Inverse Problem of Total Weighted Completion Time Objective with Unit Processing Time on Identical Parallel Machines

In inverse scheduling problems, a job sequence is given and the objective is to determine the minimal perturbation to process times or weights of jobs so that the given schedule becomes optimal with respect to a preselected objective function. In this paper, we study the inverse problem of the total weighted completion time objective with unit processing time on identical parallel machines. The weights are minimally adjusted so that a given target job sequence becomes an optimal schedule for different norms under the constraints that the resulting objective value based on the adjusted weights is no more than the original objective value.