Robust Optimization of Resource-constrained Multi-Project Scheduling Problem with Uncertain Activities Duration

Document Type : Research Paper

Authors

Department of Industrial Engineering, Khajeh Nasir Toosi University of Technology, Tehran, Iran

Abstract

Multi-project scheduling problem is one of the most important problems in the project scheduling applications, which has attracted considerable attention in the past decades. Due to the importance of resources in the multi-project scheduling problem, the resource sharing policy is used in this research. In addition, in each project, the activities durations are subject to the considerable uncertainty. Due to the rapid changing of the environment and also the uniqueness of the projects, one cannot estimate the probability distribution for the activity uncertain durations with certainty. In addition, the problem in multi-project scale needs a more conservative approach when facing with uncertainty. Therefore, the robust optimization approach is employed in this paper. So that the maximum total weighted tardiness of the projects should become minimum. The robust resource-constrained multi-project scheduling problem (RRCMPSP) is investigated in this paper as a two-stage model. A scenario relaxation algorithm is applied resulting optimal solutions for the RRCMPSP, which is tested on the examples produced by the RanGen. So, in this paper, an overall optimal structure containing all of the projects for the multi-project problem is obtained in a way that the maximum differences between the finish time of projects and their due date would become minimum.

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Main Subjects


1. PMI. (2012). Project Management Body of Knowledge, PMBOK Guide. 5th. Ed. Atlanta, USA.
2. Payne, J. H. (1995). “Management of Multiple Simultaneous Projects: A State-of-The-Art Review”, International Journal of Project Management, Vol. 13, No. 3, PP. 163–168.
3. Lova, A., and Tormos, P. (2001). “Analysis of Scheduling Schemes and Heuristic Rules Performance in Resource-Constrained Multiproject Scheduling”, Annals of Operations Research, Vol. 102, PP. 263–286.
4. Aritua, B., Smith, N. J., and Bower, D. (2009). “Construction Client Multi-Projects – A Complex Adaptive Systems Perspective”, International Journal of Project Management, Vol. 27, PP. 72–79.
5. Bertsimas, D., and Sim, M. (2004). “The Price of Robustness”, Operations Research, Vol. 52, No. 1, PP. 35-53.
6. Bruni, M. E. et al. (2017). “An Adjustable Robust Optimization Model for the Resource-Constrained Project Scheduling Problem with Uncertain Activity Durations”, Omega, Vol. 71, PP. 66-84.
7. Herroelen, W., and Leus, R. (2005). “Project Scheduling Under Uncertainty: Survey and Research Potentials”, European Journal of Operational Research, Vol. 165, PP. 289–306.
8. Yamashita, D. S., Armentano, V. A., and Laguna, M. (2007). “Robust Optimization Models for Project Scheduling with Resource Availability Cost”, Journal of Scheduling, Vol. 10, PP. 67–76.
9. Kerzner, H. (2013). Project Management: A Systems Approach to Planning, Scheduling, and Controlling. 11th. Ed. PP. 1, 7, 42, 66, Hoboken: Wiley.
10. Walter, M. (2014). “Multi-Project Management with a Multi-Skilled Workforce, a Quantitative Approach Aiming at Small Project Teams”, Phd Dissertation. Clausthal University Of Technology.
11. Blismass, N. et al. (2004). “Factors Influencing Delivery Within Construction Clients’ Multi-Project Environments”, Engineering, Construction and Architectural Management, Vol.11, No. 2, PP. 113–125.
12. Zheng, Z. et al. (2013). “Resource Constraint Multi Project Scheduling with Priority and Uncertain Activity Durations”, International Journal of Computational Intelligence Systems, Vol. 6 No. 3, PP. 530-547.
13. Singh, A. (2014). “Resource Constrained Multi-Project Scheduling with Priority Rules and Analytic Hierarchy Process”, Procedia Engineering, Vol. 69, PP. 725 – 734.
14. Wauters, T. et al. (2013). “The Multi-Mode Resource-Constrained Multi-Project Scheduling Problem”, Journal of Scheduling, The MISTA 2013 Challenge.
15. Besikci, U., Bilge, U., and Ulusoy, G. (2015). “Multi-Mode Resource Constrained Multi-Project Scheduling and Resource Portfolio Problem”, European Journal of Operational Research, Vol. 240, PP. 22–31.
16. Zheng, Z. et al. (2014). “A Critical Chains-Based Distributed Multi-Project Scheduling Approach”, Neurocomputing, Vol. 143, PP. 282–293.
17. Besikci, U., Bilge, U., and Ulusoy, G. (2013). “Resource Dedication Problem in a Multi-Project Environment”, Flexible Services and Manufacturing Journal, Vol.25, PP. 206–229.
18. Klerides, E., and Hadjiconstantinou, E. (2010). “A Decomposition-Based Stochastic Programming Approach for the Project Scheduling Problem Under Time/ Cost Trade-Off Settings and Uncertain Durations”, Computers And Operations Research, Vol. 37, No. 12, PP. 2131–2140.
19. Chiang, A. J., and Jeang, A. (2015). “Stochastic Project Management Via Computer Simulation and Optimisation Method”, International Journal of Systems Science: Operations and Logistics, Vol. 2, No. 4, PP. 211–230.
20. Xiong, J. et al. (2012). “A Hybrid Multi Objective Genetic Algorithm for Robust Resource Constrained Project Scheduling with Stochastic Durations”, Mathematical Problems in Engineering, P. 24.
21. Duc Long, L., and Ohsato, A. (2008). “Fuzzy Critical Chain Method for Project Scheduling Under Resource Constraints and Uncertainty”, International Journal of Project Management, Vol. 26, PP. 688–698.
22. Knyazeva, M., Bozhenyuk, B., and Rozenberg, I. (2015). “Resource-Constrained Project Scheduling Approach Under Fuzzy Conditions”, Procedia Computer Science, Vol. 77, PP. 56-64.
23. Dixit, V., Srivastava, R. K., and Chaudhuri, A. (2014). “Procurement Scheduling for Complex Projects with Fuzzy Activity Durations and Lead Times”, Computers and Industrial Engineering, Vol. 76, PP. 401–414.
24. Masmoudi, M., and Haït,  A. (2013). “Project Scheduling Under Uncertainty Using Fuzzy Modelling and Solving Techniques”, Engineering Applications of Artificial Intelligence, Vol. 26, No. 1, PP. 135–149.
25. Artigues, C., Leus, R., and Nobibon, F. T. (2013). “Robust Optimization for Resource-Constrained Project Scheduling with Uncertain Activity Durations”, Flexible Services and Manufacturing Journal, Vol. 25, PP. 175–205.
26. Chakrabortty, R. K., Sarker, R. A., and Essam, D. L. (2017). “Resource Constrained Project Scheduling with Uncertain Activity Durations”, Computers and Industrial Engineering, Http://Dx.Doi.Org/10.1016/J.Cie.2016.12.040.
27. Balas, E. (1971). “Project Scheduling with Resource Constraints”, In E.M.L. Beale, (Ed.), Applications of Mathematical Programming Techniques, PP. 187-200, The English Universities Press Ltd.
28. Demeulemeester, E., Vanhoucke, M., and Herroelen, W. (2003). “A Random Network Generator for Activity-on-The-Node Networks”, Journal of Scheduling, Vol. 6, PP. 13-34.
29. Patterson, J. H. (1976). “Project Scheduling: The Effects of Problem Structure on Heuristic Performance”, Naval Research Logistic, Vol. 23, No. 1, PP. 95-123
30. Hazir, O., Erel, E., and Gnalay, Y. (2011). “Robust Optimization Models for the Discrete Time/ Cost Trade-Off Problem”, International Journal of Production Economics. Vol. 130, No. 1, PP. 87–95.
31. Moghani Ghahremanlouie, S., and Fathi Hafashjani, K. (2014). “A Novel Robust Model for Discrete Time-Cost Trade off Problem”, International Journal of Industrial Engineering and Production Management, Vol. 25, No. 1, PP. 1-14.