a single machine sequencing problem with idle insert: simulated annealing and branch-and-bound methods

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.