Single machine problem with multi-rate-modifying activities under a time-dependent deterioration

The single machine scheduling problem with multi-rate-modifying activities under a time-dependent deterioration to minimize makespan is studied. After examining the characteristics of the problem, a number of properties and a lower bound are proposed. A branch and bound algorithm and a heuristic algorithm are used in the solution, and two special cases are also examined. The computational experiments show that, for the situation with a rate-modifying activity, the proposed branch and bound algorithm can solve situations with 50 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal solution with an error percentage less than 0.053 in a very short time. In situations with multi-rate-modifying activities, the proposed branch and bound algorithm can solve the case with 15 jobs within a reasonable time, and the heuristic algorithm can obtain the near-optimal with an error percentage less than 0.070 in a very short time. The branch and bound algorithm and the heuristic algorithm are both shown to be efficient and effective. Huang et al.