pp 1–24 | Cite as

Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms

  • Erfan Babaee Tirkolaee
  • Alireza Goli
  • Milad Hematian
  • Arun Kumar Sangaiah
  • Tao HanEmail author


This study addresses the multi-objective multi-mode resource-constrained project scheduling problem with payment planning where the activities can be done through one of the possible modes and the objectives are to maximize the net present value and minimize the completion time concurrently. Moreover, renewable resources including manpower, machinery, and equipment as well as non-renewable ones such as consumable resources and budget are considered to make the model closer to the real-world. To this end, a non-linear programming model is proposed to formulate the problem based on the suggested assumptions. To validate the model, several random instances are designed and solved by GAMS-BARON solver applying the ε-constraint method. For the high NP-hardness of the problem, we develop two metaheuristics of non-dominated sorting genetic algorithm II and multi-objective simulated annealing algorithm to solve the problem. Finally, the performances of the proposed solution techniques are evaluated using some well-known efficient criteria.


Multi-mode resource-constrained project scheduling problem NPV Payment planning ε-Constraint method NSGA-II MOSA 

Mathematics Subject Classification

90Cxx 90-08 68Txx 90B35 90B50 



This work was supported in part by International Scientific and Technological Cooperation Project of Dongguan (2016508102011), in part by Science and Technology Planning Project of Guangdong Province (2016A020210142) and in part by Guangdong provincial key platform and major scientific research projects (2017GXJK174).


Funding was provided by International Scientific and Techological Cooperation Project of Dongguan (Grant No. 2016508102011).


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Copyright information

© Springer-Verlag GmbH Austria, part of Springer Nature 2019

Authors and Affiliations

  • Erfan Babaee Tirkolaee
    • 1
    • 2
  • Alireza Goli
    • 3
  • Milad Hematian
    • 1
  • Arun Kumar Sangaiah
    • 4
  • Tao Han
    • 5
    Email author
  1. 1.Department of Industrial EngineeringMazandaran University of Science and TechnologyBabolIran
  2. 2.Young Researchers and Elite Club, Ayatollah Amoli BranchIslamic Azad UniversityAmolIran
  3. 3.Department of Industrial EngineeringYazd UniversityYazdIran
  4. 4.School of Computing Science and EngineeringVellore Institute of TechnologyVelloreIndia
  5. 5.DGUT-CNAM InstituteDongguan University of TechnologyDongguanPeople’s Republic of China

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