The unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan

AbstractIn this paper we consider the unbounded single machine parallel batch scheduling problem with family jobs and release dates to minimize makespan. We show that this problem is strongly NP-hard, and give an O(n(n/m+1)m) time dynamic programming algorithm and an O(mkk+1P2k−1) time dynamic programming algorithm, where n is the number of jobs, m is the number of families, k is the number of distinct release dates and P is the sum of the processing times of all families. We further give a heuristic with a performance ratio 2. We also give a polynomial-time approximation scheme for the problem