We study a single-machine supply chain scheduling problem with one unavailability constraint, in which the actual processing time of a job depends on the deteriorating operator and the beginning time of processing and the interrupted job is non-resumable. The sufficient available vehicles without capacity limit deliver batches of completed jobs to the customer. And the completed jobs before the unavailability interval must be delivered before or by the start time of the unavailability interval. The objective is to minimize the sum of total delivery time and total delivery cost. We show that the problem is NP-hard, and present a pseudo-polynomial-time dynamic programming. Moreover, we achieve a full polynomial time approximation scheme (FPTAS) based on the lower bound and the upper bound of the objective function value of the problem.