Generator scheduling is a combinatorial optimization problem and this paper presents a new version of annealing (SA) method to model and solve the scheduling problem. Firstly, solution is decomposed into hourly schedules and each hourly schedule is modified by decomposed-SA using bits flipping. If the generated new hourly schedule is better, by convention it is accepted deterministically. A worse hourly schedule is accepted with temperature dependent SA probability. A new solution consists of these hourly schedules of entire scheduling period after repair as unit-wise constraints may not be fulfilled at the time of individual hourly schedule modification. This helps to direct and modify schedules of appropriate hours. Secondly, this new solution is accepted for the next iteration if its cost is less than that of current solution. A higher cost new solution is accepted with temperature dependent SA probability again. Besides, problem dependent other features are incorporated to save the execution time. The proposed method is tested using the reported problem data sets. Simulation results are compared to previous reported results. Numerical results show an improvement in solution cost and time compared to the results obtained from powerful algorithms.