Expectation and chance-constrained models and algorithms for insuring critical paths

Siqian Shen, J. Cole Smith, Shabbir Ahmed

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


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 nonde-creasing 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.

Original languageEnglish (US)
Pages (from-to)1794-1814
Number of pages21
JournalManagement Science
Issue number10
StatePublished - Oct 2010
Externally publishedYes


  • Chance-constrained programming
  • Integer programming
  • Project management
  • Reformulation-linearization technique
  • Sample average approximation

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research

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