An improved branch-and-bound algorithm to minimize the weighted flowtime on identical parallel machines with family setup times

This article investigates identical parallel machines scheduling with family setup times.The objective function being the weighted sum of completion times,the problem is known to be strongly NP-hard.We propose a constructive heuristic algorithm and three complementary lower bounds.Two of these bounds proceed by elimination of setup times or by distributing each of them to jobs of the corresponding family,while the third one is based on a lagrangian relaxation.The bounds and the heuristic are incorporated into a branch-and-bound algorithm.Experimental results obtained outperform those of the methods presented in previous works,in term of size of solved problems.