Scheduling jobs under simple linear deterioration

We consider simple linear deterioration of processing times, i.e. P_i = α_it, where α_i is a job dependent deterioration rate and t > 0 is the job's starting time. In this environment, we study most classical n-job, non-preemptive, single machine scheduling models, i.e. most commonly used performance measures are considered: makespan, flow-time, total tardiness, number of tardy jobs, etc. We show that all these models remain polynomially solvable.