Single-machine scheduling of proportional-linearly deteriorating jobs with positional due indices

In this paper, we study the scheduling of proportional-linearly deteriorating jobs with positional due indices, release dates, deadlines and precedence relations on a single machine. The scheduling criteria studied in this paper include the makespan, maximum lateness, maximum tardiness, maximum flow time, maximum weighted completion time, maximum scheduling cost, total completion time, and the number of tardy jobs. By applying Lawler’s rule and Smith’s rule, polynomially solvable problems are processed by using two unified methods. We also present some new NP-hardness results when processing times of the jobs have no deterioration. Our results generalize a series of known achievements in the literature.