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Resource Allocation in a PERT Network Under Continuous Activity Time-Cost Functions

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  • E. B. Berman

    (Consultant, Research Analysis Corporation and Institute for Defense Analysis)

Abstract

This paper describes a conceptual model which allocates resources in a PERT network, the activities of which are subject to continuous concave-upward time-cost functions, in such a way as to achieve a minimum cost solution for a given completion date for the program described by the network. A parametric solution for the minimum cost solution at various total program times is also briefly described. The effect of uncertainty in the time of completion of an activity has also been investigated in a highly simplified model; and a tentative conclusion is presented that such uncertainty tends to divert resources toward the earlier part of the program, as compared to the solution under certainty.

Suggested Citation

  • E. B. Berman, 1964. "Resource Allocation in a PERT Network Under Continuous Activity Time-Cost Functions," Management Science, INFORMS, vol. 10(4), pages 734-745, July.
    • Handle: RePEc:inm:ormnsc:v:10:y:1964:i:4:p:734-745
    DOI: 10.1287/mnsc.10.4.734
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    Cited by:

    1. Marcin Anholcer & Helena Gaspars-Wieloch, 2011. "Efficiency analysis of the Kaufmann and Dezbazeille algorithm for the deadline problem," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(1), pages 5-18.
    2. Dayal Madhukar & Verma, Sanjay, 2014. "Breadth-first and Best-first Exact Procedures for Regular Measures of the Multi-mode RCPSP," IIMA Working Papers WP2014-10-04, Indian Institute of Management Ahmedabad, Research and Publication Department.
    3. S. Selcuk Erenguc & Taeho Ahn & Daniel G. Conway, 2001. "The resource constrained project scheduling problem with multiple crashable modes: An exact solution method," Naval Research Logistics (NRL), John Wiley & Sons, vol. 48(2), pages 107-127, March.
    4. 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.
    5. Ahn, Taeho & Erenguc, S. Selcuk, 1998. "The resource constrained project scheduling problem with multiple crashable modes: A heuristic procedure," European Journal of Operational Research, Elsevier, vol. 107(2), pages 250-259, June.
    6. 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.
    7. R L Bregman, 2009. "Preemptive expediting to improve project due date performance," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 60(1), pages 120-129, January.
    8. Babu, A. J. G. & Suresh, Nalina, 1996. "Project management with time, cost, and quality considerations," European Journal of Operational Research, Elsevier, vol. 88(2), pages 320-327, January.
    9. 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.
    10. Thomas A. Roemer & Reza Ahmadi & Robert H. Wang, 2000. "Time-Cost Trade-Offs in Overlapped Product Development," Operations Research, INFORMS, vol. 48(6), pages 858-865, December.
    11. Dayal Madhukar & Verma, Sanjay, 2015. "Multi-processor Exact Procedures for Regular Measures of the Multi-mode RCPSP," IIMA Working Papers WP2015-03-25, Indian Institute of Management Ahmedabad, Research and Publication Department.
    12. 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.
    13. Thomas A. Roemer & Reza Ahmadi, 2004. "Concurrent Crashing and Overlapping in Product Development," Operations Research, INFORMS, vol. 52(4), pages 606-622, August.
    14. Choi, Byung-Cheon & Park, Myoung-Ju, 2015. "A continuous time–cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research, Elsevier, vol. 244(3), pages 748-752.
    15. 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.

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