Multi-objective energy-efficient flexible flow shop scheduling problem: integrating renewable energy and demand response programs

This study tackles an energy-efficient flexible flow shop scheduling problem motivated by the increasing need for sustainable manufacturing under volatile energy markets. The proposed framework jointly integrates photovoltaic generation, energy storage systems, Time-of-Use pricing, and demand bidding mechanisms, while explicitly accounting for machine On/Off strategies with realistic turn-on time constraints. A bi-objective mixed-integer linear programming model is first solved using the augmented ϵ-constraint method, simultaneously minimising makespan and total electricity cost minus demand-response incentives for small-scale instances. For larger problems, a constructive heuristic and a Non-dominated Sorting Genetic Algorithm II are proposed and compared with two state-of-the-art metaheuristics from the literature. Computational experiments demonstrate the efficiency of the proposed approach in generating well-distributed Pareto fronts, revealing valuable trade-offs between production performance and energy expenditure. A case study and a sensitivity analysis are conducted to evaluate the practical relevance of the framework, examining the effects of key energy pricing and infrastructure parameters on scheduling decisions. The results provide actionable insights for manufacturers, showing how integrating renewable energy and demand response programs can reduce electricity costs without compromising production efficiency, thereby contributing to the broader transition toward low-carbon and cost-aware factories.