Bachman and Janiak provided a sketch of the proof that the problem 1|r i ,p i (v) ¼ a i /v|C max is NP-hard in the strong sense. However, they did not show how to avoid using harmonic numbers whose encoding is not pseudo-polynomial, which makes the proof incomplete. In this corrigendum, we provide a new complete proof.

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Abstract.A bicriterion problem of scheduling jobs on a single machine is studied. The processing time of each job is a linear decreasing function of the amount of a common discrete resource allocated to the job. A solution is specified by a sequence of the jobs and a resource allocation. The quality of a solution is measured by two criteria, F 1 and F 2 . The first criterion is the maximal or total (weighted) resource consumption, and the second criterion is a regular scheduling criterion depending on the job completion times. Both criteria have to be minimized. General schemes for the construction of the Pareto set and the Pareto set -approximation are presented. Computational complexities of problems to minimize F 1 subject to F 2 ≤ K and to minimize F 2 subject to F 1 ≤ K, where K is any number, are studied for various functions F 1 and F 2 . Algorithms for solving these problems and for the construction of the Pareto set and the Pareto set -approximation for the corresponding bicriterion problems are presented.

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