Abstract The Chance-Constrained Stochastic Programming (CCSP) is one of the models for decision making under uncertainty. In this paper, we consider the special case of the CCSP in which only the righthand side vector is random with a discrete distribution having a finite support. The unit commitment problem is one of the applications of the special case of the CCSP. Existing methods for exactly solving the CCSP problems require an enumeration of scenarios when they model a CCSP problem using a Mixed Integer Programming (MIP). We show how to reduce the number of scenarios enumerated in the MIP model. In addition, we give another compact MIP formulation to approximately solve the CCSP problems.