Management Science and Financial Engineering

The Korean Operations Research and Management Science Society (한국경영과학회)
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Some Special Cases of a Continuous Time-Cost Tradeoff Problem with Multiple Milestones under a Chain Precedence Graph

  • Choi, Byung-Cheon (Department of Business Administration, Chungnam National University) ;
  • Chung, Jibok (Department of Retail Management, Kongju National University)
  • Received : 2016.03.17
  • Accepted : 2016.05.16
  • Published : 2016.05.31
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Abstract

We consider a time-cost tradeoff problem with multiple milestones under a chain precedence graph. In the problem, some penalty occurs unless a milestone is completed before its appointed date. This can be avoided through compressing the processing time of the jobs with additional costs. We describe the compression cost as the convex or the concave function. The objective is to minimize the sum of the total penalty cost and the total compression cost. It has been known that the problems with the concave and the convex cost functions for the compression are NP-hard and polynomially solvable, respectively. Thus, we consider the special cases such that the cost functions or maximal compression amounts of each job are identical. When the cost functions are convex, we show that the problem with the identical costs functions can be solved in strongly polynomial time. When the cost functions are concave, we show that the problem remains NP-hard even if the cost functions are identical, and develop the strongly polynomial approach for the case with the identical maximal compression amounts.

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References

  1. Ahuja, R. A., K. Mehlhorn, and J. B. Orlin, "Faster algorithm for the shortest path problem," Journal of the Association for Computing Machinery l37 (1990), 213-223. https://doi.org/10.1145/77600.77615
  2. Artigues, C., D. Demassey, and E. Neron, "Resource-Constrained Project Scheduling," Wiley, 2008.
  3. Bell, J., "Beauty is in the eye of the beholder: Establishing a fair and equitable value for embryonic hightech enterprises," Venture Capital Journal 40 (2000), 33-34.
  4. Brucker, P., A. Drexl, R. Mohring, K. Neumann, and E. Pesch, "Resource-constrained project scheduling: Notations, classification, models and methods," European Journal of Operational Research 112 (1999), 3-41. https://doi.org/10.1016/S0377-2217(98)00204-5
  5. Berman, E. B., "Resource allocation in a PERT network under continuous activity time-cost function," Management Science 10 (1964), 734-745. https://doi.org/10.1287/mnsc.10.4.734
  6. Choi, B. C. and J. B. Chung, "Complexity results for the linear time-cost tradeoff problem with multiple milestones and completely ordered jobs," European Journal of Operational Research 236 (2014), 61-68. https://doi.org/10.1016/j.ejor.2013.11.009
  7. Choi, B. C. and M. J. Park, "A continuous time-cost trade off problem with multiple milestones and comple tely ordered jobs," European Journal of Operational Research 224 (2015), 748-752.
  8. Demeulemeester, E. L. and W. S. Herroelen, Project Scheduling-A Research Handbook, Kluwer Academic, 2002.
  9. Falk, J. E. and J. L. Horowitz, "Critical path problems with concave cost-time curves," Management Science 19 (1972), 446-455. https://doi.org/10.1287/mnsc.19.4.446
  10. Fulkerson, D. R., "A network flow computation for project cost curves," Management Science l7 (1961), 167-178. https://doi.org/10.1287/mnsc.7.2.167
  11. Ford, L. R. and D. R. Fulkerson, Flows in Networks, Princeton University Press, 1962.
  12. Garey, M. R. and D. S. Johnson, "Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, 1979.
  13. Kelley, J. E., "Critical path planning and scheduling: Mathematical basis," Operations Research 9 (1961), 296-320. https://doi.org/10.1287/opre.9.3.296
  14. Lamberson, L. R. and R. R. Hocking, "Optimum time compression in project scheduling," Management Science 16 (1970), 597-606. https://doi.org/10.1287/mnsc.16.10.B597
  15. Moussourakis, J. and C. Haksever, "Project compression with nonlinear cost functions," Journal of Construction Engineering and Management 136 (2010), 251-259. https://doi.org/10.1061/(ASCE)CO.1943-7862.0000123
  16. Roemer, T. A. and R. Ahmadi, "Concurrent crashing and overlapping in product development," Operations Research 52 (2004), 606-622. https://doi.org/10.1287/opre.1040.0125
  17. Sahlman, W. A., "Insights from the ventures capital model of project governance," Business Economics 29 (1994), 35-41.
  18. Weglarz, J., Project Scheduling-Recent Models, Algorithms and Applications, Kluwer Academic, 1999.
  19. Weglarz, J., J. Jozefowska, M. Mika, and G. Waligora, "Project scheduling with finite or infinite number of activity processing modes-A survey," European Journal of Operational Research 208 (2011), 177-205. https://doi.org/10.1016/j.ejor.2010.03.037

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