A branch-and-bound algorithm for a single machine sequencing to minimize the total tardiness with arbitrary release dates and position-dependent learning effects

This study considers an NP-hard problem of minimizing the total tardiness on a single machine with arbitrary release dates and position-dependent learning effects. A mixed-integer programming (MIP ) model is first formulated to find the optimal solution for small-size problem instances. Some new dominance rules are then presented which provide a sufficient condition for finding local optimality. The branch-and-bound (B& B) strategy incorporating with several dominance properties and a lower bound is proposed to derive the optimal solution for medium- to-large-size problem instances, and four marriage-in-honey-bees optimization algorithms (MBO) are developed to derive near-optimal solutions for the problem. To show the effectiveness of the proposed algorithms, 3600 situations with 20 and 25 jobs, are randomly generated for experiments.