Study on multiple due-windows assignment scheduling with learning and deteriorating effects

This paper focuses on the single-machine scheduling problems with multiple due-windows and learning and deteriorating effects, where the actual processing time of the job is a function of its starting time and position in a sequence. The aim is to minimize the weighted sum of the earliness, tardiness and the due-windows costs. Under common due-windows and slack due-windows, the optimal properties of the problems are analyzed and each of the above problems can be transformed into an assignment problem. An algorithm with a time complexity of O(n 3 ) is presented, and the effectiveness of the algorithm is verified by an example, where n is the number of jobs.