Darinka Dentcheva, Andras Prekopa, Andrzej Ruszczynski
On stochastic integer ptogramming under probabilistic constraints
Preprint series: Institut fr Mathematik, Humboldt-Universitt zu Berlin (ISSN 0863-0976)

MSC:

90C15 Stochastic programming

Abstract: We consider stochastic programming problems with
probabilistic constraints involving integer-valued random
variables. The concept of p-efficient points of a
probability distribution is used to derive various
equivalent problem formulations. Next we modify the concept
of r-concave discrete probability distributions
and analyse its relevance for problems under consideration.
These notions are used to derive new lower and upper
bounds for the optimal value of probabilistically
constrained stochastic programming problems
with integer random variables. We also show how limited
information about the distribution can be used to construct
such bounds.