A robust chance-constrained programming approach for a bi-objective pre-emptive multi-mode resource-constrained project scheduling problem with time crashing

Abstract

The presented study proposes a novel bi-objective mixed integer linear programming (MILP) framework for the multi-mode resource-constrained project scheduling problem (MRCPSP) with pre-emptive and non-preemptive activities splitting under uncertain conditions. Minimising the project makespan and resource costs are the considered objectives. Renewable and non-renewable resources along with different modes are taken into account for activities implementation. Additionally, some activities can be crashed by consuming additional renewable and non-renewable resources. Model uncertainty is efficiently addressed by utilising a fuzzy chance constrained programming (CPP) method as well as extending two robust possibilistic programming models. The capability of the presented mathematical framework is validated using problem instances from PSPLIB (j10, j14, j20, and j30) and MMLIB (MM50 and MM100). Finally, a detailed computational comparison is presented to assess the performance of the two robust possibilistic programming models.

KEYWORDS:

• MRCPSP
• activity preemption
• time crashing
• robust chance constrained programming
• time–cost trade-off

Acknowledgments

The authors would like to thank the Editor-in-Chief, Associate Editor, and anonymous reviewers for their valuable comments on this presentation for remarkable improvement. The authors would also like to express their gratitude to Ms. Fateme Nazeri and Ms. Fateme Zarei for their provision of data, as well as Dr. Hasan Shirzadi for the final validation of the obtained results.

Disclosure statement

No potential conflict of interest was reported by the authors.

Compliance with ethical standards

Availability of data and material: All data generated or analysed during this research are included in this published article.

Code availability: Not applicable

Funding: Not applicable

Consent to participate: Not applicable

Consent for publication: Not applicable

Ethics approval: The authors certify that they have no affiliation with or involvement with human participants or animals performed by any of the authors in any organisation or entity with any financial or non-financial interest in the subject matter or materials discussed in this paper.

Authors’ contributions: All authors contributed to all parts of this research including Conceptualisation; Formal analysis; Resources; Methodology; Supervision; Data collection and investigation; Software; Validation; and Writing – review & editing.

Notes

1 Total number of variables.

Additional information

Notes on contributors

Reza Shahabi-Shahmiri

Reza Shahabi-Shahmiri received an M.Sc. in systems optimisation from the University of Tehran. His master's thesis was about scheduling and routing of heterogeneous vehicles in multiple cross-docks. His current research interests and areas include developing novel mathematical optimisation models in project scheduling, supply chain management, cross-docking systems and routing and scheduling problems. He published some ISI papers in well-known journals.

Thomas S. Kyriakidis

Dr. Thomas S. Kyriakidis is currently a member of the Special Teaching Faculty and the Telecommunications and Advanced Services Laboratory at the department of electrical and computer engineering, University of Western Macedonia, Greece. His Ph.D. is on Algorithms for Optimal Project Scheduling. His current research interests include operations research, optimisation and scheduling techniques and their applications on sustainable development interdisciplinary problems.

Mohammad Ghasemi

Mohammad Ghasemi received a B.Sc. in industrial engineering and M.Sc. in systems optimisation from the University of Tehran and Shahed University, respectively. His master thesis was about the extension of resource-constrained project scheduling problem (RCPSP) under uncertainty. His current research interests and areas include extending multi-objective mathematical optimisation models in new extensions of RCPSP, network diagrams considering real-life assumptions and developing uncertain approaches. He published some related ISI papers in well-known journals. Recently, he has been engaged in research in the area of scheduling construction projects, especially in solving real case studies and practical problems.

Seyed-Ali Mirnezami

Seyed-Ali Mirnezami received an M.Sc. in systems optimisation from Shahed University. His master's thesis was about cash flow analysis in a multi-project environment using a critical chain. His current research interests and areas include project cash flow analysis, multi-criteria decision-making, transportation and logistics, and uncertainty management. He also published some academic papers in reputable journals.

Seyedali Mirjalili

Seyedali Mirjalili is a professor at the Center for Artificial Intelligence Research and Optimization at Torrens University. He has gained international recognition for his contributions to nature-inspired artificial intelligence techniques, with over 500 published works that have received more than 80,000 citations and an H-index of 85. He has been on the list of the top 1% of highly-cited researchers since 2019, and the Web of Science named him one of the most influential researchers in the world. In 2022 and 2023, The Australian newspaper recognised him as a global leader in Artificial Intelligence and a national leader in the Evolutionary Computation and Fuzzy Systems fields. He serves as a senior member of IEEE and holds editorial positions at several top AI journals, including Engineering Applications of Artificial Intelligence, Applied Soft Computing, Neurocomputing, Advances in Engineering Software, Computers in Biology and Medicine, Healthcare Analytics, Applied Intelligence and Decision Analytics.