Energy efficiency, robustness, and makespan optimality in job-shop scheduling problems

[EN] Many real-world problems are known as planning and scheduling problems, where resources must be allocated so as to optimize overall performance objectives. The traditional scheduling models consider performance indicators such as processing time, cost, and quality as optimization objectives. However, most of them do not take into account energy consumption and robustness. We focus our attention in a job-shop scheduling problem where machines can work at different speeds. It represents an extension of the classical job-shop scheduling problem, where each operation has to be executed by one machine and this machine can work at different speeds. The main goal of the paper is focused on the analysis of three important objectives (energy efficiency, robustness, and makespan) and the relationship among them. We present some analytical formulas to estimate the ratio/relationship between these parameters. It can be observed that there exists a clear relationship between robustness and energy efficiency and a clear trade-off between robustness/energy efficiency and makespan. It represents an advance in the state of the art of production scheduling, so obtaining energy-efficient solutions also supposes obtaining robust solutions, and vice versa.This research has been supported by the Spanish Government under research project MICINN TIN2013-46511-C2-1-P, the European CASES project (No. 294931) supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the FP7, and the European TETRACOM project (No. 609491) supported by FP7-ICT-2013-10. This research was also supported by the National Science Foundation of China (No. 51175262) and the Jiangsu Province Science Foundation for Excellent Youths under Grant BK2012032.Salido Gregorio, MA.; Escamilla Fuster, J.; Barber Sanchís, F.; Giret Boggino, AS.; Tang, D.; Dai, M. (2015). Energy efficiency, robustness, and makespan optimality in job-shop scheduling problems. AI EDAM. 30(3):300-312. https://doi.org/10.1017/S0890060415000335S300312303Billaut, J.-C., Moukrim, A., & Sanlaville, E. (Eds.). (2008). Flexibility and Robustness in Scheduling. doi:10.1002/9780470611432Nowicki, E., & Smutnicki, C. (2005). An Advanced Tabu Search Algorithm for the Job Shop Problem. Journal of Scheduling, 8(2), 145-159. doi:10.1007/s10951-005-6364-5Agnetis, A., Flamini, M., Nicosia, G., & Pacifici, A. (2010). A job-shop problem with one additional resource type. Journal of Scheduling, 14(3), 225-237. doi:10.1007/s10951-010-0162-4Mouzon, G., Yildirim, M. B., & Twomey, J. (2007). Operational methods for minimization of energy consumption of manufacturing equipment. International Journal of Production Research, 45(18-19), 4247-4271. doi:10.1080/00207540701450013Weinert, N., Chiotellis, S., & Seliger, G. (2011). Methodology for planning and operating energy-efficient production systems. CIRP Annals, 60(1), 41-44. doi:10.1016/j.cirp.2011.03.015Duflou, J. R., Sutherland, J. W., Dornfeld, D., Herrmann, C., Jeswiet, J., Kara, S., … Kellens, K. (2012). Towards energy and resource efficient manufacturing: A processes and systems approach. CIRP Annals, 61(2), 587-609. doi:10.1016/j.cirp.2012.05.002Laborie P. (2009). IBM ILOG CP Optimizer for detailed scheduling illustrated on three problems. Proc. 6th Int. Conf. Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, CPAIOR09.Dahmus J. , & Gutowski T. (2004). An environmental analysis of machining. Proc. ASME Int. Mechanical Engineering Congr. RD&D Exposition, Anaheim, CA.Huang, K.-L., & Liao, C.-J. (2008). Ant colony optimization combined with taboo search for the job shop scheduling problem. Computers & Operations Research, 35(4), 1030-1046. doi:10.1016/j.cor.2006.07.003IBM. (2010). Modeling With IBM ILOG CP Optimizer—Practical Scheduling Examples (white paper). Armonk, NY: IBM Software Group.Kramer L. , Barbulescu L. , & Smith S. (2007). Understanding performance tradeoffs in algorithms for solving oversubscribed scheduling. Proc. 22nd Conf. Artificial Intelligence, AAAI-07, Vancouver.Seow, Y., & Rahimifard, S. (2011). A framework for modelling energy consumption within manufacturing systems. CIRP Journal of Manufacturing Science and Technology, 4(3), 258-264. doi:10.1016/j.cirpj.2011.03.007Li, W., Zein, A., Kara, S., & Herrmann, C. (2011). An Investigation into Fixed Energy Consumption of Machine Tools. Glocalized Solutions for Sustainability in Manufacturing, 268-273. doi:10.1007/978-3-642-19692-8_47Szathmáry, E. (2006). A robust approach. Nature, 439(7072), 19-20. doi:10.1038/439019aFang, K., Uhan, N., Zhao, F., & Sutherland, J. W. (2011). A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction. Journal of Manufacturing Systems, 30(4), 234-240. doi:10.1016/j.jmsy.2011.08.004Gutowski, T., Murphy, C., Allen, D., Bauer, D., Bras, B., Piwonka, T., … Wolff, E. (2005). Environmentally benign manufacturing: Observations from Japan, Europe and the United States. Journal of Cleaner Production, 13(1), 1-17. doi:10.1016/j.jclepro.2003.10.004Garrido A. , Salido M.A. , Barber F. , & López M.A. (2000). Heuristic methods for solving job-shop scheduling problems. Proc. ECAI-2000 Workshop on New Results in Planning, Scheduling and Design, Berlín.Verfaillie G. , & Schiex T. (1994). Solution reuse in dynamic constraint satisfaction problems. Proc. 12th National Conf. Artificial Intelligence, AAAI-94.Dai, M., Tang, D., Giret, A., Salido, M. A., & Li, W. D. (2013). Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm. Robotics and Computer-Integrated Manufacturing, 29(5), 418-429. doi:10.1016/j.rcim.2013.04.001Neugebauer, R., Wabner, M., Rentzsch, H., & Ihlenfeldt, S. (2011). Structure principles of energy efficient machine tools. CIRP Journal of Manufacturing Science and Technology, 4(2), 136-147. doi:10.1016/j.cirpj.2011.06.017Mouzon, G., & Yildirim, M. B. (2008). A framework to minimise total energy consumption and total tardiness on a single machine. International Journal of Sustainable Engineering, 1(2), 105-116. doi:10.1080/19397030802257236Bruzzone, A. A. G., Anghinolfi, D., Paolucci, M., & Tonelli, F. (2012). Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops. CIRP Annals, 61(1), 459-462. doi:10.1016/j.cirp.2012.03.08