A new dynamic programming formulation of (n × m) flowshop sequencing problems with due dates

A dynamic programming formulation is presented for determining an optimal solution to a problem where n jobs are to be sequenced in a multi-stage production environment. An application of a developed formulation to a plastic pipe manufacturing factory is also presented. Conditions are such that the job sequence is the same in all stages, each job requires setups at each stage and setup times are sequence dependent. An optimal solution is such that the minimum total tardiness is achieved. A listing of the developed computer program is also provided.