Branch and bound algorithms for single-machinescheduling with batch set-up times to minimizetotal weighted completion time

This paper presents several branch and bound algorithms for a single machine scheduling problem with batching. Jobs are partitioned into families, and a set-up time is necessary when there is a switch from processing jobs of one family to jobs of another family. The objective is to minimize the total weighted completion time. A lower bound based on Lagrangean relaxation of the machine capacity constraint is derived. Also, a multiplier adjustment method to find values of the multipliers is proposed. Computational experience with instances having up to 70 jobs shows that the lower bounds are effective in restricting the search.