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Simplifying the nonlinear continuous time-cost tradeoff problem

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Abstract

Equivalent simplification is an effective method for solving large-scale complex problems. In this paper, the authors simplify a classic project scheduling problem, which is the nonlinear continuous time-cost tradeoff problem (TCTP). Simplifying TCTP is a simple path problem in a critical path method (CPM) network. The authors transform TCTP into a simple activity float problem and design a complex polynomial algorithm for its solution. First, the authors discover relationships between activity floats and path lengths by studying activity floats from the perspective of path instead of time. Second, the authors perform simplification and improve the efficiency and accuracy of the solution by deleting redundant activities and narrowing the duration intervals of non-redundant activities. Finally, the authors compare our method with current methods. The relationships between activity floats and path lengths provide new approaches for other path and correlative project problems.

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References

  1. Akkan C, Drexl A, and Kimms A, Network decomposition-based benchmark results for the discrete time-cost tradeoff problem, European Journal of Operational Research, 2005, 165: 339–358.

    Article  MATH  Google Scholar 

  2. Elmaghraby S E and Kamburowski J, The analysis of activity networks under generalized precedence relations (GPRs), Management Science, 1992, 38(9): 1245–1263.

    Article  MATH  Google Scholar 

  3. Hebert J E and Deckro R F, Combining contemporary and traditional project management tools to resolve a project scheduling problem, Computers and Operations Research, 2011, 38: 21–32.

    Article  Google Scholar 

  4. Choi K and Kwak Y H, Decision support model for incentives/disincentives time-cost tradeoff, Automation in Construction, 2012, 21: 219–228.

    Article  Google Scholar 

  5. Choi B C and Chung J, Complexity results for the linear time-cost tradeoff problem with multiple milestones and completely ordered jobs, European Journal of Operational Research, 2014, 236: 61–68.

    Article  MathSciNet  MATH  Google Scholar 

  6. Choi B C and Park M J, A continuous time-cost tradeoff problem with multiple milestones and completely ordered jobs, European Journal of Operational Research, 2015, 244: 748–752.

    Article  MathSciNet  MATH  Google Scholar 

  7. Szmerekovsky J G and Venkateshan P, An integer programming formulation for the project scheduling problem with irregular time-cost tradeoffs, Computers and Operations Research, 2012, 39: 1402–1410.

    Article  MathSciNet  MATH  Google Scholar 

  8. Kim J Y, Kang C W, and Hwang I, A practical approach to project scheduling: Considering the potential quality loss cost in the time-cost tradeoff problem, International Journal of Project Management, 2012, 30: 264–272.

    Article  Google Scholar 

  9. Demeulemeester E L and Herroelen W S, Project Scheduling: A Research Handbook, Boston/ Dordrecht/London: Kluwer Academic Publishers, 2002.

    MATH  Google Scholar 

  10. De P, Dune E J, Ghosh J B, et al., Complexity of the discrete time-cost tradeoff problem for project networks, Operations Research, 1997, 45: 302–306.

    Article  MathSciNet  Google Scholar 

  11. Nabipoor Afruzi E, Roghanian E, Najafi A A, et al., A multi-mode resource-constrained discrete time-cost tradeoff problem solving using an adjusted fuzzy dominance genetic algorithm, Scientia Iranica, 2013, 20: 931–944.

    Google Scholar 

  12. Vanhoucke M, New computational results for the discrete time/cost trade-off problem with timeswitch constraints, European Journal of Operational Research, 2005, 165: 359–374.

    Article  MATH  Google Scholar 

  13. Hadjiconstantinou E and Klerides E, A new path-based cutting plane approach for the discrete time-cost tradeoff problem, Computational Management Science, 2010, 7: 313–336.

    Article  MathSciNet  MATH  Google Scholar 

  14. Afshar A, Ziaraty A K, and Kaveh A, Nondominated archiving multicolony ant algorithm in time-cost trade-off optimization, Journal of Construction Engineering and Management, 2009, 135: 668–674.

    Article  Google Scholar 

  15. Milenkovic M, Bojovic N, Ribeiro R A, et al., A fuzzy simulated annealing approach for project time-cost tradeoff, Journal of Intelligent & Fuzzy Systems, 2012, 23: 203–215.

    MathSciNet  Google Scholar 

  16. Parveen S and Saha S K, A GA-based fuzzy optimal model for time-cost trade-off in a project with resources consideration, International Journal of Industrial and Systems Engineering, 2013, 15: 153–170.

    Article  Google Scholar 

  17. Falk J E and Horowitz J L, Critical path problem with concave cost-time curve, Management Science, 1972, 19: 446–455.

    Article  MATH  Google Scholar 

  18. Nahapetyan A and Pardalos P M, A bilinear relaxation based algorithm for concave piecewise linear networks flow problems, Journal of Industrial and Management Optimization, 2007, 3: 71–85.

    Article  MathSciNet  MATH  Google Scholar 

  19. Moussourakis J and Haksever C, Project compression with nonlinear cost functions, Journal of Construction Engineering and Management, 2010, 136(2): 251–259.

    Article  Google Scholar 

  20. Lamberson L R and Hocking R R, Optimum time compression in project scheduling, Management Science, 1970, 16: 597–606.

    Article  MATH  Google Scholar 

  21. Kapur K C, An algorithm for the project cost/duration analysis problem with quadratic and convex cost functions, IIE Transactions, 1973, 5: 314–322.

    Google Scholar 

  22. Siemens N and Gooding C, Reducing project duration at minimum cost: A time cost trade-off algorithm, Omega, 1975, 3: 569–581.

    Article  Google Scholar 

  23. Elmaghraby S E and Salem A, Optimal project compression under convex cost functions I: Quadratic cost with continuous derivative, OR Technical Report, 158, North Carolina State University, Raleigh, 1980.

    Google Scholar 

  24. Elmaghraby S E and Salem A, Optimal project compression under convex cost functions II, OR Technical Report, 157, North Carolina State University, Raleigh, 1980.

    Google Scholar 

  25. Panagiotakoplos D, A CPM time-cost computational algorithm for arbitrary activity cost function, INFOR, 1977, 15: 183–195.

    Google Scholar 

  26. Moder J J, Phillips C R, and Davis E W, Project Management with CPM, PERT and Precedence Diagramming, 3rd Edition, Van Nostrand Reinhold Company, New Jersey, 1983.

    Google Scholar 

  27. Deckro R F, Hebert J E, Verdini W A, et al., Nonlinear time/cost tradeoff model in project management, Computers & Industrial Engineering, 1995, 28: 219–229.

    Article  Google Scholar 

  28. Amir A and Reza T M, Multi-objective time-cost trade-off in dynamic PERT networks using an interactive approach, European Journal of Operational Research, 2007, 180: 1186–1200.

    Article  MATH  Google Scholar 

  29. Kwon O, Lee S, and Son J, Advanced time-cost trade-off model using mixed integer programming, Korean Journal of Construction Engineering and Management, 2015, 16(6): 53–62.

    Article  Google Scholar 

  30. Pathak B K, Srivastava S, and Srivastava K, Neural network embedded multiobjective genetic algorithm to solve non-linear time-cost tradeoff problem of project scheduling, Journal of Scientific & Industrial Research, 2008, 67: 124–131.

    Google Scholar 

  31. Wang Z and Zhu D, A line search filter secant method for nonlinear equality constrained optimization, Journal of Systems Science and Complexity, 2010, 23(2): 343–361.

    Article  MathSciNet  MATH  Google Scholar 

  32. Gu G and Zhu D, A dwindling filter line search algorithm for nonlinear equality constrained optimization, Journal of Systems Science and Complexity, 2015, 28(3): 623–637.

    Article  MathSciNet  MATH  Google Scholar 

  33. Pathak B K and Srivastava S, Integrated ANN-HMH approach for nonlinear time-cost tradeoff problem, International Journal of Computational Intelligence Systems, 2014, 7: 456–471.

    Article  Google Scholar 

  34. Halman N, Li C L, and David S L, Fully polynomial-time approximation schemes for time-cost tradeoff problems in series-parallel project networks, Operations Research Letters, 2009, 37: 239–244.

    Article  MathSciNet  MATH  Google Scholar 

  35. Yamashita D S andMorabito R, A note on time/cost tradeoff curve generation for project scheduling with multi-mode resource availability costs, International Journal of Operational Research, 2009, 5: 429–444.

    Article  MATH  Google Scholar 

  36. Li X, Qi J, and Su Z, Free float theorem and algorithm of seeking the k-th order critical path, Journal of Management Sciences in China, 2009, 12(2): 98–104.

    Google Scholar 

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Authors and Affiliations

  1. Business Administration College, Nanchang Institute of Technology, Nanchang, 330099, China

    Zhixiong Su

  2. School of Economics and Management, North China Electric Power University, Beijing, 102206, China

    Jianxun Qi

  3. Business Administration College, Nanchang Institute of Technology, Nanchang, 330099, China

    Hanying Wei

Authors
  1. Zhixiong Su
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  2. Jianxun Qi
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  3. Hanying Wei
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Corresponding author

Correspondence to Zhixiong Su.

Additional information

This research was supported by the Science and Technology Foundation of Jiangxi Provincial Department of Education in China under Grant No. GJJ161114, the Natural Science Foundation of China under Grant No. 71271081, and the Soft Science Research Base of Water Security and Sustainable Development of Jiangxi Province in China.

This paper was recommended for publication by Editor WANG Shouyang.

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Su, Z., Qi, J. & Wei, H. Simplifying the nonlinear continuous time-cost tradeoff problem. J Syst Sci Complex 30, 901–920 (2017). https://doi.org/10.1007/s11424-017-5175-z

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  • DOI: https://doi.org/10.1007/s11424-017-5175-z

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