Trade-off balancing between maximum and total completion times for no-wait flow shop production

We propose a trade-off balancing (TOB) heuristic in a no-wait flow shop to minimise the weighted sum of maximum completion time ( $C_{\max } $Cmax) and total completion time (TCT) based on machine idle times. We introduce a factorisation scheme to construct the initial sequence based on current and future idle times at the operational level. In addition, we propose a novel estimation method to establish the mathematical relationship between the objectives min( $C_{\max } $Cmax) and min(TCT) at the production line level. To evaluate the performance of the TOB heuristic, computational experiments are conducted on the classic Taillard's benchmark and one-year historical data from University of Kentucky HealthCare (UKHC). The computational results show that minimisations of $C_{\max } $Cmax and TCT yield inconsistent scheduling sequences, and these two sequences are relatively uncorrelated. We also show that our TOB heuristic performs better than the best existing heuristics with the same computational complexity and generates stable performances in balancing trade-offs.