Exact and heuristic solution approaches for energy-efficient identical parallel machine scheduling with time-of-use costs
•Advancements on energy-efficient parallel machine scheduling with time-of-use costs.•Presentation of fundamental combinatorial insights.•Description of a new compact formulation based on symmetry-breaking properties.•Development of a fast exact algorithm and an effective novel heuristic.•A novel dy...
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| Published in: | European journal of operational research Vol. 311; no. 3; pp. 845 - 866 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
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Elsevier B.V
16.12.2023
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| ISSN: | 0377-2217, 1872-6860 |
| Online Access: | Get full text |
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| Abstract | •Advancements on energy-efficient parallel machine scheduling with time-of-use costs.•Presentation of fundamental combinatorial insights.•Description of a new compact formulation based on symmetry-breaking properties.•Development of a fast exact algorithm and an effective novel heuristic.•A novel dynamic programming algorithm for single-machine scheduling.
Nowadays, energy-efficient scheduling has assumed a key role in ensuring the sustainability of manufacturing processes. In this context, we focus on the bi-objective problem of scheduling a set of jobs on identical parallel machines to simultaneously minimize the maximum completion time and the total energy consumption over a time horizon partitioned into a set of discrete slots. The energy costs are determined by a time-of-use pricing scheme, which plays a crucial role in regulating energy demand and flattening its peaks. First, we uncover a symmetry-breaking property that characterizes the structure of the solution space of the problem. As a consequence, we provide a novel, compact mixed-integer linear programming formulation at the core of an efficient exact solution algorithm. A thorough experimental campaign shows that the use of the novel mathematical programming formulation enables the solution of larger-scale instances and entails a reduction in the computational times as compared to the formulation already available in the literature. Furthermore, we propose a new heuristic that improves the state-of-the-art in terms of required computational effort and quality of solutions. Such a heuristic outperforms the existing heuristics for the problem and is also capable of speeding up the exact solution algorithm when used for its initialization. Finally, we introduce a novel dynamic programming algorithm that is able to compute the optimal timing of the jobs scheduled on each machine to further improve the performance of the new heuristic. |
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| AbstractList | •Advancements on energy-efficient parallel machine scheduling with time-of-use costs.•Presentation of fundamental combinatorial insights.•Description of a new compact formulation based on symmetry-breaking properties.•Development of a fast exact algorithm and an effective novel heuristic.•A novel dynamic programming algorithm for single-machine scheduling.
Nowadays, energy-efficient scheduling has assumed a key role in ensuring the sustainability of manufacturing processes. In this context, we focus on the bi-objective problem of scheduling a set of jobs on identical parallel machines to simultaneously minimize the maximum completion time and the total energy consumption over a time horizon partitioned into a set of discrete slots. The energy costs are determined by a time-of-use pricing scheme, which plays a crucial role in regulating energy demand and flattening its peaks. First, we uncover a symmetry-breaking property that characterizes the structure of the solution space of the problem. As a consequence, we provide a novel, compact mixed-integer linear programming formulation at the core of an efficient exact solution algorithm. A thorough experimental campaign shows that the use of the novel mathematical programming formulation enables the solution of larger-scale instances and entails a reduction in the computational times as compared to the formulation already available in the literature. Furthermore, we propose a new heuristic that improves the state-of-the-art in terms of required computational effort and quality of solutions. Such a heuristic outperforms the existing heuristics for the problem and is also capable of speeding up the exact solution algorithm when used for its initialization. Finally, we introduce a novel dynamic programming algorithm that is able to compute the optimal timing of the jobs scheduled on each machine to further improve the performance of the new heuristic. |
| Author | Paolucci, Massimo Gaggero, Mauro Ronco, Roberto |
| Author_xml | – sequence: 1 givenname: Mauro surname: Gaggero fullname: Gaggero, Mauro email: mauro.gaggero@cnr.it organization: Institute of Marine Engineering, National Research Council of Italy, Via De Marini 6, Genoa, I-16149, Italy – sequence: 2 givenname: Massimo orcidid: 0000-0003-0618-8406 surname: Paolucci fullname: Paolucci, Massimo email: massimo.paolucci@unige.it organization: Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genoa, Viale Causa 13, Genoa I-16145, Italy – sequence: 3 givenname: Roberto orcidid: 0000-0001-6846-6374 surname: Ronco fullname: Ronco, Roberto email: roberto.ronco@edu.unige.it organization: Department of Informatics, Bioengineering, Robotics and Systems Engineering, University of Genoa, Viale Causa 13, Genoa I-16145, Italy |
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| Keywords | Time-of-use prices Scheduling Dynamic programming Mixed-integer programming Fast algorithms |
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