Heuristics for the two-machine flowshop scheduling problem to minimize maximum lateness with bounded processing times

This study addresses a two-machine flowshop scheduling problem to minimize maximum lateness where processing times are random variables with lower and upper bounds. This problem is NP-hard since the corresponding deterministic problem is known to be NP-hard. Hence, we propose nine heuristics which utilize due dates and the lower and upper bounds on job processing times along with the Earliest Due Date sequence. Furthermore, we propose an algorithm which yields four heuristics. The proposed fourteen heuristics are compared with each other and with a random solution through randomly generated data. Four different distributions (uniform, negative exponential, positive exponential, and normal) of processing times within given lower and upper bounds are investigated. The computational analysis has shown that one of the proposed heuristics performs as the best over all the considered parameters and for the four distributions with an overall average percentage relative error of less than one.