Single-machine scheduling with mixed due-windows and deterioration effects

This paper focuses on the single-machine problem of minimizing the maximum earliness-tardiness cost with the mixed due-windows, in which it is assumed that the processing time of the job changes proportionally to its starting time, this is the deterioration effects. The cost function consists of the earliness penalty, the tardiness penalty, and the cost arising from the mixed due-windows. The goal is to find the optimal job schedule, and mixed due-windows to minimize the maximum earliness-tardiness cost. It is proved that the problem is polynomially solvable.