Bi-criteria single machine scheduling with a time-dependent learning effect and release times

This paper deals with a bi-criteria single machine scheduling problem with a time-dependent learning effect and release times. The objective is to minimize the weighted sum of the makespan and the total completion time. The problem is NP-hard, thus a mixed integer non-linear programming formulation is presented, and a set of dominance properties are developed. To solve the problem efficiently, a procedure is then proposed by incorporating the dominance properties with an ant colony optimization algorithm. In the proposed algorithm, artificial ants construct solutions as orders of jobs based on the heuristic information as well as pheromone trails. Then, the dominance properties are added to obtain better solutions. To evaluate the algorithm performance, computational experiments are conducted.