On the minmax common-due-date problem: extensions to position-dependent processing times, job rejection, learning effect, uniform machines and flowshops

A classical single machine minmax common due-date assignment (CON) problem is studied. The problem is extended (independently) to the following settings: (1) general position-dependent job processing times are assumed, and an efficient O(n⁴) solution procedure is introduced; (2) the option of job rejection is allowed, and this case is shown to be solved in O(n⁵); (3) a deterioration effect is considered, and an O(n²) solution algorithm is proposed; (4) parallel uniform machines are considered; and (5) the machine setting is that of a permutation flowshop. The last two settings are known to be NP hard, and efficient heuristic procedures are introduced and shown numerically to produce very small optimality gaps.