Group scheduling with group-dependent multiple due windows assignment

We consider single-machine group scheduling with group-dependent multiple due windows assignment. In the group technology environment, the jobs are divided into groups in advance according to their processing similarities, and all the jobs of the same group are processed consecutively in order to improve production efficiency. A sequence-independent machine set-up time precedes the processing of the first job of each group. Each group has group-dependent multiple due windows. The objective is to find the optimal job sequence, the set of jobs assigned to each due window sequence, the optimal group sequence, and the optimal due window assignment to minimise a total cost that comprises the earliness and tardiness penalties and the due window starting time and due window size costs. For the case where the number of jobs assigned to each due window in each group is given in advance, we show that the problem is solvable in O(n log n) time, where n is the total number of jobs. For the case where the number of jobs assigned to each due window in each group is unknown, we give an O(n(B) log n) time algorithm to solve the problem, where B = Max{h(i) - 1} and h(i) is the number of due window of the ith group.