With the rapid growth of electricity demand, many governments around the world have implemented the energy-conscious policy such as time-of-use policy. This paper addresses a bi-objective single machine scheduling with the total tardiness and electricity cost minimization under time-of-use tariffs. The problem is formulated as a mixed integer programming model. The CPLEX solver solves a small size instance to validate the model. We also describe the procedure to obtain the set of non-dominated solution using commercial solver. The complexity of the model is tested on several problem instances. The results show that the problem is hard to solve even for medium size instances. Hence, we propose a genetic algorithm with random insertion to obtain the set of Pareto solutions for large instances.