In this paper, a single machine sequencing problem is considered in order to find the sequence of jobs minimizing the sum of the maximum earliness AND tardiness with idle times (n/1/I/ETmax). Due to the time complexity function, this sequencing problem belongs to a class of NP-hard ones. Thus, a special design of a simulated annealing (SA) method is applied to solve such a hard problem. To compare the associated results, a BRANCH-AND-BOUND (B&B) method is designed AND the upper/lower limits are also introduced in this method. To show the effectiveness of these methods, a number of different types of problems are generated AND then solved. Based on the results of the test problems, the proposed SA has a small error, AND computational time for achieving the best result is very small.