Markov and Markov-regenerative PERT networks
Operations Research
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Stochastic analysis of cyclic schedules
Operations Research
Discrete Applied Mathematics
Efficient estimation of arc criticalities in stochastic activity networks
Management Science
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
The Sample Average Approximation Method for Stochastic Discrete Optimization
SIAM Journal on Optimization
On the Rate of Convergence of Optimal Solutions of Monte Carlo Approximations of Stochastic Programs
SIAM Journal on Optimization
Activity time-cost tradeoffs under time and cost chance constraints
Computers and Industrial Engineering
Stochastic Network Interdiction
Operations Research
A Stochastic Branch-and-Bound Approach to Activity Crashing in Project Management
INFORMS Journal on Computing
Persistence in discrete optimization under data uncertainty
Mathematical Programming: Series A and B
A two-stage-priority-rule-based algorithm for robust resource-constrained project scheduling
Computers and Industrial Engineering
Reformulation and sampling to solve a stochastic network interdiction problem
Networks - Games, Interdiction, and Human Interaction Problems on Networks
A Sample Approximation Approach for Optimization with Probabilistic Constraints
SIAM Journal on Optimization
A Linear Decision-Based Approximation Approach to Stochastic Programming
Operations Research
Two-stage stochastic hierarchical multiple risk problems: models and algorithms
Mathematical Programming: Series A and B
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
Operations Research Letters
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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.