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Single-machine due-window assignment scheduling based on common flow allowance, learning effect and resource allocation

This article considers a single-machine due-window assignment scheduling problem based on a common flow allowance (i.e. all jobs have slack due window (SLKW)). We assume that the actual processing time of a job is a function of its position in a sequence (learning effect) and its continuously divisible and non-renewable resource allocation. The problem is to determine the optimal due windows, the optimal resource allocation and the processing sequence simultaneously to minimise costs for earliness, tardiness, the window location, window size, makespan and resource consumption. For a linear or a convex function of the amount of a resource allocated to the job, we provide a polynomial time algorithm, respectively. Some extensions of the problem are also shown.