Efficient mixed integer programming models for family scheduling problems

This paper proposes several mixed integer programming models which incorporate optimal sequence properties into the models, to solve single machine family scheduling problems. The objectives are total weighted completion time and maximum lateness, respectively. Experiment results indicate that there are remarkable improvements in computational efficiency when optimal sequence properties are included in the models. For the total weighted completion time problems, the best model solves all of the problems up to 30-jobs within 5 s, all 50-job problems within 4 min and about 1/3 of the 75-job to 100-job problems within 1 h. For maximum lateness problems, the best model solves almost all the problems up to 30-jobs within 11 min and around half of the 50-job to 100-job problems within 1 h.