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Project time–cost trade-off scheduling: a hybrid optimization approach

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Abstract

This paper develops a hybrid approach for stochastic time–cost trade-off problem (STCTP) in PERT networks of project management, where activities are subjected to linear cost functions. The main objective of proposed approach is to improve the project completion probability in a prespecified deadline from a risky value to a confident predefined probability. To this end, we construct a nonlinear mathematical program with decision variables of activity mean durations, in which the objective function is concerned with minimization of project crashing direct cost. In order to solve the constructed model, we present a hybrid approach based on cutting plane method and Monte Carlo (MC) simulation. To illustrate the process of proposed approach, the approach was coded using MATLAB 7.6.0 and two illustrative examples are discussed. The results obtained from the computational study show that the proposed algorithm is an effective approach for the STCTP.

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References

  1. Fulkerson DR (1961) A network flow computation for project cost curve. Manag Sci 7(2):167–178

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  3. Pulat PS, Horn SJ (1996) Time–resource tradeoff problem. IEEE Trans Eng Manage 43(4):411–417

    Article  Google Scholar 

  4. Crowston W, Thompson GL, Decision CPM (1967) A method for simultaneously planning, scheduling, and control of projects. Oper Res 15(3):407–426

    Article  Google Scholar 

  5. Robinson DR (1975) A dynamic programming solution to cost-time tradeoff for CPM. Manag Sci 22(2):158–166

    Article  MATH  Google Scholar 

  6. Harvey RT, Patterson JH (1979) An implicit enumeration algorithm for the time/cost tradeoff problem in project network analysis. Found Control Eng 4:107–117

    MATH  MathSciNet  Google Scholar 

  7. Demeulemeester B, Elmaghraby SE, Herroelen W (1996) Optimal procedures for the discrete time/cost trade-off problem in project networks. Eur J Oper Res 88(1):50–68

    Article  MATH  Google Scholar 

  8. Demeulemeester B, 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(11):1153–1163

    MATH  Google Scholar 

  9. Tavares LV (1990) A multi stage non-deterministic model for a project scheduling under resource consideration. Eur J Oper Res 49(1):92–101

    Article  Google Scholar 

  10. Vanhoucke M, Debels D (2007) The discrete time/cost trade-off problem: extensions and heuristic procedures. J Sched 10(4/5):311–326

    Article  MATH  Google Scholar 

  11. Aghaie A, Mokhtari H (2009) Ant colony optimization algorithm for stochastic project crashing problem in PERT networks using MC simulation. Int J Adv Manuf Technol 45:1051–1067

    Article  Google Scholar 

  12. Lamberson LR, Hocking RR (1970) Optimum time compression in project scheduling. Manag Sci 16(10):B597–B606

    Article  Google Scholar 

  13. Berman EB (1964) Resource allocation in PERT network under continuous time–cost functions. Manag Sci 10(4):734–745

    Article  Google Scholar 

  14. Falk J, Horowitz J (1972) Critical path problem with concave cost–time curves. Manag Sci 19(4):446–455

    Article  MATH  Google Scholar 

  15. Kuyumcu A, Garcia-Diaz A. A decomposition approach to project compression with Concave activity cost functions. IIE Trans 1994;(26):63–73.

  16. Vrat P, Kriengkrairut C (1986) A goal programming model for project crashing with piecewise linear time–cost trade-off. Eng Costs Prod Econ 10(1/2):161–172

    Google Scholar 

  17. Kelley JE (1961) Critical-path planning and scheduling: mathematical basis. Oper Res 9(3):296–320

    Article  MATH  MathSciNet  Google Scholar 

  18. Deckro RF, Hebert JE, Verdini WA, Grimsurd PH, Venkateshwar E (1995) Nonlinear time–cost tradeoff models in project management. J Comput Ind Eng 28(2):219–229

    Article  Google Scholar 

  19. Leu S, Chen A, Yang C (2001) A GA-based fuzzy optimal model for construction time cost trade off. Int J Proj Manag 19(1):47–58

    Article  Google Scholar 

  20. Burns SA, Liu L, Weifeng C (1996) The Lp/Ip hybrid method for construction time cost trade off analysis. Constr Manag Econ 14(3):265–275

    Article  Google Scholar 

  21. Chua DKH, Chan WT, Govindan K (1997) A time cost trade off model with resource consideration using genetic algorithm. Civ Eng Environ Syst 14:291–311

    Article  Google Scholar 

  22. 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(1):279–295

    Article  MATH  Google Scholar 

  23. SK GOYAL (1975) A note on “A Simple CPM Time–Cost Tradeoff Algorithm”. Manag Sci 21(6):718–722

    Article  Google Scholar 

  24. Siemens N (1971) A simple CPM time–cost tradeoff algorithm. Manag Sci 17(6):354–363

    Article  Google Scholar 

  25. Herroelen W, Leus R (2005) Project scheduling under uncertainty: survey and research potentials. Eur J Oper Res 165(2):289–306

    Article  MATH  MathSciNet  Google Scholar 

  26. Bowman RA (1994) Stochastic gradient-based time–cost tradeoffs in PERT networks using simulation. Ann Oper Res 53(1):533–551

    Article  MATH  MathSciNet  Google Scholar 

  27. Abbasi G, Mukattash AM (2001) Crashing PERT networks using mathematical programming. Int J Proj Manag 19(3):181–188

    Article  Google Scholar 

  28. Arisawa S, Elmaghraby SE (1972) Optimal time–cost trade-offs in GERT networks. Manag Sci 18(11):589–599

    Article  MATH  MathSciNet  Google Scholar 

  29. 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(2):149–162

    Article  Google Scholar 

  30. Sunde L, Lichtenberg S (1995) Net-present value cost/time trade off. Int J Proj Manag 13(1):45–49

    Article  Google Scholar 

  31. Foldes S, Soumis F (1993) PERT and crashing revisited: mathematical generalization. Eur J Oper Res 64(2):286–294

    Article  MATH  Google Scholar 

  32. 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

    Article  MATH  Google Scholar 

  33. Bergman RL (2009) A heuristic procedure for solving the dynamic probabilistic project expediting problem. Eur J Oper Res 192(1):125–137

    Article  MathSciNet  Google Scholar 

  34. Mitchell G, Klastorin T (2007) An effective methodology for the stochastic project compression problem. IIE Trans 39(10):957–969

    Article  Google Scholar 

  35. Godinho PC, Costa JP (2007) A stochastic multimode model for time cost tradeoffs under management flexibility. OR Spectrum 29(2):311–334

    Article  MATH  Google Scholar 

  36. Haga W, Marold K (2004) A simulation approach to the PERT/CPM time–cost trade-off problem. Proj Manage J 35(2):31–37

    Google Scholar 

  37. Haga W, Marold K (2005) Monitoring and control of PERT networks. Bus Rev Cambridge 3(2):240–245

    Google Scholar 

  38. 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(1):140–152

    Article  Google Scholar 

  39. Feng CW, Liu L, Burns SA (2000) Stochastic construction time–cost trade off analysis. J Comput Civil Eng 14(2):117–126

    Article  Google Scholar 

  40. Azaron A, Perkgoz C, Sakawa M (2005) A genetic algorithm approach for the time–cost trade-off in PERT networks. Appl Math Comput 168(2):1317–1339

    Article  MATH  MathSciNet  Google Scholar 

  41. Azaron A, Katagiri H, Sakawa M, Kato K, Memariani A (2006) A multi objective resource allocation problem in PERT networks. Eur J Oper Res 172(3):838–854

    Article  MATH  MathSciNet  Google Scholar 

  42. Azaron A, Tavakkoli-Moghaddam R (2006) A multi objective resource allocation problem in dynamic PERT networks. Eur J Oper Res 181(1):163–174

    MATH  MathSciNet  Google Scholar 

  43. Azaron A, Katagiri H, Sakawa M (2007) Time–cost trade-off via optimal control theory in Markov PERT networks. Ann Oper Res 150(1):47–64

    Article  MATH  MathSciNet  Google Scholar 

  44. Eshtehardian E, Afshar A, Abbasnia R (2008) Time–cost optimization: using GA and fuzzy sets theory for uncertainties in cost. Constr Manag Econ 26(7):679–691

    Article  Google Scholar 

  45. Wolstenholme LC (1997) A Characterization of Phase Type Distributions, Statistical Research Paper No. 18, City University, November 1997, ISBN 1 901615 18 9

  46. Crawford, Statistical Course Textbook: 200A (2008) Department of Statistics, University of California, Berkeley, Fall 2008

  47. Kelly JE (1960) The cutting plane method for solving convex programs. J SIAM VIII(4):703–712

    Google Scholar 

  48. Martin JJ (1965) Distribution of the time through a directed, acyclic network. Oper Res 13(1):46–66

    Article  MATH  Google Scholar 

  49. Van Slyke RM (1963) Monte Carlo methods AND the PERT problem. Oper Res 11(5):839–860

    Article  Google Scholar 

  50. Signal CE, Pritsker AAB, Solberg JJ (1979) The use of cutsets in Monte Carlo analysis of stochastic networks. Math Comput Simul 21(4):376–384

    Article  Google Scholar 

  51. Bowman RA (1995) Efficient estimation of arc criticalities in stochastic activity networks. Manag Sci 41(1):58–67

    Article  MATH  MathSciNet  Google Scholar 

  52. Soroush HM (1994) The most critical path in a PERT Network. J Opl Res Soc 45(3):287–300

    MATH  MathSciNet  Google Scholar 

  53. Fatemi Ghomi SMT, Teimouri E (2002) Path critical index and activity critical index in PERT networks. Eur J Oper Res 141(1):147–152

    Article  MATH  MathSciNet  Google Scholar 

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Mokhtari, H., Aghaie, A., Rahimi, J. et al. Project time–cost trade-off scheduling: a hybrid optimization approach. Int J Adv Manuf Technol 50, 811–822 (2010). https://doi.org/10.1007/s00170-010-2543-4

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