Sustainable production through balancing trade-offs among three metrics in flow shop scheduling

In sustainable manufacturing, inconsistencies exist among objectives defined in triple-bottom-lines (TBL) of economy, society, and environment. Analogously, inconsistencies exist in flow shop scheduling among three objectives of minimizing total completion time (TCT), maximum completion time (MCT), and completion time variance (CTV), respectively. For continuous functions, the probability is zero to achieve the objectives at their optimal values, so is it at their worst values. Therefore, with inconsistencies among individual objectives of discrete functions, it is more meaningful and feasible to seek a solution with high probabilities that system performance varies within the control limits. We propose a trade-off balancing scheme for sustainable production in flow shop scheduling as the guidance of decision making. We model trade-offs (TO) as a function of TCT, MCT, and CTV, based on which we achieve stable performance on min(TO). Minimizing trade-offs provides a meaningful compromise among inconsistent objectives, by driving the system performance towards a point with minimum deviations from the ideal but infeasible optima. Statistical process control (SPC) analyses show that trade-off balancing provides a better control over individual objectives in terms of average, standard deviation, C_p and C_pk compared to those of single objective optimizations. Moreover, results of case studies show that trade-off balancing not only provides a stable control over individual objectives, but also leads to the highest probability for outputs within the specification limits. We also propose a flow shop scheduling sustainability index (FSSI). The results show that trade-off balancing provides the most sustainable solutions compared to those of the single objective optimizations.