Fuzzy mathematical models for maximizing satisfaction of contractors and clients by considering flexible start date of the project

Document Type : Article


1 Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran

2 Department of Management, Najafabad Branch, Islamic Azad University, Najafabad, Iran

3 Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University, Isfahan, P.O. Box 81595-158, Iran


Resource-Constrained Multi-Project Scheduling Problem (RCMPSP) is considered a significant topic in project management studies and many kinds of research have been carried out in this field which have been proposed numerous approaches. However, in most of them, the viewpoints of clients and contractors, two important stakeholders of the project are not directly considered. The current research tries to introduce a new approach of RCMPSP in order to schedule the project portfolio and allocate the budget as a limited resource simultaneously. In this way, first, the client's and contractors' budget satisfaction is defined. Then some budget allocation models have been proposed to maximize the clients' and the contractors’ satisfaction. These models consider constraints such as the minimum cost required for each project, the maximum budget for each period, and the flexibility for the start date of each project. To illustrate the proposed models, a real case of the project portfolio is considered.


[1] Lim, C. Teng, S. G. Al-Ghandour, M. et al. "Let Scheduling for Funding Scenario Analysis of Highway Construction Projects With a Case of NCDOT". IEEE Transactions on Engineering Management. 67(2), PP 385-395 (2018).
[2] Elazouni, A. M. and Metwally, F. G. "Finance-based scheduling: Tool to maximize project profit using improved genetic algorithms", Journal of Construction Engineering and Management, 131(4), PP 400-412 (2005).
[3] Afshar, A. and Fathi, H. "Fuzzy multi-objective optimization of finance-based scheduling for construction projects with uncertainties in cost", Engineering Optimization, 41(11), PP 1063-1080 (2009).
[4] Wang, Y. He, Z. Kerkhove, L. et al. "On the performance of priority rules for the stochastic resource constrained multi-project scheduling problem", Computers & Industrial Engineering, 114, PP 223-234 (2017).  
[5] Browning, T. and Yassine, A. "Resource-constrained multi-project scheduling: Priority rule performance revisited", International Journal of Production Economics, 126(2), PP 212-228 (2010).  
[6] Yang, K. K. and Sum, C. C. "A comparison of resource allocation and activity scheduling rules in a dynamic multi-project environment", Journal of Operations Management, 11(2), PP 207-218 (1993).
[7] Gonçalves, J. Mendes, J. and Resende, M. "A genetic algorithm for the resource constrained multi-project scheduling problem", European Journal of Operational Research, 189(3), PP 1171-1190 (2008).  
[8] Ju, C. and Chen, T. "Simplifying multiproject scheduling problem based on design structure matrix and its solution by an improved aiNet algorithm". Discrete Dynamics in Nature and Society, 2012 (2012). 
[9] Hartmann, S. and Kolisch, R. "Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem', European Journal of Operational Research, 127(2), PP 394-407(2000). 
[10] Browning, T. R. and Yassine, A. A. "Managing a portfolio of product development projects under resource constraints", Decision Sciences, 47(2), PP 333-372 (2016).   
[11] Adhau, S. Mittal, M. and Mittal, A. "A multi-agent system for distributed multi-project scheduling: An auction-based negotiation approach", Engineering Applications of Artificial Intelligence, 25(8), PP 1738-1751(2012). 
[12] Lau, J. Huang, G.Q. Mak, et al. "Distributed project scheduling with information sharing in supply chains: part I—an agent-based negotiation model", International Journal of Production Research, 43(22), PP 4813-4838(2005).  
[13] Akhbari, M. "Partnership of contractors in cooperative game theory approach to project resource management", Scientia Iranica, 27(1), PP 469-480 (2020).
[14] Singh, A. "Resource Constrained Multi-project Scheduling with Priority Rules & Analytic Hierarchy Process", Procedia Engineering, 69, PP 725-734 (2014). 
[15] Dubois, D. and Fortemps, P. "Computing improved optimal solutions to max–min flexible constraint satisfaction problems", European Journal of Operational Research, 118(1), PP 95-126 (1999).
[16] Zimmermann, H. J. "Description and optimization of fuzzy systems", International Journal of General System, 2(1), PP 209-215 (1975).
[17] Pritsker, A. Waiters, L. and Wolfe, P. "Multi Project Scheduling with Limited Resources: A Zero-One Programming Approach", Management Science, 16(1), PP 93-108 (1969).  
 [18] Kim, K. Yun, Y. Yoon, J. et al. "Hybrid genetic algorithm with adaptive abilities for resource-constrained multiple project scheduling", Computers in industry, 56(2), PP 143-160 (2005). 
[19] Tseng, C. C. "Two heuristic algorithms for a multi-mode resource-constrained multi-project scheduling problem", Journal of Science and Engineering Technology, 4(2), PP 63-74 (2008). 
[20] Majazi Dalfard, V. and Ranjbar, V. "Multi-projects scheduling with resource constraints & Priority rules by the use of Simulated Annealing Algorithm", Tehnički vjesnik, 19(3), PP 493-499 (2012).  
[21] Can, A. and Ulusoy, G. "Multi-project scheduling with two-stage decomposition", Annals of Operations Research, 217(1), PP 95-116 (2014).
[22] Chakrabortty, R. K. Sarker, R. A. and Essam, D. L. "Resource Constrained Multi-project Scheduling: A Priority Rule Based Evolutionary Local Search Approach in Intelligent and Evolutionary Systems", PP 75-86, Springer, Cham (2017). 
[23] Kurtulus, I. S. and Narula, S. C. "Multi-project scheduling: Analysis of project performance" IIE transactions, 17(1), PP 58-66 (1985).
[24] Russell, R. A. "A comparison of heuristics for scheduling projects with cash flows and resource restrictions" Management Science, 32(10), PP 1291-1300 (1986). 
[25] Chiu, H. N. and Tsai, D. M. "An efficient search procedure for the resource-constrained multi-project scheduling problem with discounted cash flows", Construction Management & Economics, 20(1), PP 55-66 (2002).
[26] Herroelen, W. "Project scheduling—Theory and practice", Production and operations management, 14(4), PP 413-432 (2005).  
[27] Vázquez, E. P.  Calvo, M. P. and Ordóñez, P. M. "Learning process on priority rules to solve the RCMPSP", Journal of Intelligent Manufacturing, 26(1), PP 123-138 (2015).  
[28] Ben Issa, S. and Yiliu, Tu. "A Survey in the Resource-Constrained Project and Multi-Project Scheduling Problems", Journal of Project Management, 5, PP 117-138 (2020).
[29] Nabipoor Afruzi, E. Aghaie, A. and Najafi, A. A. "Robust optimization for the resource-constrained multi-project scheduling problem with uncertain activity durations", Scientia Iranica, 27(1), PP 361-376 (2020).  
 [30] Zhang, Z. Xu, J. Yang, H. et al. "Bi-Level Optimization of Resource-Constrained Multiple Project Scheduling Problems in Hydropower Station Construction under Uncertainty", Scientia Iranica, 22(3), PP 650-667 (2015).
[31] Kurtulus, I. and Davis, E. W. "Multi-project scheduling: Categorization of heuristic rules performance", Management Science, 28(2), PP 161-172 (1982).   
[32] Lova, A. and Tormos, P. "Analysis of scheduling schemes and heuristic rules performance in resource-constrained multiproject scheduling", Annals of Operations Research, 102(1-4), PP 263-286 (2001).
[33] Tsang, E. "Foundations of constraint satisfaction: the classic text", PP 8-10, BoD–Books on Demand. (2014). 
[34] Kaveh, A. and Vazirinia, Y. "Chaotic Vibrating Particles System for Resource-Constrained Project Scheduling Problem", Scientia Iranica, (2019).
[35] Tavana, M. Abtahi, A. R. and Khalili-Damghani, K. "A new multi-objective multi-mode model for solving preemptive time–cost–quality trade-off project scheduling problems", Expert Systems with Applications, 41(4), PP 1830-1846 (2014).
[36] Paraskevopoulos, D. C. Tarantilis, C. D. and Ioannou, G. "Solving project scheduling problems with resource constraints via an event list-based evolutionary algorithm", Expert Systems with Applications, 39(4), PP 3983-3994 (2012).
[37] Wang, X. Chen, Q. Mao, N. et al. "Proactive approach for stochastic RCMPSP based on multi-priority rule combinations", International Journal of Production Research, 53(4), PP 1098-1110 (2014).  
[38] Wanke, P. Nwaogbe, O. R. and Chen, Z. "Efficiency in Nigerian ports: handling imprecise data with a two-stage fuzzy approach", Maritime Policy & Management, 45(5), PP 699-715 (2018).   
[39] Mirzaei, N. Niroomand, S. and Zare, R. "Application of statistical process control in service industry: A case study of the restaurant sector", Journal of Modelling in Management, 11(3), PP 763-782 (2016).