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


  • 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)


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.

Suggested Citation

  • Siqian Shen & J. Cole Smith & Shabbir Ahmed, 2010. "Expectation and Chance-Constrained Models and Algorithms for Insuring Critical Paths," Management Science, INFORMS, vol. 56(10), pages 1794-1814, October.
  • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:10:p:1794-1814

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    References listed on IDEAS

    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    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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    Cited by:

    1. Escudero Bueno, Laureano F. & Garín Martín, María Araceli & Merino Maestre, María & Pérez Sainz de Rozas, Gloria, 2015. "Some experiments on solving multistage stochastic mixed 0-1 programs with time stochastic dominance constraints," BILTOKI BILTOKI;2015-01, Universidad del País Vasco - Departamento de Economía Aplicada III (Econometría y Estadística).
    2. Li, Haitao & Womer, Norman K., 2015. "Solving stochastic resource-constrained project scheduling problems by closed-loop approximate dynamic programming," European Journal of Operational Research, Elsevier, vol. 246(1), pages 20-33.
    3. Bentaha, Mohand Lounes & Battaïa, Olga & Dolgui, Alexandre & Hu, S. Jack, 2015. "Second order conic approximation for disassembly line design with joint probabilistic constraints," European Journal of Operational Research, Elsevier, vol. 247(3), pages 957-967.
    4. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.


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