The unit commitment problem is a typical scheduling problem in an electric power system. The problem is determining the schedules for power generating units and the generating level of each unit. The decisions concern which units to commit during each time period and at what level to generate power to meet the electricity demand. In this paper we develop a stochastic programming model which incorporates the uncertainties of electric power demand. It is assumed that demand uncertainty can be represented by a scenario tree. We propose a stochastic integer programming model in which the objective is to minimize expected cost. In this model, on/off decisions for each generator are made at the first stage. The approach to solving the problem is based on Lagrangian relaxation and dynamic programming.