Document Type : Original Article


1 Department of Industrial Engineering, Mazandaran University of Science and Technology, Babol, Iran.

2 Department of Industrial Engineering & Management Systems, Amirkabir University of Technology, Tehran, Iran.

3 Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran.


One of the most important aspects of human resource management is the allocation of the workforce to activities. Human resource assignment to project activities for its scheduling is one of the most real and common issues in project management and scheduling. This becomes even more significant when human resource assignment to multiple projects simultaneously is considered. On the one hand, workforces can have multi skills due to technological and scientific development so that they can be assigned to project activities based on their skill level. On the other hand, the learning effect is also taken into account to make the model more realistic. These factors can affect completion time, total cost and execution quality of projects. In this study, a multi-objective optimization model for multi-project scheduling and multi-skilled human resource assignment problem based on the learning effect and activities' quality is presented. A mixed-integer linear programming model (MILP) is developed for the proposed problem and solved by the ε-constraint method in GAMS software. Managers can select a solution based on their priority. Finally, a sensitivity analysis is done on the learning and forgetting effect to investigate their impacts on each objective function.


Alfares, H.K., and Bailey, J.E., (1997). "Integrated project task and manpower scheduling" IIE transactions, Vol. 29, pp. 711-717.
Babaee Tirkolaee, E., Goli, A., Pahlevan, M., and Malekalipour Kordestanizadeh, R., (2019). "A robust bi-objective multi-trip periodic capacitated arc routing problem for urban waste collection using a multi-objective invasive weed optimization", Waste Management & Research, Vol. 37, No. 11, pp. 1089-1101.
Babaee Tirkolaee, E., Hadian, S., and Golpira, H., (2019). "A novel multi-objective model for two-echelon green routing problem of perishable products with intermediate depots", Journal of Industrial Engineering and Management Studies, Vol. 6, No. 2, pp. 101-110.
Balaman, Ş. Y., Matopoulos, A., Wright, D. G., and Scott, J., (2018). "Integrated optimization of sustainable supply chains and transportation networks for multi technology bio-based production: A decision support system based on fuzzy ε-constraint method", Journal of cleaner production, Vol. 172, pp. 2594-2617.
Batarlienė, N., Čižiūnienė, K., Vaičiūtė, K., Šapalaitė, I., and Jarašūnienė, A., (2017). "The impact of human resource management on the competitiveness of transport companies", procedia Engineering, Vol. 187, pp. 110-116.
Bellenguez-Morineau, O., (2008). "Methods to solve multi-skill project scheduling problem", 4OR: A Quarterly Journal of Operations Research, Vol. 6, No. 1, PP. 85-88.
Berk, L., Bertsimas, D., Weinstein, A. M., and Yan, J., (2019). "Prescriptive analytics for human resource planning in the professional services industry" European Journal of Operational Research, Vol. 272, No. 2, pp. 636-641.
Bérubé, Jean-François, Michel Gendreau, and Jean-Yves Potvin., (2009). "An exact ε-constraint method for bi-objective combinatorial optimization problems: Application to the Traveling Salesman Problem with Profits", European Journal of Operational Research, Vol. 194, No. 1, pp. 39-50.‏
Bula, G.A., Afsar, H. M., González, F.A., Prodhon, C., and Velasco, N. (2019). Bi-objective vehicle routing problem for hazardous materials transportation", Journal of cleaner production206, 976-986.
Chakrabortty, R.K., Sarker, R.A., and Essam, D.L., (2016). "Multi-mode resource-constrained project scheduling under resource disruptions", Computers & Chemical Engineering, Vol. 88, pp. 13-29.
Certa, A., Enea, M., Galante, G., and Manuela La Fata, C., (2009). "Multi-objective human resources allocation in R&D projects planning", International Journal of Production Research, Vol. 47, No. 13, pp. 3503-3523.
Davoodi, S.M.R., and Goli, A. (2019). "An integrated disaster relief model based on covering tour using hybrid Benders decomposition and variable neighborhood search: Application in the Iranian context", Computers & Industrial Engineering130, 370-380.
Deb, K., and Sundar, J., (2006). "Reference point based multi-objective optimization using evolutionary algorithms", Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, Vol. 12, pp. 635-642.‏
Ehrgott, M., and Xavier G., (2003). "Multi objective combinatorial optimization theory, methodology, and applications, multiple criteria optimization: State of the art annotated bibliographic surveys" Springer US, pp. 369-444.
Fırat, M., and Hurkens, C.A.J., (2012). "An improved MIP-based approach for a multi-skill workforce scheduling problem", Journal of Scheduling, Vol. 15, No. 3, pp. 363-380.
Fernandez-Viagas, V., and Framinan, J. M., (2014). "Integrated project scheduling and staff assignment with controllable processing times" The Scientific World Journal, Vol. 2014.
Goli, A., and Davoodi, S.M.R., (2018). "Coordination policy for production and delivery scheduling in the closed loop supply chain", Production Engineering12(5), 621-631.
Goli, A., Zare, H.K., Tavakkoli‐Moghaddam, R., and Sadegheih, A., (2019). "Multiobjective fuzzy mathematical model for a financially constrained closed‐loop supply chain with labor employment", Computational Intelligence.
Goli, A., Zare, H.K., Tavakkoli-Moghaddam, R., and Sadeghieh, A. (2019). "Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry", Computers & Industrial Engineering, Vol. 137, 106090.
Hartmann, S. and Briskorn, D., (2010). "A survey of variants and extensions of the resource-constrained project scheduling problem", European Journal of Operational Research, Vol. 207, No. 3, pp. 1-14.
Heimerl, C., and Kolisch, R., (2010). "Work assignment to and qualification of multi-skilled human resources under knowledge depreciation and company skill level targets", International Journal of Production Research, Vol. 48, No. 13, pp. 3759-3781.
Hematian M., Seyyed Esfahani M.M., Mahdavi I, Mahdavi-Amiri N, Rezaeian J., (2019). "A multi-objective integrated multi-project scheduling and multi-skilled workforce assignment model considering learning effect under uncertainty", Computational Intelligence, pp. 1–21.
Karam, A., Attia, E. A., and Duquenne, P., (2017). "A MILP model for an integrated project scheduling and multi-skilled workforce allocation with flexible working hours", IFAC-Papers Online, Vol. 50, No. 1, pp. 13964-13969.
Kianto, A., Sáenz, J., and Aramburu, N., (2017). "Knowledge-based human resource management practices, intellectual capital and innovation", Journal of Business Research, Vol. 81, pp. 11-20.
Lian, J., Liu, C., Li, W., and Yin, Y., (2018). "A multi-skilled worker assignment problem in seru production systems considering the worker heterogeneity", Computers & Industrial Engineering, Vol. 118, pp. 366-382.
Maenhout, B., and Vanhoucke, M., (2017). "A resource type analysis of the integrated project scheduling and personnel staffing problem", Annals of Operations Research, Vol. 252, No. 2, pp. 407-433.
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.
Markoulli, M.P., Lee, C.I., Byington, E., and Felps, W.A., (2017). "Mapping Human Resource Management: Reviewing the field and charting future directions", Human Resource Management Review, Vol. 27, No. 3, pp. 367-396.
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 on the employee efficiency", IEEE International Conference on Industrial Engineering and Engineering Management, pp. 400-404.
Nie, H., and Liu, B., (2013). "Combining MILP with Memetic Algorithm for Scheduling and Staffing Construction Project with a Multi-skilled Workforce", International Conference on Computational and Information Sciences, pp. 1150-1153.
Qin, S., Liu, S., and Kuang, H., (2016). "Piecewise linear model for multi-skilled workforce scheduling problems considering learning effect and project quality", Mathematical Problems in Engineering, Vol. 2016.
Tirkolaee, E.B., Goli, A., and Weber, G.W. (2019). Multi-objective Aggregate Production Planning Model Considering Overtime and Outsourcing Options Under Fuzzy Seasonal Demand, In Advances in Manufacturing II (pp. 81-96). Springer, Cham.
Tirkolaee, E.B., Goli, A., Hematian, M., Sangaiah, A.K., and Han, T. (2019). "Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms", Computing, Vol. 101, No. 6, pp. 547-570.
Tirkolaee, E.B., Hadian, S., Weber, G. W., and Mahdavi, I. (2019). "A robust green traffic‐based routing problem for perishable products distribution", Computational Intelligence.
Tirkolaee, E. B., Mahdavi, I., Esfahani, M.M.S., and Weber, G. W. (2020). "A robust green location-allocation-inventory problem to design an urban waste management system under uncertainty", Waste Management, Vol. 102, pp. 340-350.
Tirkolaee, E.B., Mardani, A., Dashtian, Z., Soltani, M., and Weber, G. W. (2019). "A novel hybrid method using fuzzy decision making and multi-objective programming for sustainable-reliable supplier selection in two-echelon supply chain design. Journal of Cleaner Production, 119517.
Tiwari, V., Patterson, J. H., and Mabert, V.A., (2009). "Scheduling projects with heterogeneous resources to meet time and quality objectives", European Journal of Operational Research, Vol. 193, No. 3, pp. 780-790.
Schwindt, C., and Zimmermann, J., (2015). "Handbook on Project Management and Scheduling" Springer International Publishing Switzerland, Vol. 1.
Shen, X. N., Minku, L. L., Marturi, N., Guo, Y. N., and Han, Y., (2018). "A Q-learning-based memetic algorithm for multi-objective dynamic software project scheduling", Information Sciences, Vol. 428, pp. 1-29.
Vafaeenezhad, T., Tavakkoli-Moghaddam, R., and Cheikhrouhou, N., (2019). "Multi-objective mathematical modeling for sustainable supply chain management in the paper industry", Computers & Industrial Engineering, Vol. 135, pp. 1092-1102.
Van Peteghem, V., and Vanhoucke, M., (2015). "Influence of learning in resource-constrained project scheduling", Computers & Industrial Engineering, Vol. 87, pp. 569-579.
Wu, M.C. and Sun, S.H., (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.