Document Type : Original Article


1 Assistant Professor, University of Tehran.

2 MBA, Institute of Higher Education Mehr Alborz.


The project management is planning and conducting projects within time, cost and quality is determined towards the creation of specific results. The aim of this research was to develop mathematical models for the trade off time, cost, quality and risk of the project which parameters of its activities have been estimated randomly with grey numbers. In the projects, managers are looking for the optimal combination of time, cost and quality of the project and considering the risk, while information is limited and insufficient in this area. Using the proposed method with grey numbers can help to manage projects well in these conditions. For solving the model / methodology, the hybrid of fuzzy goal programming and grey linear planning has been predicted. By examining the responses, it seems that there is a possibility for them to be improved with goal programming; therefore, the further stages with goal programming for better satisfactory answers were presented to the project manager. For a case study, the project(s) in Iran Khodro Company is selected.


1. Abtahi, S. (1391). Project Scheduling Model with Multi Obejective Integrated Approach: Time-Cost-Quality-Risk- Trade off Multimode Activity Based on a metaheuristic approach. Retrieved from
2. Amiri,M. (1392) Provides a method for ranking the activities of the project using the CPM network and the TOPSIS method in fuzzy mode. Journal of Industrial Management Perspective, (10): 169-183.
3. Ashtiani, B., & gholi Arianezhad, m. (1388). Preventive Methods - Response to Scheduling. Tehran: Iran University of Science and Technology.
4. Charnes, A., Cooper, W., & Fergusen, R. (1955). Optimal estimation of executive compensation by linear programming. Manag Sci, 1(2): 138-151.
5. Chen, L., & Tsai, F. (2001). Fuzzy goal programming with different importance and priorities. Eur J Oper Res, 133(3): 548-556.
6. Deng, J. (1989). Introduction to grey system theory. J. Grey System, 1: 1-24.
7. Ebrahimnezhad, S., Ahmadi, V., & Javanshir, H. (2013). Time-Cost-Quality Trade-off in a CPM Network Using Fuzzy Logic and Genetic Algorithm. International Journal of Industrial Engineering & Production Management, (24): 362-376.
8. Evangeline Jebaseeli, M., & Paul Dhayabaran, D. (2015). Integer Programming Model for Fuzzy Time Cost and Quality Trade off Problem. International Journal of Engineering Science and Innovative Technology (IJESIT), 4(3): 97-106.
9. Huang, G. (1994). Grey Mathematical Programming and Its Application to Municipal. McMaster University USA: Department of civil Engineering.
10 . Ignizio, J. (1976). Goal programming and extension. London: Heath Lexington Books.
11. Kayacan, E., Ulutas, B., & Kaynak, O. (2010). Grey system theory-based models in time series prediction. Expert Systems with Applications, 37(2): 1784–1789.
12. Kerzner, H. (2009). Project management:A system approach to planning, scheduling& controlling. Newjersey: John wiley&Son Inc.
13.Ketabi, S., Faregh , N., & Ghandehari, M. (1391). Project Scheduling with Time-Cost-Quality Trade off in Fuzzy Conditions- Case Study in Kimia Bona Gostar Yazd Co. Retrieved from Center for Advanced Science and Technology Development:
14. Marasinlan, R. (1980). Goal Programming in Fuzzy Enilironment. Decision Science, (11): 325-336.
15. Mehregan, M. (1386‎). Decision making models with several objectives.‎ Tehran: Tehran University-management Deprtement
16.Memariani, A. (1378). Fuzzy Goal Planning Techniques. Management Knowledge, (46): 23-34.
17.  Mohammadi, A., Hosseinzadeh, M., & Bagherzadeh Azar, M. (1390). Introducing a fuzzy hierarchy Hubrid model, gray relationship analysis, and multi-objective planning in order to select a business partner. Journal of Industrial Management Perspective, (1): 17-37.
18. Mohammadipour, F., & Sadjadi, S. (2016). Project cost-quality-risk tradeoff analysis in a time-constrained problem. Computer and Industrial engineering. doi:
19. Movahedian Atar, O., Esmaeeilian, M., & Mohammadi Zanjirani, D. (1394, winter). Selection and scheduling of several projects with limited resources in several executive modes in order to maximize net present value. Journal of Industrial Management Perspective, (20): 79-100.
20. Papageorgiou, E., & Salmeron, J. (2012). Learning Fuzzy Grey Cognitive Maps using Nonlinear Hebbian-based approach. International Journal of Approximate Reasoning, 53: 54-65.
21. Project Management Institute. (2013). A Guide to the Project Management Body of Knowledge (5th ed.). Pennsylvania: Project Management Institute, Inc.
22.Razavi Hajiagha, S., Amoozad Mehdiraji, H., & Hashemi, S. (1393). Multi-criteria decision making under conditions of confidence and uncertainty. Tehran: Termeh.
23. Razavi Hajiagha, S.; Amoozad Mahdiraji, H.; Hashemi, Sh. (2013). A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff. Int J Adv Manuf Technol. .22-32.DOI 10.1007/s00170-013-5463-2
24. Shahsavari Pour, N., Modarres, M., & Tavakkoli-Moghaddam, R. (2012). Time-Cost-Quality Trade-off in Project Scheduling with Linguistic Variables. World Applied Sciences Journal, 18(3): 404-413.
25. Tiwari , R., Dharmar, S., & Rao , J. (1986). Priority structure in fuzzy goal programming. . Fuzzy Sets Syst, 19(3): 251–259.
26. Zimmermann, H. (1978). Fuzzy Orogramming and Linear Programming with several objective functions. Fuzzy sets and Systems, 1(1): 45-55