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Resource allocation in dynamic PERT networks with finite capacity

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  • Yaghoubi, Saeed
  • Noori, Siamak
  • Azaron, Amir
  • Tavakkoli-Moghaddam, Reza

Abstract

This article models the resource allocation problem in dynamic PERT networks with finite capacity of concurrent projects (COnstant Number of Projects In Process (CONPIP)), where activity durations are independent random variables with exponential distributions, and the new projects are generated according to a Poisson process. The system is represented as a queuing network with finite concurrent projects, where each activity of a project is performed at a devoted service station with one server located in a node of the network. For modeling dynamic PERT networks with CONPIP, we first convert the network of queues into a stochastic network. Then, by constructing a proper finite-state continuous-time Markov model, a system of differential equations is created to solve and find the completion time distribution for any particular project. Finally, we propose a multi-objective model with three conflict objectives to optimally control the resources allocated to the servers, and apply the goal attainment method to solve a discrete-time approximation of the original multi-objective problem.

Suggested Citation

  • Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2011. "Resource allocation in dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 215(3), pages 670-678, December.
    • Handle: RePEc:eee:ejores:v:215:y:2011:i:3:p:670-678
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    References listed on IDEAS

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    1. Linda Nozick & Mark Turnquist & Ningxiong Xu, 2004. "Managing Portfolios of Projects under Uncertainty," Annals of Operations Research, Springer, vol. 132(1), pages 243-256, November.
    2. Azaron, Amir & Tavakkoli-Moghaddam, Reza, 2007. "Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1186-1200, August.
    3. A. Alan B. Pritsker & Lawrence J. Waiters & Philip M. Wolfe, 1969. "Multiproject Scheduling with Limited Resources: A Zero-One Programming Approach," Management Science, INFORMS, vol. 16(1), pages 93-108, September.
    4. Gonçalves, J.F. & Mendes, J.J.M. & Resende, M.G.C., 2008. "A genetic algorithm for the resource constrained multi-project scheduling problem," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1171-1190, September.
    5. Papadopoulos, H. T. & Heavey, C., 1996. "Queueing theory in manufacturing systems analysis and design: A classification of models for production and transfer lines," European Journal of Operational Research, Elsevier, vol. 92(1), pages 1-27, July.
    6. Antonio Lova & Pilar Tormos, 2001. "Analysis of Scheduling Schemes and Heuristic Rules Performance in Resource-Constrained Multiproject Scheduling," Annals of Operations Research, Springer, vol. 102(1), pages 263-286, February.
    7. Izack Cohen & Boaz Golany & Avraham Shtub, 2005. "Managing Stochastic, Finite Capacity, Multi-Project Systems through the Cross-Entropy Methodology," Annals of Operations Research, Springer, vol. 134(1), pages 183-199, February.
    8. Paul S. Adler & Avi Mandelbaum & Viên Nguyen & Elizabeth Schwerer, 1995. "From Project to Process Management: An Empirically-Based Framework for Analyzing Product Development Time," Management Science, INFORMS, vol. 41(3), pages 458-484, March.
    9. Oualid Jouini & Yves Dallery & Zeynep Aksin, 2009. "Queueing models for full-flexible multi-class call centers with real-time anticipated delays," Post-Print hal-00565481, HAL.
    10. Amir Azaron & Hideki Katagiri & Masatoshi Sakawa, 2007. "Time-cost trade-off via optimal control theory in Markov PERT networks," Annals of Operations Research, Springer, vol. 150(1), pages 47-64, March.
    11. Jerome D. Wiest, 1967. "A Heuristic Model for Scheduling Large Projects with Limited Resources," Management Science, INFORMS, vol. 13(6), pages 359-377, February.
    12. Osorio, Carolina & Bierlaire, Michel, 2009. "An analytic finite capacity queueing network model capturing the propagation of congestion and blocking," European Journal of Operational Research, Elsevier, vol. 196(3), pages 996-1007, August.
    13. Jouini, Oualid & Dallery, Yves & Aksin, Zeynep, 2009. "Queueing models for full-flexible multi-class call centers with real-time anticipated delays," International Journal of Production Economics, Elsevier, vol. 120(2), pages 389-399, August.
    14. Chen, Vincent Y. X., 1994. "A 0-1 goal programming model for scheduling multiple maintenance projects at a copper mine," European Journal of Operational Research, Elsevier, vol. 76(1), pages 176-191, July.
    15. Balasubramanian Kanagasabapathi & Chandrasekharan Rajendran & Kuppuswamy Ananthanarayanan, 2009. "Performance analysis of scheduling rules in resource-constrained multiple projects," International Journal of Industrial and Systems Engineering, Inderscience Enterprises Ltd, vol. 4(5), pages 502-535.
    16. Tan, BarIs & Gershwin, Stanley B., 2009. "Analysis of a general Markovian two-stage continuous-flow production system with a finite buffer," International Journal of Production Economics, Elsevier, vol. 120(2), pages 327-339, August.
    17. V. G. Kulkarni & V. G. Adlakha, 1986. "Markov and Markov-Regenerative pert Networks," Operations Research, INFORMS, vol. 34(5), pages 769-781, October.
    18. I. Kurtulus & E. W. Davis, 1982. "Multi-Project Scheduling: Categorization of Heuristic Rules Performance," Management Science, INFORMS, vol. 28(2), pages 161-172, February.
    19. Azaron, Amir & Katagiri, Hideki & Sakawa, Masatoshi & Kato, Kosuke & Memariani, Azizollah, 2006. "A multi-objective resource allocation problem in PERT networks," European Journal of Operational Research, Elsevier, vol. 172(3), pages 838-854, August.
    20. Lova, Antonio & Maroto, Concepcion & Tormos, Pilar, 2000. "A multicriteria heuristic method to improve resource allocation in multiproject scheduling," European Journal of Operational Research, Elsevier, vol. 127(2), pages 408-424, December.
    21. Tsubakitani, Shigeru & Deckro, Richard F., 1990. "A heuristic for multi-project scheduling with limited resources in the housing industry," European Journal of Operational Research, Elsevier, vol. 49(1), pages 80-91, November.
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    1. Yaghoubi, Saeed & Noori, Siamak & Azaron, Amir & Fynes, Brian, 2015. "Resource allocation in multi-class dynamic PERT networks with finite capacity," European Journal of Operational Research, Elsevier, vol. 247(3), pages 879-894.
    2. Mohsen Aliahmadi & Saeed Yaghoubi & Mohammad Sadeghi, 2024. "Inventory-scheduling problem in sustainable project supply chain under uncertainty," Environment Systems and Decisions, Springer, vol. 44(4), pages 836-852, December.
    3. Mahtab Afsari & Hesam Javadi Vasigh, 2016. "A Mathematical Modeling for Delivery Time in Dynamic PERT Networks," Modern Applied Science, Canadian Center of Science and Education, vol. 10(3), pages 214-214, March.

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