Multi-line hybrid flow-shop scheduling problem with energy considerations

This article introduces a novel scheduling problem consisting of a multi-line hybrid flow-shop with energy considerations. The scheduling problem aims at optimising energy cost under time of use pricing structure with respect to production and energy-efficiency constraints. A 0–1 integer linear program based on a time-indexed formulation is proposed and allows to consider of variable power profiles for operations. Subsequently, a multi-start iterated local search-based heuristic is developed in order to address the resolution of large-scale instances. The performance of the proposed approaches is then assessed on randomly generated instances of various scales. Numerical experiments on an industrial case study also illustrate the economic benefits of considering a time of use pricing scheme with over 20% reduction in energy cost. Furthermore, it is demonstrated the importance of considering the system as a whole when considering energy in such a multi-line shop floor by examining three distinct optimisation strategies. Indeed, the benefits of a multi-line optimisation strategy compared to a sequential one are around 24% on average.