A hybrid model of fuzzy goal programming and grey numbers in continuous project time, cost, and quality tradeoff

Seyed Hossein Razavi Hajiagha, Hannan Amoozad Mahdiraji, Shide Sadat Hashemi

Research output: Contribution to journalArticlepeer-review

26 Citations (Scopus)


The purpose of this paper is to develop current mathematical models of cost, time, and quality tradeoffs in conditions that parameters of project activities are estimated uncertainly by grey numbers. In some projects like construction projects, activities can be done within a much shorter time by increasing in the resources, while project's cost may rise at the same time. In such situations, managers are usually required to determine the best combination of cost, time, and quality parameters of the activities, although their information regarding these parameters is limited and rather incomplete. The greyness of these parameters in the proposed method can aid managers to deal with these conditions. The most important aspect of the proposed model is that it considers uncertainty of the project planning data in the form of grey numbers. A combination of fuzzy goal programming and grey linear programming is also developed to solve the proposed model. Finally, this model will provide the managers with a stronger ability to face with uncertainty in project management and planning. The application of this model is examined in a numerical example. As its major finding, the model determines an optimal range in which the project managers can respond to intrinsic changes that may occur in the parameters during a project.
Original languageEnglish
Pages (from-to)117–126
Number of pages10
JournalThe International Journal of Advanced Manufacturing Technology
Issue number1-4
Early online date20 Nov 2013
Publication statusPublished - Mar 2014
Externally publishedYes


  • Project management
  • Time, cost, and quality tradeoff
  • The iron triangle
  • Fuzzy goal programming
  • Grey numbers


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