A Three-Stage Lexicographic Constraint Programming Approach for an Energy-Efficient Scheduling Problem

The increasing heterogeneity of energy sources and the rising demand for energy are pushing industrial systems toward more sophisticated scheduling strategies. This paper addresses an energy-efficient schedulingproblem motivated by a real-world consortium involved in the storage, distribution, and sale of apples. Theproblem concerns the coordination of daily refrigeration cycles for multiple cooling cells, whose availabilityis subject to stochastic variation. Each cell must alternate between cooling and idle phases while complyingwith technological and operational constraints. The system is modeled as an Energy-Efficient Identical Par-allel Machine Scheduling Problem with precedence constraints and three objectives: minimizing peak energy consumption; achieving a balanced temporal allocation of cooling cycles; and ensuring robustness with re-spect to all possible availability scenarios. A three-stage lexicographic Constraint Programming approach isproposed, with each stage optimizing one objective while preserving the solutions obtained in the previousstage. Computational experiments based on real operational data show that the proposed approach providessolutions that have good quality on all considered objectives, by requiring a limited computational effort.