Journal of Mathematical Modelling and Algorithms

, Volume 9, Issue 4, pp 357–373 | Cite as

Tri-directional Scheduling Scheme: Theory and Computation

  • H. R. YoosefzadehEmail author
  • Hamed R. Tareghian
  • M. H. Farahi


In this paper we introduce a new scheduling scheme based on so called tri-directional scheduling strategy to solve the well known resource constrained project scheduling problem. In order to demonstrate the effectiveness of tri-directional scheduling scheme, it is incorporated into a priority rule based parallel scheduling scheme. Theoretical and numerical investigations show that the tri-directional scheduling scheme outperforms forward, backward and even bidirectional schemes depending on the problem structure and the priority rule used. Based on empirical evidence, it seems that as the number of activities are increased, the tri-directional scheduling scheme performs better irrespective of the priority rule used. This suggests that tri-directional scheme should also be applied within the category of heuristic methods.


Project management Scheduling schemes Heuristic algorithms Bidirectional scheduling scheme 


  1. 1.
    Agarwal, R., Tiwari, M.K.., Mukherjee, S.K.: Artificial immune system based approach for solving resource constraint project scheduling problem. Int. J. Adv. Manuf. Technol. 34, 584–593 (2007). doi: 10.1007/s00170-006-06312 CrossRefGoogle Scholar
  2. 2.
    Blazewicz, J., Lenstra, J., Rinnoy, K.A.: Scheduling subject to resource constraints: classification and complexity. Discrete Appl. Math. 5, 11–24 (1983)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bouleimen, K., Lecocq, H.: A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple modes version. Eur. J. Oper. Res. 149, 268–281 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Brucker, P., Knust, S., Schoo, A., Thiele, O.: A branch and bound algorithm for the resource-constrained project scheduling problem. Eur. J. Oper. Res. 107, 272–288 (1998)zbMATHCrossRefGoogle Scholar
  5. 5.
    Cho, J., Kim, Y.D.: A simulated annealing algorithm for resource-constrained project scheduling problems. J. Oper. Res. Soc. 48, 736–744 (1997)zbMATHGoogle Scholar
  6. 6.
    Hartmann, S.: A self-adapting genetic algorithm for project scheduling under resource constraints. Nav. Res. Logist. 49, 433–448 (2002)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Icmeli, O., Rom, W.O.: Solving resource constrained project scheduling problem with optimization subroutine library. Comput. Oper. Res. 23, 801–817 (1996)zbMATHCrossRefGoogle Scholar
  8. 8.
    Klein, R.: Bidirectional planning: improving priority rule-based heuristics for scheduling resource-constrained projects. Eur. J. Oper. Res. 127, 619–638 (2000)zbMATHCrossRefGoogle Scholar
  9. 9.
    Klein, R.: Scheduling of Resource Constrained Projects. Kluwer, Dordrecht (2000)zbMATHGoogle Scholar
  10. 10.
    Kolisch, R.: Project Scheduling Under Resource Constraints Efficient Heuristics for Several Problem Classes. Physica, Heidelberg (1995)Google Scholar
  11. 11.
    Kolisch, R.: Serial and parallel resource-constrained project scheduling methods revisited—theory and computation. Eur. J. Oper. Res. 90, 320–333 (1996)zbMATHCrossRefGoogle Scholar
  12. 12.
    Kolisch, R., Schwindt, C., Sprecher, A.: Benchmark instances for project scheduling problems. In: Weglarz, J. (ed.) Project Scheduling. Recent Methods, Algorithms and Applications. Kluwer’s International Series (1998)Google Scholar
  13. 13.
    Kolisch, R., Hartmann, S.: Experimental investigation of heuristics for resource-constrained project scheduling: an update. Eur. J. Oper. Res. 174, 23–37 (2006)zbMATHCrossRefGoogle Scholar
  14. 14.
    Kumanan, S., Jose, G.J., Raja, K.: Multi-project scheduling using a heuristic and a genetic algorithm. Int. J. Adv. Manuf. Technol. 31, 360–366 (2006)CrossRefGoogle Scholar
  15. 15.
    Kuo-Ching, Y., Shih-Wei, L., Zne-Jung, L.: Hybrid-directional planning: improving improvement heuristics for scheduling resource-constrained projects. Int. J. Adv. Manuf. Technol. 41, 358–366 (2009)CrossRefGoogle Scholar
  16. 16.
    Petrovic, R.: Optimization of resource allocation in project planning. Oper. Res. 16, 559–586 (1968)CrossRefGoogle Scholar
  17. 17.
    Pritsker, A., Watters, L., Wolfe, P.: Multi-project scheduling with limited resources: a zero-one programming approach. Manage. Sci. 16, 93–107 (1969)CrossRefGoogle Scholar
  18. 18.
    Reddy, J.P., Kumanan, S., Chetty, O.V.K.: Application of Petri nets and a genetic algorithm to multi-mode multi-resource constrained project scheduling. Int. J. Adv. Manuf. Technol. 17, 305–314 (2001)CrossRefGoogle Scholar
  19. 19.
    Schrage, L.: Solving resource-constrained network problems by implicit enumeration—nonpreemptive case. Oper. Res. 18, 263–278 (1970)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Shukla, S.K., Son, Y.J., Tiwari, M.K.: Fuzzy-based adaptive samplesort simulated annealing for resource-constrained project scheduling. Int. J. Adv. Manuf. Technol. 36, 982–995 (2008). doi: 10.1007/s00170-006-0907-6 CrossRefGoogle Scholar
  21. 21.
    Thomas, P.R., Salhi, S.: A tabu search approach for the resource constrained project scheduling problem. J. Heuristics 4, 123–139 (1998)zbMATHCrossRefGoogle Scholar
  22. 22.
    Valss, V., Ballestin, F., Quintanilla, S.: Justification and RCPSP: a technique that pays. Eur. J. Oper. Res. 165, 375–386 (2005)CrossRefGoogle Scholar
  23. 23.
    Zamani, M.R.: A high-performance exact method for the resource-constrained project scheduling problem. Comput. Oper. Res. 28, 1387–1401 (2001)zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • H. R. Yoosefzadeh
    • 1
    Email author
  • Hamed R. Tareghian
    • 1
  • M. H. Farahi
    • 1
  1. 1.Faculty of Mathematical SciencesFerdowsi University of MashhadMashhadIran

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