In inverse scheduling problems, a job sequence is given and the objective is
to determine the minimal perturbation to processing times on weights of jobs so that the
given sequence becomes optimal with respect to a pre-selected objective function. In this
paper we study the inverse problem of the total weighted completion time problem 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 larger than
the original objective value.

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