International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

A branch-and-bound procedure for resource leveling in multi-mode resource constraint project scheduling problem

Author Affiliations

  • 1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, IRAN

Res. J. Recent Sci., Volume 1, Issue (7), Pages 33-38, July,2 (2012)


This paper presents an exact solution for MRCPSP model (Multi Mode Resource Constraints Project Scheduling Problem). Each activity could be performed in various ways (mode) and in every style of performance (mode) a specific amount of time and resources are used for each activity. The solution used here includes branch and bound and the study aims to level resources. In the end some sample problems are solved using expanded algorithm and the results are reported and analyzed


  1. Slowinski R., Two approaches to problems of resource allocation among project activities – A comparative study, J.Oper. Res. Soci.,, 711–723 (1980)
  2. Speranza M. and Vercellis C., Hierarchical models for multi-project planning and scheduling, Eur.J. Oper Res.,64, 312–325 (1993)
  3. Hartmann S. and Sprecher A., A note on hierarchical models for multi-project planning and scheduling, Eur. J. Oper Res., 94, 377– 383 (1996)
  4. Sprecher A., Hartmann S. and Drexl A., An exact algorithm for the project scheduling with multiple modes, OR. Spe., 19, 195–203 (1997)
  5. Hartmann S. and Drexl A., Project scheduling with multiple modes: A comparison of exact algorithms, Net., 32, 283–297 (1998)
  6. Sprecher A. and Drexl A., Solving multi-mode resource-constrained project scheduling problems by a simple, general and powerful sequencing algorithm, Eur. J. Oper Res.,107, 431–450 (1998)
  7. Zhu G., Bard J. and Tu G., A branch-and-cut procedure for the multimode resource-constrained project-scheduling problem, J. Comp., 18(3), 377–390 (2006)
  8. Boctor F., Heuristics for scheduling projects with resource restrictions and several resource-duration modes, Int. J. of Prod. Res., 31(11), 2547–2558 (1993)
  9. Drexl A. and Grόnewald J., Non preemptive multi-mode resource-constrained project scheduling, IIE Trans., 25, 74–81 (1993)
  10. Ozdamar L. and Ulusoy G., A local constraint based analysis approach to project scheduling under general resource constraints, Eur. J. Oper Res., 79, 287–298 (1994)
  11. Boctor F., A new and efficient heuristic for scheduling projects with resource restrictions and multiple execution modes, Eur. J. Oper Res., 90, 349–361 (1996)
  12. Kolisch R., Drexl A., Local search for non-preemptive multi-mode resource constrained project scheduling, IIE. Trans., 29, 987–999 (1997)
  13. Knotts G., Dror M., Hartman B., Agent-based project scheduling, IIE. Trans., 32 (5), 387–401(2000)
  14. Lova A., Tormos P. and Barber F., Multi-mode resource constrained project scheduling: Scheduling schemes, priority rules and mode selection rules, Intelig. Artif., 30, 69–86 (2006)
  15. Patel M., Jain S., Jain D. and Patel B., Prevalence of Different Factors Responsible for Infertility, Res. J. Recent Sci., 1(ISC-2011), 207-211 (2012)
  16. Zangeneh M., Simulation of Perturbation in the PG, Res. J. Recent Sci., 1(1), 77-80 (2012)
  17. Φzdamar L., A genetic algorithm approach to a general category project scheduling problem,IEEE.Trans. on Sys., Man, and Cybernetics, Part C: Applications and Reviews 29, 44–59 (1999)
  18. Hartmann S., Project scheduling with multiple modes: A genetic algorithm,Ann. of Oper. Res.,102, 111-135 (2001)
  19. Alcaraz J., Maroto C. and Ruiz R., Solving the multi-mode resource-constrained project scheduling problem with genetic algorithms, J. Oper. Res. Soci.,54, 614–626 (2003)
  20. Lova A., Tormos P., Cervantes M. and Barber F., An efficient hybrid genetic algorithm for scheduling projects with resource constraints and multiple execution modes, Int. J. of Prod. Econ.,117 (2), 302-316 (2009)
  21. Jozefowska J., Mika M., Rozycki R., Waligora G. and Weglarz J., Simulated annealing for multi-mode resource-constrained project scheduling, Ann. of Oper. Res.,102, 137–155 (2001)
  22. Bouleimen K. and Lecocq H., A new efficient simulated annealing algorithm for the resource-constrained project scheduling problem and its multiple modeversion, Eur. J. Oper Res.,149, 268–281 (2003)
  23. Zhang H., Tam C. and Li H., Multimode project scheduling based on particle swarm optimization, Comp Aided. Civ. and Infra. Eng., 21, 93–103(2006)
  24. Ranjbar M., De Reyck B., and Kianfar F., A hybrid scatter-search for the discrete time/resource trade-off problem in project scheduling, Eur. J. Oper Res.,193 (1), 35–48 (2008)
  25. Bandelloni M., Tucci M. and Rinaldi R., Optimal resource leveling using non-serial dynamic programming,Eur. J. Oper Res.,78, 162-177 (1994)
  26. Demeulemeester E., Minimizing resource availability costs in time-limited project networks, Manag. Sci., 41, 1590-1598 (1995)
  27. Savin D., Alkass S. and Fazio P., A procedure for calculating the weight-matrix of a neural network for resource leveling, Adv. in Eng. Soft., 28, 277-283 (1997)
  28. Neumann K. and Zimmermann J., Procedures for resource leveling and net present value problems in project scheduling with general temporal and resource constraints, Eur. J. Oper Res.,127, 425-443 (2000)