We consider stochastic integer programming problems with probabilistic constraints. The concept of p-efficient points of a probability distribution is used to derive various equivalent problem formulations. Next we introduce new methods for constructing lower and upper bounds for probabilistically constrained integer programs. We also show how limited information about the distribution can be used to construct such bounds. The concepts and methods are illustrated on an example of a vehicle routing problem.
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics
- Column generation
- Integer programming
- Probabilistic constraints
- Stochastic programming