The two-machine flow-shop problem with weighted late work criterion and common due date

The paper is on the two-machine non-preemptive flow-shop scheduling problem with a total weighted late work criterion and a common due date (F2|di=d|Yw). The late work performance measure estimates the quality of the obtained solution with regard to the duration of late parts of tasks not taking into account the quantity of this delay. We prove the binary NP-hardness of the problem mentioned by showing a transformation from the partition problem to its decision counterpart. Then, a dynamic programming approach of pseudo-polynomial time complexity is formulated.