Single machine scheduling with unequal release times and idle insert for minimizing the sum of maximum earliness and tardiness

This paper addresses the problem of minimizing the sum of maximum earliness and tardiness on a single machine with unequal release times and idle insert as realistic assumptions and based on actual manufacturing environments. This problem is shown in the literature that is NP-hard in the strong sense, so there is no polynomial-time algorithm to solve it. Therefore, an exact branch-and-bound scheme is proposed to sequence the jobs by means of efficient dominance rules, lower and upper bounds. Moreover, a polynomial time algorithm to optimally minimize the objective function is developed to insert idle times and schedule the known sequence of jobs in each node of the search tree. To evaluate the efficiency of the proposed algorithm, 720 instances in nine series are randomly generated. Considering the complexity of the problem, the algorithm is capable of solving problems of up to 20 jobs. In addition, two evolutionary metaheuristic algorithms, genetic algorithm and particle swarm optimization, are provided and compared for large-job sizes. Computational results in 3420 randomly generated instances have shown that the proposed genetic algorithm improves the solutions in terms of both quality and time efficiency and that it would be capable of solving the problem of small to large sizes.