Minimizing sum of completion times on a single machine with sequence-dependent family setup times

This paper presents a branch- and- bound ( B& B) algorithm for minimizing the sum of completion times in a single-machine scheduling setting with sequence- dependent family setup times. The main feature of the B& B algorithm is a new lower bounding scheme that is based on a network formulation of the problem. With extensive computational tests, we demonstrate that the B& B algorithm can solve problems with up to 60 jobs and 12 families, where setup and processing times are uniformly distributed in various combinations of the [ 1,50] and [ 1,100] ranges.