Electricity cost minimisation for optimal makespan solution in flow shop scheduling under time-of-use tariffs

The industrial sector consumes half of the world delivered energy and is responsible for a third of carbon dioxide emissions which cause severe environmental pollution. The industry has to change its behaviour concerning the energy consumption. Since two-machine flow shop scheduling ( $F2|perm|C_{{\rm max}} $F2|perm|Cmax) is one of the typical problems of the manufacturing industry, this paper aims to build an energy-cost-aware scheduling plan. This work tackles the joint optimisation of makespan and electricity cost in two-machine flow shop scheduling problem under electricity pricing. We enhance the financial aspect of the optimal solution of $F2|perm|C_{{\rm max}} $F2|perm|Cmax by minimising the electricity cost without increasing the makespan. Firstly, we show the contribution of the generation of several optimal equivalent solutions of $F2|perm|C_{{\rm max}} $F2|perm|Cmax. The optimal equivalent solutions have different electricity costs but present the same makespan. Then, we determine the optimal starting time of jobs on several equivalent optimal solutions to get the best production plan. Finally, the numerical tests show that our proposed approach improves the electricity cost significantly under optimal makespan. The results provide good solutions to managers and decision makers to achieve energy cost savings without sacrificing the productivity which can contribute to sustainable development of the manufacturing industry.