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Keywords:
project planning; PERT; Erlang distribution
project planning; PERT; Erlang distribution
Summary:
It is assumed that activity times in stochastic activity networks (SANs) are independent Erlang random variable (r.v.). A recurrence method of determining the $k$th moments of the completion time is presented. Applications are provided for illustration and are used to evaluate the applicability and appropriateness of the Erlang model to represent activity network.
References:
[1] Bendell A., Solomon, D., Carter J. M.: Evaluating project completion times when activity times are Erlang distributed. J. Opl. Res. Soc. 46 (1995), 867–882 DOI 10.1057/jors.1995.118
[2] Devroye L. P.: Inequalities for the completion times of stochastic PERT networks. Math. Oper. Res. 4 (1979), 441–447 DOI 10.1287/moor.4.4.441 | MR 0549130 | Zbl 0427.90053
[3] Elmaghraby S. E.: On the expected duration of PERT type networks. Management Sci. 13 (1967), 299–306 DOI 10.1287/mnsc.13.5.299 | Zbl 0158.38303
[4] Elmaghraby S. E.: The estimation of some network parameters in PERT model of activity network: review and critique. In: Advances in Project Scheduling, Chapter I, Part III (R. Slowinski and J. Weglarz, eds.), Elsevier, Amsterdam 1989, pp. 371–432 MR 1060141
[5] Elmaghraby S. E.: On criticality and sensitivity in activity networks. European J. Oper. Res. 127 (2000), 220–238 DOI 10.1016/S0377-2217(99)00483-X | Zbl 0990.90119
[6] Fulkerson D. R.: Expected critical path lengths in PERT networks. Oper. Res. 10 (1962), 808–817 DOI 10.1287/opre.10.6.808 | Zbl 0124.36304
[7] Kamburowski J.: Normally distributed activity durations in PERT networks. J. Opl. Res. Soc. 36 (1985), 1051–1057 DOI 10.1057/jors.1985.184 | Zbl 0579.90052
[8] Kamburowski J.: An upper bound on the expected completion time of PERT networks. European J. Oper. Res. 21 (1985), 2, 206–212 DOI 10.1016/0377-2217(85)90032-3 | MR 0811084 | Zbl 0569.90047
[9] Kleinrock L.: In: Queuing Systems, Volume I. Wiley, New York 1975
[10] Kulkarni V. G., Adlakha V. G.: Markov and Markov regenerative PERT networks. Oper. Res. 34 (1986), 5, 769–781 DOI 10.1287/opre.34.5.769 | MR 0884303 | Zbl 0615.90042
[11] Loulou R., Beale T.: A comparison of variance reducing techniques in PERT simulations. INFOR Canadian J. Opl. Res. 14 (1976), 259–269 Zbl 0354.62027
[12] Magott J., Skudlarski K.: Estimating the mean completion time of PERT networks with exponentially distributed duration of activities. European J. Oper. Res. 71 (1993), 70–79 DOI 10.1016/0377-2217(93)90261-K
[13] Robillard P.: Expected completion time in PERT networks. Oper. Res. 24 (1976), 177–182 DOI 10.1287/opre.24.1.177 | MR 0406447 | Zbl 0324.90025
[14] Ross S. M.: Stochastic Process. Wiley, New York 1983
[15] Sculli D.: The completion time of PERT networks. J. Opl. Res. Soc. 34 (1983), 155–158 DOI 10.1057/jors.1983.27 | Zbl 0502.90045
[16] Tavares L. V.: A review of the contribution of operational research to project management. European J. Oper. Res. 136 (2002), 1–18 DOI 10.1016/S0377-2217(01)00097-2 | Zbl 1086.90532
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