This article studies a single-machine scheduling problem involving coupled-tasks and hard due dates. A genetic algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA) II model is proposed to carry out a bi-objective optimization of both holding cost and setup-related waste generation. Results show that the multi-objective genetic algorithm outperforms the previous approaches regarding both computation time and objective functions, showing that a reduction of setups of 36% is possible at the expense of an 11% increase in inventory with acceptable computation times. It also highlights the importance of multi-objective optimization for decision-making in case of conflicting objective functions.