A tabu method for a two-agent single-machine scheduling with deterioration jobs

In recent 10 years, the multi-agent idea applied in scheduling issues has received continuing attention. However, the study of the multi-agent scheduling with deteriorating jobs is relatively limited. In light of this, this paper deliberates upon a two-agent single-machine scheduling problem with deteriorating jobs. Taking the proposed model, the actual processing time of a job from both the first agent and the second agent is modeled as a linearly increasing function of its starting time. The goal of this paper is to minimize the total weighted number of tardy jobs of the first agent subject to the condition that the maximum lateness of the second agent is allowed to have an upper bound. The complexity of the model concerned in the paper is claimed as an NP-hard one. Following that, several dominance rules and a lower bound are proposed to be applied in a branch-and-bound algorithm for the optimal solution, and a tabu algorithm is applied to find near-optimal solutions for the problem. The simulation results obtained from all the proposed algorithms are also reported.