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Critical Path Analyses Via Chance Constrained and Stochastic Programming

Author

Listed:
  • A. Charnes

    (Northwestern University, Evanston, Illinois)

  • W. W. Cooper

    (Carnegie Institute of Technology, Pittsburgh, Pennsylvania)

  • G. L. Thompson

    (Carnegie Institute of Technology, Pittsburgh, Pennsylvania)

Abstract

Chance-constrained programming methods are applied to examine some statistical properties of PERT networks. Using duality, the PERT method is shown to be equivalent to use of the crudest linear decision rule and the confidence (or lack thereof) in meeting constraints is explicitly presented. The distribution of completion times (= Tintner's stochastic programming) follows easily and may often be multimodal, contrasting with (erroneous) central limit theorem usages in the literature. Possible extensions and developments of PERT using more adequate chance-constrained models and techniques are suggested and will be presented elsewhere.

Suggested Citation

  • A. Charnes & W. W. Cooper & G. L. Thompson, 1964. "Critical Path Analyses Via Chance Constrained and Stochastic Programming," Operations Research, INFORMS, vol. 12(3), pages 460-470, June.
    • Handle: RePEc:inm:oropre:v:12:y:1964:i:3:p:460-470
    DOI: 10.1287/opre.12.3.460
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    Cited by:

    1. 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.
    2. Jorgensen, Trond & Wallace, Stein W., 2000. "Improving project cost estimation by taking into account managerial flexibility," European Journal of Operational Research, Elsevier, vol. 127(2), pages 239-251, December.
    3. Elise D. Miller-Hooks & Hani S. Mahmassani, 2000. "Least Expected Time Paths in Stochastic, Time-Varying Transportation Networks," Transportation Science, INFORMS, vol. 34(2), pages 198-215, May.
    4. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Modelling complex assemblies as a queueing network for lead time control," European Journal of Operational Research, Elsevier, vol. 174(1), pages 150-168, October.
    5. 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.
    6. Azaron, Amir & Fatemi Ghomi, S.M.T., 2008. "Lower bound for the mean project completion time in dynamic PERT networks," European Journal of Operational Research, Elsevier, vol. 186(1), pages 120-127, April.
    7. Davaadorjin Monhor, 2011. "A new probabilistic approach to the path criticality in stochastic PERT," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 19(4), pages 615-633, December.
    8. Stefano Benati, 2006. "An Optimization Model for Stochastic Project Networks with Cash Flows," Computational Management Science, Springer, vol. 3(4), pages 271-284, September.
    9. Linguo Gong, 1992. "Chance‐constrained linear programming with location scale distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(7), pages 997-1007, December.
    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. Elmaghraby, Salah E. & Soewandi, Hanijanto & Yao, Ming-Jong, 2001. "Chance-constrained programming in activity networks: A critical evaluation," European Journal of Operational Research, Elsevier, vol. 131(2), pages 440-458, June.
    12. Metaxas Theodore & Deffner Alex, 2015. "Using Critical Path Analysis (Cpa) in Place Marketing Process: a Methodological Approach in the Case of Rostock, Germany," European Spatial Research and Policy, Sciendo, vol. 22(1), pages 135-151, June.
    13. Metaxas, Theodore & Deffner, Alex, 2013. "Using Critical Path Analysis (CPA) in Place Marketing process," MPRA Paper 51231, University Library of Munich, Germany.
    14. Bregman, Robert L., 2009. "A heuristic procedure for solving the dynamic probabilistic project expediting problem," European Journal of Operational Research, Elsevier, vol. 192(1), pages 125-137, January.
    15. Azaron, Amir & Fynes, Brian & Modarres, Mohammad, 2011. "Due date assignment in repetitive projects," International Journal of Production Economics, Elsevier, vol. 129(1), pages 79-85, January.
    16. Glover, Fred & Sueyoshi, Toshiyuki, 2009. "Contributions of Professor William W. Cooper in Operations Research and Management Science," European Journal of Operational Research, Elsevier, vol. 197(1), pages 1-16, August.
    17. Ke, Hua & Liu, Baoding, 2007. "Project scheduling problem with mixed uncertainty of randomness and fuzziness," European Journal of Operational Research, Elsevier, vol. 183(1), pages 135-147, November.
    18. Masoud Arjmand & Amir Abbas Najafi & Majid Ebrahimzadeh, 2020. "Evolutionary algorithms for multi-objective stochastic resource availability cost problem," OPSEARCH, Springer;Operational Research Society of India, vol. 57(3), pages 935-985, September.
    19. Azaron, Amir & Katagiri, Hideki & Kato, Kosuke & Sakawa, Masatoshi, 2006. "Longest path analysis in networks of queues: Dynamic scheduling problems," European Journal of Operational Research, Elsevier, vol. 174(1), pages 132-149, October.

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