Document Type : Research Paper
Authors
Abstract
In this paper, a nonlinear multi objective mathematical model for
crashing the PERT network is presented. The main purpose of this
model is minimizing the pessimistic time of critical activities by
allocating more budget. In fact, this model indicates how the budget is
allocated among critical activities. The results show that decreasing
the pessimistic of critical activities lead to decreasing the time and
variance of project completion. This model increases the probability
of project completion on time scheduling. A genetic algorithm is use
to solve the nonlinear model
Keywords
1. Abbasi, Ghaleb Y., Mukattash, Adnan M., Crashing PERT networks
using mathematical programming, International Journal of Project
Management 19, 181-188, 2001.
2. Azaron, Amir, Katagiri, Hideki, Sakawa, Masatoshi, Kato, Kosuke, and
Memariani, Azizollah, A multi-objective resource allocation problem in
PERT networks, European Journal of Operational Research, 2005.
3. Azaron, Amir, Perkgoz, Cahit, and Sakawa, Masatoshi, A genetic
algorithm approach for the time-cost trade-off in PERT networks,
Applied Mathematics and Computation 168, 1317–1339, 2005.
4. Bazaraa MS, Shetty CM. Nonlinear programming theory and
algorithms. New York: Wiley, 1979.
5. Cho JG, Yum BJ. An uncertainty importance measure of activities in
PERT networks. Int J Prod Res, 35(10):2737-2757, 1997.
6. Feng, C.W., Liu, L., Burns, S.A., Using genetic algorithms to solve
construction time-cost trade-off problems, Journal of Construction
Engineering and Management, ASCE 11 ,184–189, 1997.
7. Golenkoginzburg D, Gonik A. A heuristic for network project
scheduling with random activity duration's depending on the resource
allocation. International Journal of Production Eco- nomics ,55(22):149-
162, 1998.
8. Johnson GA, Schou CD. Expediting projects in PERT with stochastic
time estimates. Project Management Journal, 21(2):29-33, 1990.
9. Keefer DL, Verdini WA. Better estimation of PERT activity time
parameters. Management Science , 39(9), 1993
10. Lau Ahl, Lau HS, Zhang Y. A simple and logic alternative for making
PERT time estimates. IIE Transaction ,28(3):183-192, 1996.
11. Pongcharoen, P., Hicks, C., Braiden, P.M., Stewardson, D.J.,
Determining optimum genetic algorithm parameters for scheduling
the manufacturing and assembly of complex products, International
Journal of Production Economics 78 , 311–322, 2002.
12. Saman M. Crashing in PERT Networks. M.Sc. thesis submitted at the
Faculty of Graduate Studies, University of Jordan, Amman-Jordan,
August ,1991.
13. Yang, I-Tung Performing complex project crashing analysis with aid
of particle swarm optimization algorithm, International Journal of
Project Management 25 (6), 637–646, 2007.
14. Mouhoub, Nasser Eddine, Benhocine, Abdelhamid and Belouadah,
Hocine A new method for constructing a minimal PERT network
Applied Mathematical Modelling 35 (9), 4575–4588, 2011
using mathematical programming, International Journal of Project
Management 19, 181-188, 2001.
2. Azaron, Amir, Katagiri, Hideki, Sakawa, Masatoshi, Kato, Kosuke, and
Memariani, Azizollah, A multi-objective resource allocation problem in
PERT networks, European Journal of Operational Research, 2005.
3. Azaron, Amir, Perkgoz, Cahit, and Sakawa, Masatoshi, A genetic
algorithm approach for the time-cost trade-off in PERT networks,
Applied Mathematics and Computation 168, 1317–1339, 2005.
4. Bazaraa MS, Shetty CM. Nonlinear programming theory and
algorithms. New York: Wiley, 1979.
5. Cho JG, Yum BJ. An uncertainty importance measure of activities in
PERT networks. Int J Prod Res, 35(10):2737-2757, 1997.
6. Feng, C.W., Liu, L., Burns, S.A., Using genetic algorithms to solve
construction time-cost trade-off problems, Journal of Construction
Engineering and Management, ASCE 11 ,184–189, 1997.
7. Golenkoginzburg D, Gonik A. A heuristic for network project
scheduling with random activity duration's depending on the resource
allocation. International Journal of Production Eco- nomics ,55(22):149-
162, 1998.
8. Johnson GA, Schou CD. Expediting projects in PERT with stochastic
time estimates. Project Management Journal, 21(2):29-33, 1990.
9. Keefer DL, Verdini WA. Better estimation of PERT activity time
parameters. Management Science , 39(9), 1993
10. Lau Ahl, Lau HS, Zhang Y. A simple and logic alternative for making
PERT time estimates. IIE Transaction ,28(3):183-192, 1996.
11. Pongcharoen, P., Hicks, C., Braiden, P.M., Stewardson, D.J.,
Determining optimum genetic algorithm parameters for scheduling
the manufacturing and assembly of complex products, International
Journal of Production Economics 78 , 311–322, 2002.
12. Saman M. Crashing in PERT Networks. M.Sc. thesis submitted at the
Faculty of Graduate Studies, University of Jordan, Amman-Jordan,
August ,1991.
13. Yang, I-Tung Performing complex project crashing analysis with aid
of particle swarm optimization algorithm, International Journal of
Project Management 25 (6), 637–646, 2007.
14. Mouhoub, Nasser Eddine, Benhocine, Abdelhamid and Belouadah,
Hocine A new method for constructing a minimal PERT network
Applied Mathematical Modelling 35 (9), 4575–4588, 2011
)