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Expectation and Chance-Constrained Models and Algorithms for Insuring Critical Paths

Listed author(s):
  • Siqian Shen


    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • J. Cole Smith


    (Department of Industrial and Systems Engineering, University of Florida, Gainesville, Florida 32611)

  • Shabbir Ahmed


    (H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Registered author(s):

    In this paper, we consider a class of two-stage stochastic optimization problems arising in the protection of vital arcs in a critical path network. A project is completed after a series of dependent tasks are all finished. We analyze a problem in which task finishing times are uncertain but can be insured a priori to mitigate potential delays. A decision maker must trade off costs incurred in insuring arcs with expected penalties associated with late project completion times, where lateness penalties are assumed to be lower semicontinuous nondecreasing functions of completion time. We provide decomposition strategies to solve this problem with respect to either convex or nonconvex penalty functions. In particular, for the nonconvex penalty case, we employ the reformulation-linearization technique to make the problem amenable to solution via Benders decomposition. We also consider a chance-constrained version of this problem, in which the probability of completing a project on time is sufficiently large. We demonstrate the computational efficacy of our approach by testing a set of size-and-complexity diversified problems, using the sample average approximation method to guide our scenario generation.

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    Article provided by INFORMS in its journal Management Science.

    Volume (Year): 56 (2010)
    Issue (Month): 10 (October)
    Pages: 1794-1814

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    Handle: RePEc:inm:ormnsc:v:56:y:2010:i:10:p:1794-1814
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    1. Herroelen, Willy & Leus, Roel, 2005. "Project scheduling under uncertainty: Survey and research potentials," European Journal of Operational Research, Elsevier, vol. 165(2), pages 289-306, September.
    2. Thomas J. Hindelang & John F. Muth, 1979. "A Dynamic Programming Algorithm for Decision CPM Networks," Operations Research, INFORMS, vol. 27(2), pages 225-241, April.
    3. Elmaghraby, S. E. & Ferreira, A. A. & Tavares, L. V., 2000. "Optimal start times under stochastic activity durations," International Journal of Production Economics, Elsevier, vol. 64(1-3), pages 153-164, March.
    4. 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.
    5. Golenko-Ginzburg, Dimitri & Gonik, Aharon, 1998. "A heuristic for network project scheduling with random activity durations depending on the resource allocation," International Journal of Production Economics, Elsevier, vol. 55(2), pages 149-162, July.
    6. R. A. Bowman, 1995. "Efficient Estimation of Arc Criticalities in Stochastic Activity Networks," Management Science, INFORMS, vol. 41(1), pages 58-67, January.
    7. John M. Burt, Jr. & Mark B. Garman, 1971. "Conditional Monte Carlo: A Simulation Technique for Stochastic Network Analysis," Management Science, INFORMS, vol. 18(3), pages 207-217, November.
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