This study addresses a scheduling problem involving a single-machine with coupled-tasks and bi-objective optimisation considering simultaneously inventory and environmental waste. A Mixed Integer Linear Program representing the problem is first developed. Subsequently, a Genetic Algorithm (GA) is presented, followed by numerical experiments on multiple instances. Pareto fronts are determined using the ϵ-constraint and weighted sum methods, and a trade-off point is selected according to a distance criterion. Numerical experiments on both small and large instances show near-optimal results for small instances, and considerably reduced computing times for large ones when using the GA. The results show that a compromise can be found, with a decrease in setup-related waste up to 36% for an increase of inventory of 12%. This will help decision-makers to better consider the environmental aspect when designing schedules, as well as reduce their production environmental impact and waste-management costs.