Single-machine scheduling with upper bounded actual processing times and maintenance times

We consider the scheduling problem of setting the upper bounds for the actual processing times and maintenance times under assumption that the actual processing times of a job is a position-dependent power function. The maintenance duration is a position-dependent exponential function. Through building a corresponding jobs scheduling model, we found the scheduling problem can be transformed as a classic assignment problem to solve and obtained jointly the optimal frequency to perform maintenances and the optimal job sequence to minimize the total cost, which is a linear function of makespan and total tardiness. Through applying polynomial time algorithm to solve the scheduling problem we studied, we proved that the jobs scheduling model is computable and the computational complexity of the scheduling problem is .