Theory of linear and integer programming
Theory of linear and integer programming
Integer and combinatorial optimization
Integer and combinatorial optimization
Numerical techniques for stochastic optimization
Numerical techniques for stochastic optimization
Facet identification for the symmetric traveling salesman polytope
Mathematical Programming: Series A and B
Optimization of static simulation models by the score function method
Mathematics and Computers in Simulation
Stochastic decomposition: an algorithm for two-state linear programs with recourse
Mathematics of Operations Research
A faster algorithm for finding the minimum cut in a graph
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Sample-path optimization of convex stochastic performance functions
Mathematical Programming: Series A and B
A simulation-based approach to two-stage stochastic programming with recourse
Mathematical Programming: Series A and B
A branch and bound method for stochastic global optimization
Mathematical Programming: Series A and B
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
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
On Optimal Allocation of Indivisibles Under Uncertainty
Operations Research
Introduction to Stochastic Programming
Introduction to Stochastic Programming
Monte Carlo bounding techniques for determining solution quality in stochastic programs
Operations Research Letters
Approximation algorithms for stochastic and risk-averse optimization
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Sequential sampling for solving stochastic programs
Proceedings of the 39th conference on Winter simulation: 40 years! The best is yet to come
A comparative study of decomposition algorithms for stochastic combinatorial optimization
Computational Optimization and Applications
Commitment under uncertainty: Two-stage stochastic matching problems
Theoretical Computer Science
A two-stage stochastic programming model for transportation network protection
Computers and Operations Research
The mathematics of continuous-variable simulation optimization
Proceedings of the 40th Conference on Winter Simulation
Arc-Routing Models for Small-Package Local Routing
Transportation Science
Fast Approaches to Improve the Robustness of a Railway Timetable
Transportation Science
Integration and coordination of multirefinery networks: a robust optimization approach
MS '08 Proceedings of the 19th IASTED International Conference on Modelling and Simulation
The Stochastic Multiperiod Location Transportation Problem
Transportation Science
Stochastic Root Finding and Efficient Estimation of Convex Risk Measures
Operations Research
An empirical study of optimization for maximizing diffusion in networks
CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
The stochastic root-finding problem: Overview, solutions, and open questions
ACM Transactions on Modeling and Computer Simulation (TOMACS)
OR PRACTICE---R&D Project Portfolio Analysis for the Semiconductor Industry
Operations Research
Computers and Operations Research
The Reliable Facility Location Problem: Formulations, Heuristics, and Approximation Algorithms
INFORMS Journal on Computing
A Sequential Sampling Procedure for Stochastic Programming
Operations Research
Quantified linear programs: a computational study
ESA'11 Proceedings of the 19th European conference on Algorithms
Approximation algorithms for 2-stage stochastic optimization problems
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Monte-Carlo optimizations for resource allocation problems in stochastic network systems
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
Plan b: uncertainty/time trade-offs for linear and integer programming
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
On complexity of multistage stochastic programs
Operations Research Letters
Commitment under uncertainty: two-stage stochastic matching problems
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
On sample size control in sample average approximations for solving smooth stochastic programs
Computational Optimization and Applications
Hi-index | 0.00 |
The sample average approximation (SAA) method is an approach for solving stochastic optimization problems by using Monte Carlo simulation. In this technique the expected objective function of the stochastic problem is approximated by a sample average estimate derived from a random sample. The resulting sample average approximating problem is then solved by deterministic optimization techniques. The process is repeated with different samples to obtain candidate solutions along with statistical estimates of their optimality gaps.We present a detailed computational study of the application of the SAA method to solve three classes of stochastic routing problems. These stochastic problems involve an extremely large number of scenarios and first-stage integer variables. For each of the three problem classes, we use decomposition and branch-and-cut to solve the approximating problem within the SAA scheme. Our computational results indicate that the proposed method is successful in solving problems with up to 21694 scenarios to within an estimated 1.0% of optimality. Furthermore, a surprising observation is that the number of optimality cuts required to solve the approximating problem to optimality does not significantly increase with the size of the sample. Therefore, the observed computation times needed to find optimal solutions to the approximating problems grow only linearly with the sample size. As a result, we are able to find provably near-optimal solutions to these difficult stochastic programs using only a moderate amount of computation time.