Energy-aware flow shop scheduling with uncertain renewable energy

This paper investigates an energy-aware flow shop scheduling problem with on-site renewable and grid energy resources. To deal with the uncertainty of renewable energy resources, we first develop two two-stage stochastic programming formulations based on pulse and step models to minimize the total energy cost purchased from the grid. Next, we develop two robust models where in the first one we assume the cost of buying energy from the grid is limited to a given budget and we aim to maximize the number of scenarios that comply with this limitation. In the second robust model, we aim to minimize the grid energy cost by considering a predetermined confidence level. To solve the stochastic and robust models, we develop Benders decomposition algorithms and incorporate the warm-up technique for Benders algorithm. Computational experiments on randomly generated test instances demonstrate that the step formulation outperforms the pulse formulation for larger instances. Additionally, each developed Benders decomposition algorithm outperforms its corresponding model, and the warm-up technique improves the performance of the Benders decomposition algorithms.