Robust project scheduling considering resource idle costs from a resource flow perspective

In uncertain environments, the asynchronous arrival of multiple resource types during project execution often results in a significant resource idleness problem. However, existing robust scheduling studies seldom consider resource-flow coordination, making it difficult to jointly manage schedule robustness and resource idle costs. To address this challenge, this paper develops a project scheduling scheme that effectively balances schedule stability with the control of resource idle costs. Methodologically, we introduce a pioneering bi-objective scheduling model that integrates resource idle costs with robustness, systematically refining the surrogate robustness measure from a resource flow perspective. Furthermore, a surrogate measure for realised schedule is proposed based on the mean and standard deviation of activity-duration distributions. Comparative experiments utilising the PSPLIB benchmark dataset demonstrate that the proposed approach reduces resource idle costs by an average of 82.25% compared with traditional methods, while preserving schedule robustness. Additionally, the improved NSGA-II demonstrates strong overall competitiveness against benchmark algorithms on most test instances. This research provides a theoretical framework that integrates solution robustness with resource flow coordination for project management under uncertainty, offering effective theoretical support for ensuring execution stability and comprehensive cost control in project management practice.