A note on reverse scheduling with maximum lateness objective

The inverse and reverse counterparts of the single-machine scheduling problem 1||Lmax are studied in [2], in which the complexity classification is provided for various combinations of adjustable parameters (due dates and processing times) and for five different types of norm: ℓ1,ℓ2,ℓ∞,ℓΣH , and ℓmaxH . It appears that the O(n2) -time algorithm for the reverse problem with adjustable due dates contains a flaw. In this note, we present the structural properties of the reverse model, establishing a link with the forward scheduling problem with due dates and deadlines. For the four norms ℓ1,ℓ∞,ℓΣH , and ℓmaxH , the complexity results are derived based on the properties of the corresponding forward problems, while the case of the norm ℓ2 is treated separately. As a by-product, we resolve an open question on the complexity of problem 1||∑αjT2j .