Energy optimization in a manufacturing plant Journée GOThA Ordonnancement avec contraintes d’énergie et/ou de ressources périssables LAAS-CNRS Toulouse 16 Juin 2014 Grigori German, Claude Lepape, Chloé Desdouits

Introduction Test Data Day Night Time Cost

Journée GOThA Ordonnancement avec contraintes d’énergie et/ou de ressources périssables LAAS-CNRS Toulouse 16 Juin 2014 Problem Description

Overview of the scheduling problem

Adding the energy dimension act 3 time Res r cap r stet calendar capacity cost interval capacity calendar interval cmax cmin act 1 act 2

Optimization Input Day Night Time Cost Constraints Objectives

Resolution Methods Journée GOThA Ordonnancement avec contraintes d’énergie et/ou de ressources périssables LAAS-CNRS Toulouse 16 Juin 2014

Simple, classical formulation Branching strategy: Earliest Due Date No simple formulation for computing the energy cost Time-based formulation Perspective: global constraint Generates a good first solution Method 1: Constraint Programming

Overlap Variables Method 2: MIP How to express the energy cost? Taille du bucket act dépasse à gauche Durée de act act dépasse à droite act et le bucket sont disjoints

Constraints Method 2: MIP How to express the energy cost?

Algorithm Perspectives Adapted time windows size Sliding time windows Intensification Method 3: Hybrid local search Constraint Programming S Local search While there is still time Find a time window F Set all the variables outside F Keep the best between S and S’ Optimize F with MIP S’ S

Journée GOThA Ordonnancement avec contraintes d’énergie et/ou de ressources périssables LAAS-CNRS Toulouse 16 Juin 2014 Tests and results

Adapted benchmark instances from the literature CP, MIP & LS versus best known results CPMIPLS All instances (38) = Best known results Relative deviation 20%47%7% NCGS (20 instances) = Best known results Relative deviation 30%0%11% NCOS (18 instances) = Best known results 1112 Relative deviation 8%99%3% CPMIPLS All instances (38) = Best known results Relative deviation 20%4%7% NCGS (20 instances) = Best known results Relative deviation 30%0%11% NCOS (18 instances) = Best known results 1112 Relative deviation 8% 3% Comparison of the 3 methods without the energy

MIP versus LS Local search with and without energy And with energy ? MIP All instances (34) ≤ Local search 9 Relative deviation 14% NCGS (18 instances) ≤ Local search 3 Relative deviation 0% NCOS (16 instances) ≤ Local search 6 Relative deviation 31% ObjectivesSavings All instances (29) Tardiness0% Energy-0,95% Total cost-0,12%

Conclusion Journée GOThA Ordonnancement avec contraintes d’énergie et/ou de ressources périssables LAAS-CNRS Toulouse 16 Juin 2014 Application Use case Multi-objectifs : ordonnancements Pareto- optimaux Coûts de l’énergie affines par morceaux Application Use case Multi-objectifs : ordonnancements Pareto- optimaux Coûts de l’énergie affines par morceaux

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