Modeling the diffusion of dexterity among workers in the multi-skilled resource-constrained project scheduling problem

Document Type : Research Paper


گروه مهندسی صنایع، دانشگاه آزاد اسلامی واحد تهران شمال، تهران، ایران


This paper proposes a new mixed-integer mathematical formulation for the multi-objective multi-skilled resource-constrained project scheduling problem. The objectives of the proposed model are to minimize the make-span and cost of project, simultaneously. In this problem, the workforces can cooperate with each other in working groups to carry out required skills of activities. In the proposed model, workforces have different efficiencies in performing each of their skills and they can improve their efficiencies by learning from more efficient co-workers. Instructing relations between workers have been presented as multiple directed and weighted networks. The problem is NP-hard in the strong sense. Therefore, four multi-objective meta-heuristics have been developed to solve the problem. The performances of algorithms have been compared to each other in terms of convergence, diversity of solutions and computation time. The results show that each of the algorithms has been more successful in providing better results in terms of some performance measures.


Main Subjects

  1. Maghsoudlou, H. M., Afshar-Nadjafi, B., and Niaki, S. T. A., (2017). “Multi-Skilled Project Scheduling with Level-Dependent Rework Risk; Three Multi-Objective Mechanisms Based on Cuckoo Search”, Applied Soft Computing, Vol. 54, PP. 46-61. DOI:
  2. Nguyen, H., and Zheng, R., (2013). “On Budgeted Influence Maximization in Social Networks”, IEEE Journal on Selected Areas in Communications, Vol. 31, No. 6, PP. 1084-1094.
  3. Bagherinejad, J., Jolai, F., and Rafiee Majd, Z., (2013). “Solving the MRCPSP/Max with the Objective of Minimizing Tardiness Costs and Maximizing Earliness Rewards of Activities with a Two-Stage Genetic Algorithm”, Journal of Industrial Engineering, Vol. 47, No. 1, PP. 1-13.
  4. Panahi, I., and Nahavandi, N., (2017). “An Efficient Imperialist Competitive Algorithm for Resource Constrained Project Scheduling Problem”, Journal of Industrial Engineering, Vol. 51, No. 2, PP. 161-174.
  5. Bellenguez O., Néron E. (2005). “Lower Bounds for the Multi-skill Project Scheduling Problem with Hierarchical Levels of Skills”, In: Burke E., Trick M. (eds) Practice and Theory of Automated Timetabling V. PATAT 2004. Lecture Notes in Computer Science, vol 3616. Springer, Berlin, Heidelberg. DOI:
  6. Wu, M., and Sun, S., (2006). “A Project Scheduling and Staff Assignment Model Considering Learning Effect”, The International Journal of Advanced Manufacturing Technology, Vol. 28, No. 11, PP. 1190-1195.
  7. Mehmanchi, E., and Shadrokh, S., (2013). “Solving a New Mixed Integer Non-Linear Programming Model of the Multi-Skilled Project Scheduling Problem Considering Learning and Forgetting Effect”, Proceedings of the 2013 IEEE IEEM, Bangkok, Thailand, DOI: 10.1109/IEEM.2013.6962442.
  8. Kazemipoor, H., Tavakkoli Moghaddam, R., Shahnazari Shahrezaei, P., and Azaron, A., (2013). “A Differential Evolution Algorithm to Solve Multi-Skilled Project Portfolio Scheduling Problems”, The International Journal of Advanced Manufacturing Technology, Vol. 64, No. 5-8, PP. 1099-1111.
  9. Tabrizi, B. H., Tavvakoli Moghaddam, R., and Ghaderi, S. F., (2014). “A Two-Phase Method for a Multi-Skilled Project Scheduling Problem with Discounted Cash Flows”, Scientia Iranica, Vol. 21, No. 3, PP. 1083-1095.
  10. Myszkowski, P. B., Skowronski, M., Olech, L. P., and Oslizlo, K., (2015). “Hybrid Ant Colony Optimization in Solving Multi Skill Resource-Constrained Project Scheduling Problem”, Soft Computing, Vol. 19, No. 12, PP. 3599-3619.
  11. Javanmard, S., Afshar-Nadjafi, B., and Niaki, S. T. A., (2017). “Preemptive Multi-Skilled Resource Investment Project Scheduling Problem; Mathematical Modelling and Solution Approaches”, Computers and Chemical Engineering, Vol. 96, PP. 55-68. DOI:
  12. Maghsoudlou, H., Afshar-Nadjafi, B., and Niaki, S.T.A., (2016). “A Multi-Objective Invasive Weeds Optimization Algorithm for Solving Multi-Skill Multi-Mode Resource Constrained Project Scheduling Problem”, Computers and Chemical Engineering, Vol. 8, PP. 157-169. DOI:
  13. Chen, R., Liang, C., Gu, D., and Leung, J., (2017), “A Multi-Objective Model for Multi-Project Scheduling and Multi-Skilled Staff Assignment for IT Product Development Considering Competency Evolution”, International Journal of Production Research, Vol. 55, No. 21, PP. 6207-6234.
  14. Hosseinian, A.H., Baradaran, V., and Bashiri, M., (2019), “Modeling of the time-dependent multi-skilled RCPSP considering learning effect: An evolutionary solution approach”, Journal of Modelling in Management, Vol. 14, No. 2, PP. 521-558.
  15. Hosseinian, A.H., and Baradaran, V., (2019), “An Evolutionary Algorithm Based on a Hybrid Multi-Attribute Decision Making Method for the Multi-Mode Multi-Skilled Resource-constrained Project Scheduling Problem”, Journal of Optimization in Industrial Engineering, Vol. 12, No. 2, PP. 155-178.
  16. Hosseinian, A.H., and Baradaran, V., (2019), “Detecting communities of workforces for the multi-skill resource-constrained project scheduling problem: A dandelion solution approach”, Journal of Industrial and Systems Engineering, Vol. 12, Special issue on Project Management and Control, 72-99.
  17. Hartmann, S., (2013). “Project Scheduling with Resource Capacities and Requests Varying with Time: A Case Study”, Flexible Services And Manufacturing Journal, Vol. 25, No. 1, PP. 74-93.
  18. Pargar F., Zandieh, M., Kauppila, O., and Kujala, J., (2018). “The Effect of Worker Learning on Scheduling Jobs in a Hybrid Flow Shop: A Bi-Objective Approach”, Journal of Systems Science and Systems Engineering, Vol. 27, No. 3, PP. 265-291.
  19. Najafi, A. A., and Arjmand, M., (2016). “Three Developed Meta-Heuristic Algorithms to Solve RACP Minimizing Makespan and Total Resource Costs Simultaneously”, Journal of Industrial Engineering, Vol. 50, No. 3, PP. 471-482.
  20. Amin Tahmasbi, H., Daghbandan, A., and Bagherpour, R., (2017). “Dual-Objective Preemptive Multi-Mode Resource-Constrained Project Scheduling Problem Optimization Model”, Journal of Industrial Engineering, Vol. 51, No. 1, PP. 29-44.
  21. Murata, T., and Ishibuchi, H., (1995). "MOGA: Multi-Objective Genetic Algorithms", Proceedings of 1995 IEEE International Conference on Evolutionary Computation, Perth, WA, Australia, PP. 289-294.
  22. Gadhvi, B., Savsani, V., and Patel, V., (2016). “Multi-Objective Optimization of Vehicle Passive Suspension System Using NSGA-II, SPEA2 And PESA-II”, Procedia Technology, Vol. 23, PP. 361-368. DOI: 23. Rahmati, S. H. A., Hajipour, V., and Niaki, S. T. A., (2013). “A Soft-Computing Pareto-Based Meta-Heuristic Algorithm for a Multi-Objective Multi-Server Facility Location Problem”, Applied Soft Computing, Vol. 13, No. 4, PP. 1728-1740.
  23. Gao, J., Chen, R., and Deng, W., (2013), “An Efficient Tabu Search Algorithm for the Distributed Permutation Flowshop Scheduling Problem”, International Journal of Production Research, Vol. 51, No. 3, PP. 641-651