Stochastic programming with binary second stage variables

We consider a class of stochastic programming with binary recourse variables in which a fixed cost is imposed if the value of the continuous recourse variable is strictly positive. The algorithm of a branch-and-cut method to solve the problem is developed by using the property of the expected recourse function. The problem is applied to a power generating system. The numerical experiments show that the proposed algorithm is quite efficient. The mathematical programming model defined in this paper is quite useful for a variety of design and operational problems.