We consider the following single-machine time-dependent scheduling problem with constraints on the machine availability. There is given a set of independent and deteriorating jobs Jj , 1 ≤ j ≤ n, to be processed on a single machine, starting from time t0 > 0. The processing time pj of job Jj is a proportional function of the starting time Sj of this job, pj = αjSj, where Sj ≥ t0 and deteriorati...