Optimization for Due-Date Assignment Single-Machine Scheduling under Group Technology

Algorithm 1

Optimal algorithm.

	Step 1: for the problem , we calculate of each group according to Lemma 3 and calculate according to equation (19). For the problem , we calculate of each group according to Lemma 4 and calculate according to equation (21). For the problem , we calculate according to equation (23).
	Step 2: we assign the smallest ( and ) value to the job with the largest value, the second smallest ( and ) value to the job with the second largest value, and so on, with ties broken arbitrarily, and then obtain the internal job sequence of each group.
	Step 3: we arrange the groups in nondecreasing order of by Lemma 7.
	Step 4: according to Lemma 3, we calculate for the problem . According to Lemma 4, we calculate for the problem . According to Lemma 6, we calculate for the problem .