# Linear programming with stochasticity?

Suppose I have implemented an LP, where some constraint coefficients are implemented as the mean of some probability distribution.

Now, I would like to solve the same problem but with stochasticity reintroduced based on the probability distributions.

Can this still be solved using LP techniques?

If not, what are the natural alternatives?

• How are your coefficients distributed? Some discrete distribution? Normal? Uniform? In what sense do you want the constraint to be satisfied? In expected value (on average)? with specified high probability? May 22 '17 at 0:22

There is a huge literature on "stochastic programming", but you're probably interested in what is called "chance constrained programming", in which the constraint coefficients are random variables, and you want to find a solution $x$ such that each constraint is individually satisfied with probability $\eta$ ($\eta$ might 0.95, 0.99, etc.)