Group scheduling in a cellular manufacturing shop to minimise total tardiness and nT: a comparative genetic algorithm and mathematical modelling approach

In this paper, family and job scheduling in a cellular manufacturing shop is addressed where jobs have individual due dates. The objectives are to minimise total tardiness and the number of tardy jobs. Family splitting among cells is allowed but job splitting is not. Two optimisation methods are employed in order to solve this problem, namely mathematical modelling (MM) and genetic algorithm (GA). The results showed that GA found the optimal solution for most of the problems with high frequency. Furthermore, the proposed GA is efficient compared to the MM especially for larger problems in terms of execution times. Other critical aspects of the problem such as family preemption only, impact of family splitting on common due date scenarios and dual objective scenarios are also solved. In short, the proposed comparative approach provides critical insights for the group scheduling problem in a cellular manufacturing shop with distinctive cases.