Allocating slacks in stochastic PERT network


The SPERT problem was defined, in a game theory framework, as the fair allocation of the slack or float among the activities in a PERT network previous to the execution of the project. Previous approaches tackle with this problem imposing that the durations of the activities are deterministic. In this paper, we extend the SPERT problem into a stochastic framework defining a new solution that tries also to maintain the good performance of some other approaches that have been defined for the deterministic case. Afterward, we present a polynomial algorithm for this new solution that also could be used for the calculation of other approaches founded in the deterministic SPERT literature.

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    Let us observe that for the case in which the weight is the range, this assumption is not too restrictive since the maximum and the minimum expected duration are usually calculated in terms of workdays.


  1. 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

    Article  Google Scholar 

  2. Bergantiños G, Sánchez E (2002a) NTU PERT games. Oper Res Lett 30:130–140

    Article  Google Scholar 

  3. Bergantiños G, Sánchez E (2002b) The proportional rule for problems with constraints and claims. Math Soc Sci 43:225–249

    Article  Google Scholar 

  4. Bergantiños G, Lorenzo L (2008) The equal award principle in problems with constraints and claims. Eur J Oper Res 188:224–239

    Article  Google Scholar 

  5. Brânzei R, Ferrari G, Fragnelli V, Tijs S (2002) Two approaches to the Problem of Sharing Delay Costs in Joint Projects. Ann Oper Res 109:359–374

    Article  Google Scholar 

  6. Brânzei R, Ferrari G, Fragnelli V, Tijs S (2010) A bonus-malus approach to project management. Cent Eur J Oper Res. doi:10.1007/s10100-010-0139-6

  7. Castro J, Gómez D, Tejada J (2008a) A polynomial rule for the problem of sharing delay costs in PERT networks. Comput Oper Res 35:2376–2387

    Article  Google Scholar 

  8. Castro J, Gómez D, Tejada J (2008b) A rule for slack allocation proportional to the duration in a PERT network. Eur J Oper Res 187:556–570

    Article  Google Scholar 

  9. Dodin B (1985) Bounding the project completion time distribution in PERT networks. Oper Res 33:862–880

    Article  Google Scholar 

  10. Lida T (2000) Computing bounds on project duration distribution for stochastic PERT. Nav Res Log 47(7):559–580

    Article  Google Scholar 

  11. Monden Y (1983) Toyota production systems. Industrial Engineering and Management Press, Norcross

    Google Scholar 

  12. Monhor D (2005) On the relevance of the convolution of uniform distributions to the theory of errors. Acta Geod Geophys Hung 40:53–68

    Article  Google Scholar 

  13. Monhor D (2010) A new probabilistic approach to the path criticality in stochastic PERT. Cent Eur J Oper Res. doi:10.1007/s10100-010-0151-x

  14. Rogalska M, Bozejko W, Hejducki Z (2008) Time/cost optimization using hybrid evolutionary algorithm in construction project scheduling. Autom Constr 18:24–31

    Article  Google Scholar 

  15. Shragowitz E, Youseff H, Lu B (2003) Iterative converging algorithms for computing bounds on durations of activities in pert and pert-like models. J Comb Optim 7:5–22

    Article  Google Scholar 

  16. Talbot F, Patterson JH (1978) Efficient integer programming algorithm with network cuts for solving resource-constrained scheduling problems. Manag Sci 24:1163–1174

    Article  Google Scholar 

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Correspondence to Javier Castro.

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Castro, J., Gómez, D. & Tejada, J. Allocating slacks in stochastic PERT network. Cent Eur J Oper Res 22, 37–52 (2014).

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  • Game theory
  • Project scheduling
  • PERT network
  • Slack allocation
  • Polynomial algorithms