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A Dynamic Programming Solution to Cost-Time Tradeoff for CPM

Author

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  • Don R. Robinson

    (Illinois State University)

Abstract

To solve the problem of time-cost tradeoff in project management with available models, a choice must be made between heuristic approaches and algorithms based upon restrictive assumptions about the shape of the cost-time functions of the activities. The algorithm presented in this article involves a dynamic-programming approach to determine the allocation which minimizes the duration of the project (critical path). The main advantage of this model is its ability to determine the optimum allocation among activities with arbitrary cost-time functions. Also, computational shortcuts for functions with special properties can be used to increase the efficiency of the model. Objective functions of networks with special structures decompose into sequences of one-dimensional optimization problems. Although some complex networks have objective functions which cannot be fully decomposed, the dimensions of these functions are considerably less than the number of activities involved. If the activities have nonincreasing cost-time functions, an optimal policy can be used to eliminate the usual search procedure for one-dimensional problems which involve minimizing the maximum of stage returns.

Suggested Citation

  • Don R. Robinson, 1975. "A Dynamic Programming Solution to Cost-Time Tradeoff for CPM," Management Science, INFORMS, vol. 22(2), pages 158-166, October.
    • Handle: RePEc:inm:ormnsc:v:22:y:1975:i:2:p:158-166
    DOI: 10.1287/mnsc.22.2.158
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    Citations

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    Cited by:

    1. Martin Skutella, 1998. "Approximation Algorithms for the Discrete Time-Cost Tradeoff Problem," Mathematics of Operations Research, INFORMS, vol. 23(4), pages 909-929, November.
    2. Vanhoucke, Mario, 2005. "New computational results for the discrete time/cost trade-off problem with time-switch constraints," European Journal of Operational Research, Elsevier, vol. 165(2), pages 359-374, September.
    3. A B Hafızoğlu & M Azizoğlu, 2010. "Linear programming based approaches for the discrete time/cost trade-off problem in project networks," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 61(4), pages 676-685, April.
    4. Helena Gaspars, 2006. "A conception of a new algorithm for the project time-cost analysis," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 16(3-4), pages 5-27.
    5. 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.
    6. Aniruddha Dutta, 2019. "Capacity Allocation of Game Tickets Using Dynamic Pricing," Data, MDPI, vol. 4(4), pages 1-12, October.
    7. Said, Samer S. & Haouari, Mohamed, 2015. "A hybrid simulation-optimization approach for the robust Discrete Time/Cost Trade-off Problem," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 628-636.
    8. Brucker, Peter & Drexl, Andreas & Mohring, Rolf & Neumann, Klaus & Pesch, Erwin, 1999. "Resource-constrained project scheduling: Notation, classification, models, and methods," European Journal of Operational Research, Elsevier, vol. 112(1), pages 3-41, January.
    9. De, Prabuddha & James Dunne, E. & Ghosh, Jay B. & Wells, Charles E., 1995. "The discrete time-cost tradeoff problem revisited," European Journal of Operational Research, Elsevier, vol. 81(2), pages 225-238, March.
    10. M. Vanhoucke, 2007. "An electromagnetic time/cost trade-off optimization in project scheduling," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 07/457, Ghent University, Faculty of Economics and Business Administration.
    11. Demeulemeester, Erik L. & Herroelen, Willy S. & Elmaghraby, Salah E., 1996. "Optimal procedures for the discrete time/cost trade-off problem in project networks," European Journal of Operational Research, Elsevier, vol. 88(1), pages 50-68, January.
    12. He, Zhengwen & Wang, Nengmin & Jia, Tao & Xu, Yu, 2009. "Simulated annealing and tabu search for multi-mode project payment scheduling," European Journal of Operational Research, Elsevier, vol. 198(3), pages 688-696, November.
    13. Akkan, Can & Drexl, Andreas & Kimms, Alf, 2005. "Network decomposition-based benchmark results for the discrete time-cost tradeoff problem," European Journal of Operational Research, Elsevier, vol. 165(2), pages 339-358, September.
    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. Akkan, Can & Drexl, Andreas & Kimms, Alf, 2000. "Network decomposition-based lower and upper bounds for the discrete time-cost tradeoff problem," Manuskripte aus den Instituten für Betriebswirtschaftslehre der Universität Kiel 527, Christian-Albrechts-Universität zu Kiel, Institut für Betriebswirtschaftslehre.
    16. Heng Kuang & S. Jack Hu & Jeonghan Ko, 2016. "A dynamic programming approach to integrated assembly planning and supplier assignment with lead time constraints," International Journal of Production Research, Taylor & Francis Journals, vol. 54(9), pages 2691-2708, May.
    17. Hua, N. Grace & Willems, Sean P., 2016. "Optimally configuring a two-stage serial line supply chain under the guaranteed service model," International Journal of Production Economics, Elsevier, vol. 181(PA), pages 98-106.

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