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

A dynamic programming formulation was proposed in the paper entitled A new dynamic programming formulation of (nm) flowshop sequencing problems with due dates [Sonmez, A.I. and Baykasoglu, A., 1998, International Journal of Production Research, 36 (8), 2269-2283] to deal with a flow shop problem considering sequence-dependent setup times to minimise the total weighted tardiness. Since the original dynamic programming formulation is confusing and of the six examples given in the original paper four are partially or totally wrong, both the dynamic programming formulation and the examples need to be rectified. In this note, the confusing interpretations of the original formulation are analysed, and a more accurate dynamic programming formulation is proposed. Based on the new dynamic programming formulation, all four incorrect examples are recalculated.