Solution algorithms to minimise the total family tardiness for job shop scheduling with job families

This study addresses a job shop scheduling problem in which jobs are grouped into job families, but they are processed individually using their distinct routings. Unlike the previous studies, we consider a due-date-based objective of minimising the total family tardiness, i.e., sum of positive deviations between the due-dates and the completion times of job families. A mixed integer programming model is developed to represent the problem mathematically. Then, an optimal algorithm is proposed using the branch and bound technique while developing a job family-based lower bound. For practical applications up to large sized instances, two types of heuristics, modified shifting bottleneck and priority scheduling algorithms, are also proposed. To test the performances of the three types of solution algorithms, computational experiments were done on a number of test instances and the results are reported.