(751a) Novel Approach to Scheduling of Energy-Efficient Flexible Job Shops
Nikolaos Rakovitis1, Nan Zhang1, Jie Li1, Liping Zhang2
1Centre for Process Integration, School of Chemical Engineering and Analytical Science, The University of Manchester
2School of Machinery and Automation, Wuhan University of Science and Technology
Scheduling of process industry has gained a lot of attention in the last three decades [1-2]. A great number of mathematical models for different types of batch processes, such as single-stage, multi-stage and multiproduct batch processes and continuous processes have been presented. Different modelling approaches such as discrete time , global event-based [4-5], unit-specific event based [6-7], slot based  and sequence based  have been presented, while different process representations such as the state task network  and the resource task network  have been used. Most of these models did not consider energy consumptions.
With more and more emphasis on the environmental issues and energy cost, it is of great importance for process industries to consider energy consumptions in their scheduling decisions. It is evidence that assigning jobs to certain pre-defined machines at right time reduces the energy consumption . In addition, switching on/off machines at right time is also considered as an efficient way for energy saving . Most efforts considering energy efficiency mainly focused on single machine or flow shop problems. Although there is some existing work that indeed considered energy efficiency in flexible job shops, they did not consider energy consumption resulting from switching off/on machines . Recently, Zhang et al.  developed a mathematical model for scheduling of energy-efficient flexible job shops considering energy consumption during switching off/on machines. In addition, they also considered energy consumption when a machine is standby. However, their proposed model requires excessive computational time even for small-scale examples. They also developed an efficient Gene Expression Programming (eGEP) algorithm instead of exact methods and metaheuristics method [15-16] to generate dispatching rules automatically, which are very efficient for solving large-scale problems.
In this work, we first use the state-task network  to represent the energy-efficient flexible job shops. In the state-task network, each operation within a job is denoted as a task. Each operation within a job can consume a âstateâ and produce another âstateâ. Two operations within a job related to the same âstateâ will be automatically sequenced. We then develop two novel unit-specific event-based mathematical models for scheduling the energy-efficient flexible job shops. While the first model is developed through direct application of the recent general model proposed by Rakovitis et al. , the other one is developed specifically using the features of the flexible job shops. We solve sixty-three examples from Zhang et al. . The computational results demonstrate that the proposed models lead to significantly smaller model sizes with less than half binary variables and at least one magnitude less constraints than the model of Zhang et al. . As a result, the proposed model requires significantly less computational time to generate the same optimal solution. In addition, the proposed models could generate better solutions for some examples. In order to solve large-scale examples, we develop a rolling-horizon based decomposition approach and improve the efficient Gene Expression Programming (eGEP) algorithm of Zhang et al.  to generate more efficient dispatch rules which could generate better solutions compared to those of Zhang et al. . The 43 large-scale examples from Zhang et al.  are used to illustrate the capability of the proposed solution approaches.
 Harjunkoski I., Maravelias C. T., Bongers, P., Castro, P. M., Engell S., Grossmann I. E., Hooker J., Mandez C., Sand G., Wassick J. Scope for industrial applications of production scheduling models and solution methods. Computers & Chemical Engineering, 2014, 62, 161-193.
 Floudas C. A., Lin X. Continuous-time versus discrete-time approaches for scheduling of chemical processes: A review. Computers & Chemical Engineering, 2004, 28, 2109â2129.
 Lee H., Maravelias C. Discrete-time mixed-integer programming models for short-term scheduling in multipurpose environments, Computers and Chemical Engineering, 2017, 107, 171-183.
 Castro P., Barbosa-PÃ³voa A. P. F. D., Matos H. An improved RTN continuous-time formulation for the short-term scheduling of multipurpose batch plants. Industrial and Engineering Chemistry research, 2001, 40, 2059-2068
 Maravelias C T, Grossmann I E. New General Continuous-Time State-Task Network Formulation for Short-Term Scheduling of Multipurpose Batch Plants. Industrial Engineering and Chemistry research, 2003, 42, 3056-3074
 Shaik M., Floudas C. Novel Unified Modeling Approach for Short-Term Scheduling, Industrial & Engineering Chemistry Research, 2009 48, 2947-2964
 Li J., Floudas C. Optimal event point determination for short-term scheduling of multipurpose batch plants via unit-specific event-based continuous-time approaches, Industrial & Engineering Chemistry Research, 2010, 49, 7446-7469.
 Sursala N., Li J., Karimi I. A Novel Approach to Scheduling Multipurpose Batch Plants Using Unit-Slots, AlChe Journal, 2010, 56, 1859-1879
 Méndez C. A., Cerdá J. Optimal scheduling of a resource-constrained multiproduct batch plant supplying intermediates to nearby end-product facilities. Computers and Chemical Engineering, 2000, 24, 369-376
 Kondili E., Pantelides C. C., Sargent R. W. H. A general algorithm for short-term scheduling of batch operations-I MILP formulation. Computers & Chemical Engineering, 1993, 17, 211-227
 Pantelides C. Unified frameworks for optimal process planning and scheduling. Proc. Second Conf. on Foundations of Computer Aided Operations, 1994, 253-274
 Li Y., He Y., Wang Y, Wang Y., Yan P., Lin S., A modelling method for hybrid energy behavior in flexible machine systems. Energy, 2015, 86, 164-174.
 Cahm C, Denz F, Dirr M, Tuma A. Energy-efficient scheduling in manufacturing companies: A review and research framework. Eur J Oper Res. 2016, 248, 744-757.
 Zhang L., Tang Q., Wu Z., Wang F. Mathematical modelling and evolutionary generation of rule sets for energy-efficient flexible job shops. Energy, 2017, 138, 210-227
 Mouzon G., Yildirim M.B. A framework to minimize total energy consumption and total tardiness on a single machine. International journal of sustainable engineering, 2008, 1, 105-116.
 May G., Stahl B., Taisch M., Prabhu V. Multi-objective genetic algorithm for energy-efficient job shops, International Journal of Production Research, 2015, 53, 7071-7089.
 Rakovitis N, Zhang N., Li J., Zhang L. A new approach for scheduling of multipurpose batch processes with unlimited intermediate storage policy, Front. Chem. Sci. Eng. 2018, accepted for publication