transform TCTP into a simple activity float problem and design a complex polynomial algorithm for its solution. First, the authors discover relationships between activity floats and path lengths by studying activity floats from the perspective of path instead of time. Second, the authors perform simplification and improve the efficiency and accuracy of the solution by deleting redundant activities and narrowing the duration intervals of non-redundant activities. Finally, the authors compare our method with current methods. The relationships between activity floats and path lengths provide new approaches for other path and correlative project problems.