Production scheduling is one of the very important problems that industry and production are confronted with it. Production scheduling is often planned in the industrial environments while productivity in production can improve significantly the expansion of simultaneous optimization of the scheduling plan. Production scheduling and production are two areas that have attracted much attention in the industry literature and production and research in the operation systems. In this study, the problem of single-machine scheduling with linear earliness and tardiness costs considering the work failure, energy consumption restriction, and the allowed idleness have been investigated and a new nonlinear mathematical model has been presented for the single-machine scheduling problem. Considering complexity in solution, this problem has been regarded as NP-hard problem. However, using methods that produce optimized results, it is just suitable for small size problems. Based on this, a genetic algorithm has been presented for solving this problem in average and large sizes. Numerical samples show that the presented algorithm is effective and efficient.