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In this paper, we consider the slack due-window assignment model and study a single machine scheduling problem of linear time-dependent deteriorating jobs and a deteriorating maintenance activity. The cost for each job consists of four components: earliness, tardiness, window location and window size. The objective is to schedule the jobs and to assign the maintenance activity and due-windows such that the total cost among all the jobs is minimized. A polynomial-time algorithm with the running time not exceeding $O(n^2logn)$ to give a solution to this problem is introduced, where $n$ is the number of jobs.

Single Machine Slack Due-Window Assignment and Scheduling of Linear Time-Dependent Deteriorating Jobs and a Deteriorating Maintenance Activity