A sequencing problem with family setup times Original Research Article

We study the single-machine scheduling problem with release and delivery times in which the set of jobs to be scheduled consists of job families requiring a machine setup between two consecutively scheduled jobs from two different families. The setup time depends only on the family to be sequenced next, and the objective is to minimize the makespan. For the case where all the jobs of each family have to be scheduled contiguously, called the family sequencing problem, a generalization of the extended Jacksonʹs rule is introduced and its properties are analyzed. As a result, a branch and bound algorithm is developed which is capable of solving problem instances with hundreds of jobs in very short time. Results of computational experiments are reported. For the problem with families divisible into batches, several heuristics are proposed and analyzed. The general approach consists in successively applying one of the family sequencing algorithms, heuristic or exact, to the set of batches, each time modifying the current partition of families. Results of the worst-case analysis and computational experiments are shown.