A Branch-and-Bound Algorithm for Minimizing the Total Tardiness of a Three-Agent Scheduling Problem Considering the Overlap Effect and Environmental Protection

Due to serious air pollution, some machines may be forced to shut down for short periods. During such periods, companies will make no progress on the yields. Maintenance also leads to reductions. If we view such two indispensable things such as shutdown and maintenance as jobs, the two can overlap with each other, i.e., the schedule can be shorter. However, this phenomenon is seldom discussed in scheduling. In this paper, we consider a three-agent scheduling problem with the overlap effect. The objective is to minimize the total tardiness of jobs from agent 3 under the restrictions that the PM 2.5 emissions of agent 1 cannot exceed a limit and that each maintenance activity requested by agent 2 must be conducted within its specific maintenance window. A branch-and-bound algorithm is developed to generate the optimal schedules. Computational experiments are conducted to show the solution quality and execution speed of the proposed algorithm.