Dominance rules for single machine scheduling to minimize weighted multi objective functions

This work investigates a multi-objective functions for machine scheduling problems. The objective is to find the optimal schedule for n jobs to minimize the total cost of sum weighted earliness, the weighted tardiness, the weighted completion time, the weighted late work and the number of weighted late jobs where the problem is 1//∑i=1n(αjEj+βjTj+θjCj+γjUj+ωjVj). For this problem, several special cases and dominance rules are proven to decrease the branching nodes which are applied to solve the suggested problem in reasonable time.