Skip to main content
SpringerLink
Log in

Ant colony optimization algorithm for stochastic project crashing problem in PERT networks using MC simulation

  • ORIGINAL ARTICLE
  • Published:
The International Journal of Advanced Manufacturing Technology Aims and scope Submit manuscript

Abstract

This paper describes a new approach based on ant colony optimization (ACO) metaheuristic and Monte Carlo (MC) simulation technique, for project crashing problem (PCP) under uncertainties. To our knowledge, this is the first application of ACO technique for the stochastic project crashing problem (SPCP), in the published literature. A confidence-level-based approach has been proposed for SPCP in program evaluation and review technique (PERT) type networks, where activities are subjected to discrete cost functions and assumed to be exponentially distributed. The objective of the proposed model is to optimally improve the project completion probability in a prespecified due date based on a predefined probability. In order to solve the constructed model, we apply the ACO algorithm and path criticality index, together. The proposed approach applies the path criticality concept in order to select the most critical path by using MC simulation technique. Then, the developed ACO is used to solve a nonlinear integer mathematical programming for selected path. In order to demonstrate the model effectiveness, a large scale illustrative example has been presented and several computational experiments are conducted to determine the appropriate levels of ACO parameters, which lead to the accurate results with reasonable computational time. Finally, a comparative study has been conducted to validate the ACO approach, using several randomly generated problems.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Crowston W, Thompson GL (1967) Decision CPM: a method for simultaneous planning, scheduling, and control of projects. Oper Res 15:407–426. doi:10.1287/opre.15.3.407

    Article  Google Scholar 

  2. Robinson DR (1975) A dynamic programming solution to cost-time tradeoff for CPM. Manage Sci 22:158–166. doi:10.1287/mnsc.22.2.158

    Article  MATH  Google Scholar 

  3. Demeulemeester E, Elmaghraby SE, Herroelen W (1996) Optimal procedures for the discrete time/cost trade-off problem in project networks. Eur J Oper Res 88:50–68. doi:10.1016/0377-2217(94) 00181-2

    Article  MATH  Google Scholar 

  4. Demeulemeester E, De Reyck B, Foubert B, Herroelen W, Vanhoucke M (1998) New computational results on the discrete time/cost trade-off problem in project networks. J Oper Res Soc 49:1153–1163

    Article  MATH  Google Scholar 

  5. Tavares LV (1990) A multi-stage non-deterministic model for a project scheduling under resource constraints. Eur J Oper Res 49:92–101. doi:10.1016/0377-2217(90)90123-S

    Article  Google Scholar 

  6. Vanhoucke M, Debels D (2007) The discrete time/cost trade-off problem: extensions and heuristic procedures. J Sched 10:311–326. doi:10.1007/s10951-007-0031-y

    Article  MATH  Google Scholar 

  7. Fulkerson DR (1961) A network flow computation for project cost curves. Manage Sci 7:167–178. doi:10.1287/mnsc.7.2.167

    Article  MATH  MathSciNet  Google Scholar 

  8. Cohen I, Golany B, Shtub A (2007) The stochastic time–cost tradeoff problem: a robust optimization approach. Networks 49(2):175–188. doi:10.1002/net.20153

    Article  MATH  MathSciNet  Google Scholar 

  9. Pulat PS, Horn SJ (1996) Time–resource tradeoff problem. IEEE Trans Eng Manage 43(4):411–417. doi:10.1109/17.543983

    Article  Google Scholar 

  10. Lamberson LR, Hocking RR (1970) Optimum time compression in project scheduling. Manage Sci 16:B597–B606. doi:10.1287/mnsc.16.10.B597

    Article  Google Scholar 

  11. Berman EB (1964) Resource allocation in a PERT network under continuous activity time–cost functions. Manage Sci 10:734–745. doi:10.1287/mnsc.10.4.734

    Article  Google Scholar 

  12. Falk JE, Horowitz JL (1972) Critical path problems with concave cost–time curves. Manage Sci 19:446–455. doi:10.1287/mnsc.19.4.446

    Article  MATH  Google Scholar 

  13. Vrat P, Kriengkrairut C (1986) A goal programming model for project crashing with piecewise linear time–cost trade-off. Eng Costs Prod Econ 10:161–172

    Google Scholar 

  14. James E, Kelley JR (1961) Critical-path planning and scheduling: mathematical basis. Oper Res 9:296–320. doi:10.1287/opre.9.3.296

    Article  MATH  Google Scholar 

  15. Deckro RF, Hebert JE, verdini WA, Grimsrud PH, Venkateshwar S (1995) Nonlinear time/cost trade off models in project management. Comput Ind Eng 28(2):219–229. doi:10.1016/0360-8352(94)00199-W

    Article  Google Scholar 

  16. Leu S, Chen A, Yang C (2001) A GA-based fuzzy optimal model for construction time–cost trade-off. Int J Proj Manag 19:47–58. doi:10.1016/S0263-7863(99)00035-6

    Article  Google Scholar 

  17. Burns SA, Liu L, Weifeng C (1996) The LP/IP hybrid method for construction time cost trade off analysis. Construct Manag Econ 14:265–275. doi:10.1080/014461996373511

    Article  Google Scholar 

  18. Buddhakulsomsiri J, Kim D (2006) Properties of multi-mode resource-constrained project scheduling problems with resource vacations and activity splitting. Eur J Oper Res 175:279–295. doi:10.1016/j.ejor.2005.04.030

    Article  MATH  Google Scholar 

  19. Goyal SK (1975) A note on a simple CPM time–cost trade off algorithm. Manage Sci 21:718–722. doi:10.1287/mnsc.21.6.718

    Article  MATH  Google Scholar 

  20. Siemens N (1971) A simple CPM time–cost trade off algorithm. Manage Sci 17:B354–B363. doi:10.1287/mnsc.17.6.B354

    Article  Google Scholar 

  21. Herroelen W, Leus R (2005) Project scheduling under uncertainty: survey and research potentials. Eur J Oper Res 165:289–306. doi:10.1016/j.ejor.2004.04.002

    Article  MATH  Google Scholar 

  22. Bowman RA (1994) Stochastic gradient-based time-cost tradeoffs in PERT networks using simulation. Ann Oper Res 53:533–551. doi:10.1007/BF02136842

    Article  MATH  MathSciNet  Google Scholar 

  23. Abbasi GY, Mukattash AM (2001) Crashing PERT networks using mathematical programming. Int J Proj Manag 19:181–188. doi:10.1016/S0263-7863(99)00061-7

    Article  Google Scholar 

  24. Arisawa S, Elmaghraby SE (1972) Optimal time–cost trade-offs in GERT networks. Manage Sci 18(11):589–599. doi:10.1287/mnsc.18.11.589

    Article  MATH  MathSciNet  Google Scholar 

  25. Golenko-Ginzberg D, Gonik A (1998) A heuristic for network project scheduling with random activity durations depending on the resource allocation. Int J Prod Econ 55:149–162. doi:10.1016/S0925-5273(98)00044-9

    Article  Google Scholar 

  26. Sunde L, Lichtenberg S (1995) Net-present-value cost/time trade off. Int J Proj Manag 13(1):45–49. doi:10.1016/0263-7863(95)95703-G

    Article  Google Scholar 

  27. Foldes S, Soumis F (1993) PERT and crashing revisited: mathematical generalization. Eur J Oper Res 64:286–294. doi:10.1016/0377-2217(93) 90183-N

    Article  MATH  Google Scholar 

  28. Gutjahr WJ, Strauss C, Wagner E (2000) A stochastic branch-and-bound approach to activity crashing in project management. INFORMS J Comput 12(2):125–135. doi:10.1287/ijoc.12.2.125.11894

    Article  MATH  Google Scholar 

  29. Bergman RL (2009) A heuristic procedure for solving the dynamic probabilistic project expediting problem. Eur J Oper Res 192(1):125–137. doi:10.1016/j.ejor.2007.09.010

    Article  MathSciNet  Google Scholar 

  30. Mitchell G, Klastorin T (2007) An effective methodology for the stochastic project compression problem. IIE Trans 39:957–969. doi:10.1080/07408170701315347

    Article  Google Scholar 

  31. Godinho PC, Costa JP (2007) A stochastic multimode model for time–cost trade offs under management flexibility. OR Spectrum 29:311–334. doi:10.1007/s00291-006-0037-4

    Article  MATH  Google Scholar 

  32. Yau C, Ritche E (1990) Project compression: a method for speeding up resource constrained projects which preserve the activity schedule. Eur J Oper Res 49:140–152. doi:10.1016/0377-2217(90)90125-U

    Article  Google Scholar 

  33. Feng CW, Liu L, Burns SA (2000) Stochastic construction time–cost trade off analysis. J Comput Civ Eng 14(2):117–126. doi:10.1061/(ASCE) 0887-3801(2000)14:2(117)

    Article  Google Scholar 

  34. Azaron A, Perkgoz C, Sakawa M (2005) A genetic algorithm approach for the time–cost trade-off in PERT networks. Appl Math Comput 168:1317–1339. doi:10.1016/j.amc.2004.10.021

    Article  MATH  MathSciNet  Google Scholar 

  35. Azaron A, Tavakkoli-Moghaddam R (2006) A multi objective resource allocation problem in dynamic PERT networks. Appl Math Comput 181:163–174. doi:10.1016/j.amc.2006.01.027

    Article  MATH  MathSciNet  Google Scholar 

  36. Azaron A, Katagiri H, Sakawa M (2007) Time–cost trade-off via optimal control theory in Markov PERT networks. Ann Oper Res 150:47–64. doi:10.1007/s10479-006-0149-x

    Article  MATH  MathSciNet  Google Scholar 

  37. Eshtehardian E, Afshar A, Abbasnia R (2008) Time–cost optimization: using GA and fuzzy sets theory for uncertainties in cost. Construct Manag Econ 26:679–691. doi:10.1080/01446190802036128

    Article  Google Scholar 

  38. Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE Trans Syst Man Cybern Part B Cybern 26(1):29–41. doi:10.1109/3477.484436

    Article  Google Scholar 

  39. Dorigo M, Gambardella LM (1997) Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE Trans Evol Comput 7(1):53–66. doi:10.1109/4235.585892

    Article  Google Scholar 

  40. Heinonen J, Pettersson F (2007) Hybrid ant colony optimization and visibility studies applied to a job-shop scheduling problem. Appl Math Comput 187:989–998. doi:10.1016/j.amc.2006.09.023

    Article  MATH  MathSciNet  Google Scholar 

  41. Seckiner SU, Kurt M (2008) Ant colony optimization for the job rotation scheduling problem. Appl Math Comput 201:149–160. doi:10.1016/j.amc.2007.12.006

    Article  MATH  MathSciNet  Google Scholar 

  42. Talbi E-G, Roux O, Fonlupt C, Robillard D (2001) Parallel ant colonies for the quadratic assignment problem. Future Gener Comput Syst 17(4):441–449. doi:10.1016/S0167-739X(99)00124-7

    Article  MATH  Google Scholar 

  43. Kong M, Tian P, Kao Y (2008) A new ant colony optimization algorithm for the multidimensional knapsack problem. Comput Oper Res 35:2672–2683

    MATH  Google Scholar 

  44. Hani Y, Amodeo L, Yalaoui F, Chen H (2007) Ant colony optimization for solving an industrial layout problem. Eur J Oper Res 183:633–642. doi:10.1016/j.ejor.2006.10.032

    Article  MATH  Google Scholar 

  45. Yin PY, Wang JY (2006) Ant colony optimization for the nonlinear resource allocation problem. Appl Math Comput 174:1438–1453. doi:10.1016/j.amc.2005.05.042

    Article  MATH  MathSciNet  Google Scholar 

  46. Chaharsooghi SK, Meimand Kermani AH (2008) An effective ant colony optimization algorithm (ACO) for multi-objective resource allocation problem (MORAP). Appl Math Comput 200:167–177. doi:10.1016/j.amc.2007.09.070

    Article  MATH  MathSciNet  Google Scholar 

  47. Martin JJ (1965) Distribution of the time through a directed, acyclic network. Oper Res 13:46–66. doi:10.1287/opre.13.1.46

    Article  MATH  Google Scholar 

  48. Van Slyke RM (1963) Monte Carlo methods and the PERT problem. Oper Res 11:839–860. doi:10.1287/opre.11.5.839

    Article  Google Scholar 

  49. Sigal CE, Pritsker AAB, Solberg JJ (1979) The use of cut sets in Monte Carlo analysis of stochastic networks. Math Comput Simul 21:376–384. doi:10.1016/0378-4754(79)90007-7

    Article  MATH  MathSciNet  Google Scholar 

  50. Bowman RA (1995) Efficient estimation of arc criticalities in stochastic activity networks. Manage Sci 41(1):58–67. doi:10.1287/mnsc.41.1.58

    Article  MATH  MathSciNet  Google Scholar 

  51. Soroush HM (1994) The most critical path in a PERT network. J Oper Res Soc 45(3):287–300

    Article  MATH  MathSciNet  Google Scholar 

  52. Fatemi Ghomi SM, Teimouri TE (2002) Path critical index and activity critical index in PERT networks. Eur J Oper Res 141:147–152. doi:10.1016/S0377-2217(01)00268-5

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Industrial Engineering, K.N. Toosi University of Technology, Tehran, Iran

    Abdollah Aghaie & Hadi Mokhtari

Authors
  1. Abdollah Aghaie
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hadi Mokhtari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdollah Aghaie.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aghaie, A., Mokhtari, H. Ant colony optimization algorithm for stochastic project crashing problem in PERT networks using MC simulation. Int J Adv Manuf Technol 45, 1051 (2009). https://doi.org/10.1007/s00170-009-2051-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00170-009-2051-6

Keywords

Search

Navigation