The single machine scheduling problem with sequence-dependent setup times and a learning effect on processing times

For the past few years, learning effect has been receiving wide attention in the scheduling problems. There are many studies that take into account the learning effect with several structural constraints and some specific conditions of machine scheduling problems. However, very few studies have explored the scheduling problem including learning effect and sequence-dependent setup times simultaneously, although both are found in the scheduling literature. Therefore, this study addresses an NP-Hard problem of minimizing the total tardiness on a single machine with sequence-dependent setup times and a position-based learning effect on processing times. Several dominance properties are verified and a lower bound is provided to develop a branch and bound algorithm for solving the problem. In addition, four heuristic algorithms (two genetic algorithms and two variable neighborhood search algorithms) are developed in order to obtain near optimal solutions in reasonable time limits. Furthermore, some computational experiments are performed on randomly generated test problems to evaluate the performance of the algorithms.