A branch and bound algorithm for solving large-scale single-machine scheduling problems with non-identical release dates

In this paper, we have examined minimising the total completion times in a single-machine scheduling problem with non-identical job release dates. This problem is known to be strongly NP-hard. We have proposed an effective lower bound-based. Also, a near optimal heuristic has been presented that has an average gap of less than 0.077% from the optimum solution. Additionally, in 18% of the problem instances with up to 60 jobs, the upper bound value is equal to the lower bound value. Then we provide two dominance properties. Subsequently, the proposed lower bound, upper bound and dominance properties have been applied in the branch and bound method and have been tested in a wide range of instances. Computational experiments demonstrate the ability of the proposed method to solve hard and large-size problems with up to 130 jobs within a reasonable time. [Received 19 June 2015; Revised 26 November 2016; Revised 24 January 2017; Accepted 5 September 2017]