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Elucidation of the idea of some strong NP-hardness proofs

Abstract Here we presents an elucidation of the idea of the strong NP-hardness proofs of some scheduling problems with variable job processing times presented in our papers. In the original papers, we provided the relevant fundamental calculations and additionally also brief descriptions of the ideas of the proofs. We assumed that more detailed descriptions were redundant for the considered strong NP-hardness proofs, since the calculations were given. However, we have been informed that few readers focused only on the descriptions of the ideas omitting the calculations. Therefore, the objective of this note is to clearly point out the relation between the ideas and the calculations. Although there are no new results in this note, we hope it will help to understand our proofs of the strong NP-hardness (and first of all how the transformations were obtained), if some calculation details are confusing or overlooked during reading the original papers.