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doi: 10.3934/jimo.2020010

Integrated optimization of process planning and scheduling for reducing carbon emissions

1. 

State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

2. 

School of Automobile and Traffic Engineering, Wuhan University of Science and Technology, Wuhan 430081, China

* Corresponding author: Qiong Liu

Received  October 2018 Revised  June 2019 Published  January 2020

Fund Project: The first author is supported by NSFC grant No.51675206 and No.51561125002 and FRFCU HUST:2016YXMS275.

In order to reduce environment impacts of manufacturing processes and fill in research gaps that most previous separated optimization of process planning and scheduling ignored influences of process planning on scheduling, a multi-objective integrated optimization model of process planning and scheduling for reducing carbon emissions in manufacturing processes is proposed. The model aims at minimizing makespan and carbon emissions in manufacturing processes by integrated optimizing machining methods for all machining features of workpieces, machine allocations of processes, process routes and machining sequence of workpieces. Because there are many parameters in the proposed model needed to be optimized and they are interactional, a four segment encoding method is designed and a Non-dominated Sorting Genetic Algorithm II is adopted to solve the proposed model. A case study including three workpieces with twenty-three machining features to be processed by turning, milling, drilling, boring and grinding is used to verify the proposed integrated model and algorithm. Results show that the proposed integrated optimization method can further reduce carbon emissions and makespan in manufacturing processes compared with conventional separated optimization of process planning and scheduling. The proposed integrated optimization method is validated.

Citation: Qiong Liu, Jialiang Liu, Zhaorui Dong, Mengmeng Zhan, Zhen Mei, Baosheng Ying, Xinyu Shao. Integrated optimization of process planning and scheduling for reducing carbon emissions. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020010
References:
[1]

N. AlikarS. M. MousaviR. A. R. GhazillaM. Tavana and E. U. Olugu, Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system, Reliability Engineering and System Safety, 160 (2017), 1-10.   Google Scholar

[2]

S. Bandyopadhyay and R. Bhattacharya, Solving multi-objective parallel machine scheduling problem by a modified NSGA-II, Applied Mathematical Modelling., 37 (2013), 6718-6729.  doi: 10.1016/j.apm.2013.01.050.  Google Scholar

[3]

S. Bandyopadhyay and R. Bhattacharya, Solving a tri-objective supply chain problem with modified NSGA-II algorithm, Journal of Manufacturing Systems, 104 (2012), 455-462.   Google Scholar

[4]

M. Bettwy, K. Deschinkel and S. Gomes, An Optimization Tool for Process Planning and Scheduling, Advances in Production Management Systems, Innovative and Knowledge-Based Production Management in a Global-Local World, Springer Berlin Heidelberg, 2014. Google Scholar

[5]

T. C. Chang and R. Wysk, Advances in Production Management Systems, Prentice-Hall, USA, (1985). Google Scholar

[6]

I. A. Chaudhry and M. Usman, Integrated process planning and scheduling using genetic algorithms, Tehnički Vjesnik-Technical Gazette, 24 (2017), 1401-1409.   Google Scholar

[7]

G. ChryssolourisS. Chan and N. P. Suh, An integrated approach to process planning and scheduling, Annals of the CIRP, 34 (1985), 413-417.   Google Scholar

[8]

G. ChryssolourisS. Chan and W. Cobb, Decision making on the factory floor: An integrated approach to process planning and scheduling, Robotics and Computer-Integrated Manufacturing, 1 (1984), 413-417.   Google Scholar

[9]

R. W. Conway, W. L. Maxwell and L. W. Miller, Theory of Scheduling, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967.  Google Scholar

[10]

M. DaiD. B. TangA. GiretM. A. Salido and W. D. Li, Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm, Robotics and Computer Integrated Manufacturing, 29 (2013), 418-429.   Google Scholar

[11]

K. DebS. AgrawalA. Pratap and T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, International Conference on Parallel Problem Solving From Nature, 1917 (2000), 849-858.   Google Scholar

[12]

K. FangF. ZhaoN. Uhan and J. W. Sutherland, A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction, Journal of Manufacturing Systems, 30 (2011), 234-240.   Google Scholar

[13]

S. Gomes, A. Bouras and D. Kiritsis, Advances in Production Management Systems, Innovative and Knowledge-Based Production Management in a Global-Local World, APMS 2014, IFIP Advances in Information and Communication Technology, vol 438. Springer, Berlin, Heidelberg, Reading, Mass.-London-Don Mills, Ont., 1967. Google Scholar

[14]

R. V. Grandhi and G. Bharatram, Optimization of large-scale structures, AIAA Journal, 31 (1993), 1329-1337.   Google Scholar

[15]

Z. Han, Y. Sun, C. Xu, X. Dong and Z. Lv, Flow shop equipment utilization rate with time window constraints scheduling optimization problems, IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems, (2016), 483–488 Google Scholar

[16]

J. HuangL. L. Jin and C. Y. Zhang, Mathematical modeling and a hybrid NSGA-II algorithm for process planning problem considering machining cost and carbon emission, Sustainability, 9 (2017), 1769-1786.   Google Scholar

[17]

X. W. HuangX. Y. Zhao and X. L. Ma, Improved genetic algorithm for job-shop scheduling problem with process sequence flexibility, International Journal of Simulation Modelling, 13 (2014), 510-522.   Google Scholar

[18]

M. Leung, Y. Leung and A. Chan, Carbon audit toolkit for small and medium enterprises in Hong Kong, The University of Hong Kong, Hong Kong, 13 (2010). Google Scholar

[19]

X. X. Li, W. D. Li, X. T. Cai and F. Z. He, A Hybrid Optimization Approach for Sustainable Process Planning and Scheduling, Sustainable Manufacturing and Remanufacturing Management, Springer, Cham, 2019. Google Scholar

[20]

W. W. LinD. Y. YuC. Y. ZhangX. LiuS. Q. ZhangY. H. Tian and et al., A multi-objective teaching learning-based optimization algorithm to scheduling in turning processes for minimizing makespan and carbon footprint, Journal of Cleaner Production, 101 (2015), 337-347.   Google Scholar

[21]

X. Y. LiL. GaoX. Y. ShaoC. Y. Zhang and C. Y. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Computers and Operations Research, 37 (2010), 656-667.   Google Scholar

[22]

X. Y. LiL. Gao and X. Wen, Application of an efficient modified particle swarm optimization algorithm for process planning, The International Journal of Advanced Manufacturing Technology, 67 (2013), 1355-1369.   Google Scholar

[23]

C. H. Liu and D. H. Huang, Reduction of power consumption and carbon footprints by applying multi-objective optimisation via genetic algorithms, International Journal of Production Research, 52 (2014), 337-352.   Google Scholar

[24]

G. S. LiuY. Zhou and H. D. Yan, Minimizing energy consumption and tardiness penalty for fuzzy flow shop scheduling with state-dependent setup time, Journal of Cleaner Production, 147 (2017), 470-484.   Google Scholar

[25]

X. J. LiuH. Yi and Z. H. Ni, Application of ant colony optimization algorithm in process planning optimization, Journal of Intelligent Manufacturing, 21 (2013), 1-13.   Google Scholar

[26]

X. Liu, F. Zou and X. Zhang, Mathematical model and genetic optimization for hybrid flow shop scheduling problem based on energy consumption, Control and Decision Conference, (2008), 1002–1007 Google Scholar

[27]

G. F. LuoX. Y. WenH. LiW. Y. Ming and G. Z. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, International Journal of Advanced Manufacturing Technology, 91 (2017), 3145-3158.   Google Scholar

[28]

H. S. Ma, C. H. Zhou, K. S. Wang and J. J. Xiao, The calculation of product carbon footprint and optimization design, Applied Mechanics and Materials, (2013), 2156–2159. Google Scholar

[29]

P. MohapatraA. NayakS. K. Kumar and M. K. Tiwari, Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm, International Journal of Production Research, 53 (2015), 1712-1735.   Google Scholar

[30]

S. K. Paul and A. Azeem, Minimization of work-in-process inventory in hybrid flow shop scheduling using fuzzy logic, International Journal of Industrial Engineering Theory Applications and Practice, 17 (2010), 115-127.   Google Scholar

[31]

L. H. Qiao and S. P. Lv, An improved genetic algorithm for integrated process planning and scheduling, International Journal of Advanced Manufacturing Technology, 58 (2012), 727-740.   Google Scholar

[32]

M. RajkumarP. AsokanT. Page and S. Arunachalam, GRASP algorithm for the integration of process planning and scheduling in a flexible job-shop, International Journal of Manufacturing Research, 5 (2010), 230-251.   Google Scholar

[33]

X. ShaoX. LiL. Gao and C. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Computers and Operations Research, 36 (2009), 2082-2096.   Google Scholar

[34]

K. S. ShinJ. O. Park and Y. K. Kim, Multi-objective FMS process planning with various flexibilities using a symbiotic evolutionary algorithm, Computers and Operations Research, 38 (2011), 702-712.  doi: 10.1016/j.cor.2010.08.007.  Google Scholar

[35]

X. C. Tan, F. Liu, H. J. Cao and H. Zhang, A decision-making framework model of cutting fluid selection for green manufacturing and a case study, Journal of Materials Processing Technology, (129) (2002), 467–470. Google Scholar

[36]

X. C. TanF. Liu and D. C. Liu, Research on the diagnosis and improvement method of a process route in an enterprise production process in terms of sustainable development III, International Journal of Advanced Manufacturing Technology, 33 (2007), 1256-1262.   Google Scholar

[37]

S. WangX. LuX. X. Li and W. D. Li, A systematic approach of process planning and scheduling optimization for sustainable machining, Journal of Cleaner Production, 87 (2015), 914-929.   Google Scholar

[38]

J. H. YanL. LiF. Y. Zhang and Q. L. Zhao, A multi-level optimization approach for energy-efficient flexible flow shop scheduling, Journal of Cleaner Production, 137 (2016), 1543-1552.   Google Scholar

[39]

Q. Yi, C. B. Li, Y. Tang and Q. Wang, A new operational framework to job shop scheduling for reducing carbon emissions, 8th IEEE International Conference on Automation Science and Engineering, (2012), 58–63. Google Scholar

[40]

Q. YiC. B. LiX. L. ZhangF. Liu and Y. Tan, An optimization model of machining process route for low carbon manufacturing, International Journal of Advanced Manufacturing Technology, 80 (2015), 1181-1196.   Google Scholar

[41]

R. X. YinJ. W. SutherlandH. Cao and H. Li, A process planning method for reduced carbon emission, International Journal of Computer Integrated Manufacturing, 27 (2014), 1175-1186.   Google Scholar

[42]

M. R. YuY. J. ZhangK. Chen and D. Zhang, Integration of process planning and scheduling using a hybrid GA/PSO algorithm, International Journal of Advanced Manufacturing Technology, 78 (2015), 583-592.   Google Scholar

[43]

C. Y. ZhangP. H. Gu and P. Y. Jiang, Low-carbon scheduling and estimating for a flexible job shop based on carbon footprint and carbon efficiency of multi-job processing, Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 229 (2005), 328-342.   Google Scholar

[44]

Y. Zhang and L. Ge, Method for process planning optimization with energy efficiency consideration, International Journal of Computer Integrated Manufacturing, 77 (2015), 2197-2207.   Google Scholar

[45]

Y. ZhangQ. LiuY. D. Zhou and B. S. Ying, Integrated optimization of cutting parameters and scheduling for reducing carbon emissions, Journal of Cleaner Production, 149 (2017), 886-895.   Google Scholar

[46]

Z. W. ZhangR. Z. TangT. PengL. Y. Tao and S. Jia, A method for minimizing the energy consumption of machining system: Integration of process planning and scheduling, Journal of Cleaner Production, 137 (2016), 1647-1662.   Google Scholar

show all references

References:
[1]

N. AlikarS. M. MousaviR. A. R. GhazillaM. Tavana and E. U. Olugu, Application of the NSGA-II algorithm to a multi-period inventory-redundancy allocation problem in a series-parallel system, Reliability Engineering and System Safety, 160 (2017), 1-10.   Google Scholar

[2]

S. Bandyopadhyay and R. Bhattacharya, Solving multi-objective parallel machine scheduling problem by a modified NSGA-II, Applied Mathematical Modelling., 37 (2013), 6718-6729.  doi: 10.1016/j.apm.2013.01.050.  Google Scholar

[3]

S. Bandyopadhyay and R. Bhattacharya, Solving a tri-objective supply chain problem with modified NSGA-II algorithm, Journal of Manufacturing Systems, 104 (2012), 455-462.   Google Scholar

[4]

M. Bettwy, K. Deschinkel and S. Gomes, An Optimization Tool for Process Planning and Scheduling, Advances in Production Management Systems, Innovative and Knowledge-Based Production Management in a Global-Local World, Springer Berlin Heidelberg, 2014. Google Scholar

[5]

T. C. Chang and R. Wysk, Advances in Production Management Systems, Prentice-Hall, USA, (1985). Google Scholar

[6]

I. A. Chaudhry and M. Usman, Integrated process planning and scheduling using genetic algorithms, Tehnički Vjesnik-Technical Gazette, 24 (2017), 1401-1409.   Google Scholar

[7]

G. ChryssolourisS. Chan and N. P. Suh, An integrated approach to process planning and scheduling, Annals of the CIRP, 34 (1985), 413-417.   Google Scholar

[8]

G. ChryssolourisS. Chan and W. Cobb, Decision making on the factory floor: An integrated approach to process planning and scheduling, Robotics and Computer-Integrated Manufacturing, 1 (1984), 413-417.   Google Scholar

[9]

R. W. Conway, W. L. Maxwell and L. W. Miller, Theory of Scheduling, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967.  Google Scholar

[10]

M. DaiD. B. TangA. GiretM. A. Salido and W. D. Li, Energy-efficient scheduling for a flexible flow shop using an improved genetic-simulated annealing algorithm, Robotics and Computer Integrated Manufacturing, 29 (2013), 418-429.   Google Scholar

[11]

K. DebS. AgrawalA. Pratap and T. Meyarivan, A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II, International Conference on Parallel Problem Solving From Nature, 1917 (2000), 849-858.   Google Scholar

[12]

K. FangF. ZhaoN. Uhan and J. W. Sutherland, A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction, Journal of Manufacturing Systems, 30 (2011), 234-240.   Google Scholar

[13]

S. Gomes, A. Bouras and D. Kiritsis, Advances in Production Management Systems, Innovative and Knowledge-Based Production Management in a Global-Local World, APMS 2014, IFIP Advances in Information and Communication Technology, vol 438. Springer, Berlin, Heidelberg, Reading, Mass.-London-Don Mills, Ont., 1967. Google Scholar

[14]

R. V. Grandhi and G. Bharatram, Optimization of large-scale structures, AIAA Journal, 31 (1993), 1329-1337.   Google Scholar

[15]

Z. Han, Y. Sun, C. Xu, X. Dong and Z. Lv, Flow shop equipment utilization rate with time window constraints scheduling optimization problems, IEEE International Conference on Cyber Technology in Automation, Control, and Intelligent Systems, (2016), 483–488 Google Scholar

[16]

J. HuangL. L. Jin and C. Y. Zhang, Mathematical modeling and a hybrid NSGA-II algorithm for process planning problem considering machining cost and carbon emission, Sustainability, 9 (2017), 1769-1786.   Google Scholar

[17]

X. W. HuangX. Y. Zhao and X. L. Ma, Improved genetic algorithm for job-shop scheduling problem with process sequence flexibility, International Journal of Simulation Modelling, 13 (2014), 510-522.   Google Scholar

[18]

M. Leung, Y. Leung and A. Chan, Carbon audit toolkit for small and medium enterprises in Hong Kong, The University of Hong Kong, Hong Kong, 13 (2010). Google Scholar

[19]

X. X. Li, W. D. Li, X. T. Cai and F. Z. He, A Hybrid Optimization Approach for Sustainable Process Planning and Scheduling, Sustainable Manufacturing and Remanufacturing Management, Springer, Cham, 2019. Google Scholar

[20]

W. W. LinD. Y. YuC. Y. ZhangX. LiuS. Q. ZhangY. H. Tian and et al., A multi-objective teaching learning-based optimization algorithm to scheduling in turning processes for minimizing makespan and carbon footprint, Journal of Cleaner Production, 101 (2015), 337-347.   Google Scholar

[21]

X. Y. LiL. GaoX. Y. ShaoC. Y. Zhang and C. Y. Wang, Mathematical modeling and evolutionary algorithm-based approach for integrated process planning and scheduling, Computers and Operations Research, 37 (2010), 656-667.   Google Scholar

[22]

X. Y. LiL. Gao and X. Wen, Application of an efficient modified particle swarm optimization algorithm for process planning, The International Journal of Advanced Manufacturing Technology, 67 (2013), 1355-1369.   Google Scholar

[23]

C. H. Liu and D. H. Huang, Reduction of power consumption and carbon footprints by applying multi-objective optimisation via genetic algorithms, International Journal of Production Research, 52 (2014), 337-352.   Google Scholar

[24]

G. S. LiuY. Zhou and H. D. Yan, Minimizing energy consumption and tardiness penalty for fuzzy flow shop scheduling with state-dependent setup time, Journal of Cleaner Production, 147 (2017), 470-484.   Google Scholar

[25]

X. J. LiuH. Yi and Z. H. Ni, Application of ant colony optimization algorithm in process planning optimization, Journal of Intelligent Manufacturing, 21 (2013), 1-13.   Google Scholar

[26]

X. Liu, F. Zou and X. Zhang, Mathematical model and genetic optimization for hybrid flow shop scheduling problem based on energy consumption, Control and Decision Conference, (2008), 1002–1007 Google Scholar

[27]

G. F. LuoX. Y. WenH. LiW. Y. Ming and G. Z. Xie, An effective multi-objective genetic algorithm based on immune principle and external archive for multi-objective integrated process planning and scheduling, International Journal of Advanced Manufacturing Technology, 91 (2017), 3145-3158.   Google Scholar

[28]

H. S. Ma, C. H. Zhou, K. S. Wang and J. J. Xiao, The calculation of product carbon footprint and optimization design, Applied Mechanics and Materials, (2013), 2156–2159. Google Scholar

[29]

P. MohapatraA. NayakS. K. Kumar and M. K. Tiwari, Multi-objective process planning and scheduling using controlled elitist non-dominated sorting genetic algorithm, International Journal of Production Research, 53 (2015), 1712-1735.   Google Scholar

[30]

S. K. Paul and A. Azeem, Minimization of work-in-process inventory in hybrid flow shop scheduling using fuzzy logic, International Journal of Industrial Engineering Theory Applications and Practice, 17 (2010), 115-127.   Google Scholar

[31]

L. H. Qiao and S. P. Lv, An improved genetic algorithm for integrated process planning and scheduling, International Journal of Advanced Manufacturing Technology, 58 (2012), 727-740.   Google Scholar

[32]

M. RajkumarP. AsokanT. Page and S. Arunachalam, GRASP algorithm for the integration of process planning and scheduling in a flexible job-shop, International Journal of Manufacturing Research, 5 (2010), 230-251.   Google Scholar

[33]

X. ShaoX. LiL. Gao and C. Zhang, Integration of process planning and scheduling-a modified genetic algorithm-based approach, Computers and Operations Research, 36 (2009), 2082-2096.   Google Scholar

[34]

K. S. ShinJ. O. Park and Y. K. Kim, Multi-objective FMS process planning with various flexibilities using a symbiotic evolutionary algorithm, Computers and Operations Research, 38 (2011), 702-712.  doi: 10.1016/j.cor.2010.08.007.  Google Scholar

[35]

X. C. Tan, F. Liu, H. J. Cao and H. Zhang, A decision-making framework model of cutting fluid selection for green manufacturing and a case study, Journal of Materials Processing Technology, (129) (2002), 467–470. Google Scholar

[36]

X. C. TanF. Liu and D. C. Liu, Research on the diagnosis and improvement method of a process route in an enterprise production process in terms of sustainable development III, International Journal of Advanced Manufacturing Technology, 33 (2007), 1256-1262.   Google Scholar

[37]

S. WangX. LuX. X. Li and W. D. Li, A systematic approach of process planning and scheduling optimization for sustainable machining, Journal of Cleaner Production, 87 (2015), 914-929.   Google Scholar

[38]

J. H. YanL. LiF. Y. Zhang and Q. L. Zhao, A multi-level optimization approach for energy-efficient flexible flow shop scheduling, Journal of Cleaner Production, 137 (2016), 1543-1552.   Google Scholar

[39]

Q. Yi, C. B. Li, Y. Tang and Q. Wang, A new operational framework to job shop scheduling for reducing carbon emissions, 8th IEEE International Conference on Automation Science and Engineering, (2012), 58–63. Google Scholar

[40]

Q. YiC. B. LiX. L. ZhangF. Liu and Y. Tan, An optimization model of machining process route for low carbon manufacturing, International Journal of Advanced Manufacturing Technology, 80 (2015), 1181-1196.   Google Scholar

[41]

R. X. YinJ. W. SutherlandH. Cao and H. Li, A process planning method for reduced carbon emission, International Journal of Computer Integrated Manufacturing, 27 (2014), 1175-1186.   Google Scholar

[42]

M. R. YuY. J. ZhangK. Chen and D. Zhang, Integration of process planning and scheduling using a hybrid GA/PSO algorithm, International Journal of Advanced Manufacturing Technology, 78 (2015), 583-592.   Google Scholar

[43]

C. Y. ZhangP. H. Gu and P. Y. Jiang, Low-carbon scheduling and estimating for a flexible job shop based on carbon footprint and carbon efficiency of multi-job processing, Proceedings of the Institution of Mechanical Engineers Part B Journal of Engineering Manufacture, 229 (2005), 328-342.   Google Scholar

[44]

Y. Zhang and L. Ge, Method for process planning optimization with energy efficiency consideration, International Journal of Computer Integrated Manufacturing, 77 (2015), 2197-2207.   Google Scholar

[45]

Y. ZhangQ. LiuY. D. Zhou and B. S. Ying, Integrated optimization of cutting parameters and scheduling for reducing carbon emissions, Journal of Cleaner Production, 149 (2017), 886-895.   Google Scholar

[46]

Z. W. ZhangR. Z. TangT. PengL. Y. Tao and S. Jia, A method for minimizing the energy consumption of machining system: Integration of process planning and scheduling, Journal of Cleaner Production, 137 (2016), 1647-1662.   Google Scholar

Figure 1.  Flow chart of NSGA-II
Figure 2.  Four segment encoding
Figure 3.  Crossover of genes in machining method and machine allocation codes
Figure 4.  Crossover of genes in process route code
Figure 5.  Crossover of genes in machining sequence code
Figure 6.  Mutation of genes in machining method and machine allocation code
Figure 7.  Mutation of process route code
Figure 8.  Mutation of machine allocation code
Figure 9.  Mutation of machining sequence code
Figure 10.  The workpiece 1 of sleeve
Figure 11.  The workpiece 2 of hinge
Figure 12.  The workpiece 3 of flange
Figure 13.  The Gantt chart of solution 1
Figure 14.  The Gantt chart of solution 29
Figure 15.  The relationship of two objectives
Figure 16.  Components of carbon emissions in each solution in the Pareto set
Figure 17.  Gantt chart of solution 1 for scheduling after process planning
Table 1.  Literatures on IPPS
IPPS Publication Optimization Objectives Decision Variables Optimization method
Integrated Optimization of Cutting Parameters and Scheduling Fang et al.(2011) 1. Makespan
2. Peak total power consumptions
3. Carbon footprints of machines
1. Schedule plans Schedule under limited sets of cutting speed
Lin et al. [20] 1. Makespan
2. Carbon footprints caused by energy consumption of machines in machining and idling states and material consumption of cutting tools
1. Cutting parameters
2. Schedule plans
Optimization of cutting parameters before scheduling
Zhang et al. [45] 1. Completion time
2. Carbon emissions caused by energy consumption of machines in machining and idling states, and material consumption of cutting tools and cutting fluid
1. Cutting parameters
2. Schedule plans
Real integrated optimization
Integrated Optimization of Process Planning Chaudhry and Usman [6] 1. Makespan 1. Process routes
2.Schedule plans
Select one process route for each workpiece from a predetermined process route set before scheduling
Qiao and Lv [31] 1. Makespan
2. Mean flow time
1. Process routes
2. Machining methods
Optimization of process plan before scheduling
Bettwyet al. [4] 1. Makespan 1. Process routes
2. Schedule plans
Integrated optimization, but transportation time and setup time were ignored
Li et al. [19] 1. Makespan
2. Machine utilization
3. Energy consumption of machines in powered on, idling, preheated, machining and powered off states
1. Machining sequence of workpieces
2. Machine allocation
3. Cutting tool selection
4. Cutting tool approaching direction
Scheduling based on generated process plans of workpieces
Zhang et al. [46] 1. Energy consumptions of machines in machining and idling states 1. Process plans
2. scheduling plans
Scheduling under the process plans selected from candidates
Wang et al. [37] 1. Makespan
2. Energy consumptions of machines in machining, idling, setup and tool changing states
1. Cutting parameters
2. Process routes
3. Scheduling
Integrated optimization of process routes and scheduling using the optimized cutting parameters
IPPS Publication Optimization Objectives Decision Variables Optimization method
Integrated Optimization of Cutting Parameters and Scheduling Fang et al.(2011) 1. Makespan
2. Peak total power consumptions
3. Carbon footprints of machines
1. Schedule plans Schedule under limited sets of cutting speed
Lin et al. [20] 1. Makespan
2. Carbon footprints caused by energy consumption of machines in machining and idling states and material consumption of cutting tools
1. Cutting parameters
2. Schedule plans
Optimization of cutting parameters before scheduling
Zhang et al. [45] 1. Completion time
2. Carbon emissions caused by energy consumption of machines in machining and idling states, and material consumption of cutting tools and cutting fluid
1. Cutting parameters
2. Schedule plans
Real integrated optimization
Integrated Optimization of Process Planning Chaudhry and Usman [6] 1. Makespan 1. Process routes
2.Schedule plans
Select one process route for each workpiece from a predetermined process route set before scheduling
Qiao and Lv [31] 1. Makespan
2. Mean flow time
1. Process routes
2. Machining methods
Optimization of process plan before scheduling
Bettwyet al. [4] 1. Makespan 1. Process routes
2. Schedule plans
Integrated optimization, but transportation time and setup time were ignored
Li et al. [19] 1. Makespan
2. Machine utilization
3. Energy consumption of machines in powered on, idling, preheated, machining and powered off states
1. Machining sequence of workpieces
2. Machine allocation
3. Cutting tool selection
4. Cutting tool approaching direction
Scheduling based on generated process plans of workpieces
Zhang et al. [46] 1. Energy consumptions of machines in machining and idling states 1. Process plans
2. scheduling plans
Scheduling under the process plans selected from candidates
Wang et al. [37] 1. Makespan
2. Energy consumptions of machines in machining, idling, setup and tool changing states
1. Cutting parameters
2. Process routes
3. Scheduling
Integrated optimization of process routes and scheduling using the optimized cutting parameters
Table 2.  Parameters and variables
N=(1, 2, ...n) set of workpieces M=(1, 2, ..., m) set of machines
i workpiece i $ \in $ N k machine k$ \in $ M
$ f_{ir} $ the r-th machining feature of workpiece i, r$ \in $ (1, 2, ..., $ F_{i} $) (1, 2, ...$ N_{fir} $) set of candidate machining methods for machining feature $ f_{ir} $
$ o_{ij} $ the j-th process of workpiece i, j$ \in $J, J=(1, 2, ..., $ n_{i} $) $ M_{ij} $ set of candidate machines for the j-th process of workpiece i
$ C_{p} $ carbon emissions in manufacturing processes
$ C_{Me} $ carbon emissions caused by energy consumption of machines in machining state
$ C_{Ie} $ carbon emissions caused by energy consumption of machines in idling state
$ C_{Ae} $ carbon emissions caused by energy consumption of machines in setup state
$ C_{c} $ carbon emissions caused by consumption of coolant
$ C_{l} $ carbon emissions caused by consumption of lubricant
$ C_{t} $ carbon emissions caused by energy consumption of electric fork lifts
$ \alpha_{e} $ carbon emission factor of electric energy
$ P_{ijk} $ power of machine k to machine the j-th process of workpiece i
$ t_{ijk} $ power of machine to machine the j-th process of workpiece i on machine k
$ P_{idle, k} $ idling power of machine k
$ S_{ijk} $, $ C_{ijk} $ start time and completion time of the j-th process of workpiece i on the machine k
$ C_{hlk} $ completion time of the l-th process of the immediate preceding processing workpiece h of workpiece i on machine k, $ S_{ijk} $=$ C_{hlk} $ if the j-th process of workpiece i is the first process on machine k
$ S_{fok} $ start time of the o-th process of the immediate succeeding processing workpiece h of workpiece i on machine k, $ S_{fok} $=$ C_{ijk} $ if the j-th process of workpiece i is the last process on machine k
$ P_{hik} $, $ t_{hik} $ setup power and time of machine k from processing the immediate preceding processing workpiece h to workpiece i
$ E_{k} $ energy consumption of machine in state of power on, preheating and power off
$ T_{ck} $ effective duration of coolant in machine k
$ L_{ck} $ recycling coolants in machine k
$ \alpha_{ck} $ carbon emission factor of coolant
$ T_{open, k} $, $ T_{dose, k} $ power on time and power off time of machine k; $ T_{open, k} $-$ T_{dose, k} $: operation time of machine k.
$ T_{lk} $ effective duration of lubricant in machine k
$ L_{lk} $ lubricant consumptions in machine k
$ \alpha_{l} $ carbon emission factor of lubricant
$ P_{tij} $ power of electric forklift to handle workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece
$ T_{lk} $ effective duration of lubricant in machine k
$ t_{tij} $ transmission time needed to move workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece i
$ C_{time} $ makespan in manufacturing processes
$ X_{fir} $ the selected machining method for machining feature $ f_{ir} $ of workpiece i
$ l_{z} $ the l-th flexible process section of type $ T_{z} $
$ O_{iplz} $ process p in the l-th flexible process section of type $ T_{z} $ of workpiece i
$ X_{ijk} $ decision variable
N=(1, 2, ...n) set of workpieces M=(1, 2, ..., m) set of machines
i workpiece i $ \in $ N k machine k$ \in $ M
$ f_{ir} $ the r-th machining feature of workpiece i, r$ \in $ (1, 2, ..., $ F_{i} $) (1, 2, ...$ N_{fir} $) set of candidate machining methods for machining feature $ f_{ir} $
$ o_{ij} $ the j-th process of workpiece i, j$ \in $J, J=(1, 2, ..., $ n_{i} $) $ M_{ij} $ set of candidate machines for the j-th process of workpiece i
$ C_{p} $ carbon emissions in manufacturing processes
$ C_{Me} $ carbon emissions caused by energy consumption of machines in machining state
$ C_{Ie} $ carbon emissions caused by energy consumption of machines in idling state
$ C_{Ae} $ carbon emissions caused by energy consumption of machines in setup state
$ C_{c} $ carbon emissions caused by consumption of coolant
$ C_{l} $ carbon emissions caused by consumption of lubricant
$ C_{t} $ carbon emissions caused by energy consumption of electric fork lifts
$ \alpha_{e} $ carbon emission factor of electric energy
$ P_{ijk} $ power of machine k to machine the j-th process of workpiece i
$ t_{ijk} $ power of machine to machine the j-th process of workpiece i on machine k
$ P_{idle, k} $ idling power of machine k
$ S_{ijk} $, $ C_{ijk} $ start time and completion time of the j-th process of workpiece i on the machine k
$ C_{hlk} $ completion time of the l-th process of the immediate preceding processing workpiece h of workpiece i on machine k, $ S_{ijk} $=$ C_{hlk} $ if the j-th process of workpiece i is the first process on machine k
$ S_{fok} $ start time of the o-th process of the immediate succeeding processing workpiece h of workpiece i on machine k, $ S_{fok} $=$ C_{ijk} $ if the j-th process of workpiece i is the last process on machine k
$ P_{hik} $, $ t_{hik} $ setup power and time of machine k from processing the immediate preceding processing workpiece h to workpiece i
$ E_{k} $ energy consumption of machine in state of power on, preheating and power off
$ T_{ck} $ effective duration of coolant in machine k
$ L_{ck} $ recycling coolants in machine k
$ \alpha_{ck} $ carbon emission factor of coolant
$ T_{open, k} $, $ T_{dose, k} $ power on time and power off time of machine k; $ T_{open, k} $-$ T_{dose, k} $: operation time of machine k.
$ T_{lk} $ effective duration of lubricant in machine k
$ L_{lk} $ lubricant consumptions in machine k
$ \alpha_{l} $ carbon emission factor of lubricant
$ P_{tij} $ power of electric forklift to handle workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece
$ T_{lk} $ effective duration of lubricant in machine k
$ t_{tij} $ transmission time needed to move workpiece i from machine k' for the (j-1)-th process of workpiece i to machine k for the j-th process of workpiece i
$ C_{time} $ makespan in manufacturing processes
$ X_{fir} $ the selected machining method for machining feature $ f_{ir} $ of workpiece i
$ l_{z} $ the l-th flexible process section of type $ T_{z} $
$ O_{iplz} $ process p in the l-th flexible process section of type $ T_{z} $ of workpiece i
$ X_{ijk} $ decision variable
Table 3.  Machining features, processing constraint, machining methods and machine types of workpieces
Workpiece Machining features Processing constraints on machining feature Candidate machining methods Process re-coding Machine types
Workpiece 1 $ f_{1} $ Method 1:Rough turning a(200s)-Finish turning b(160s) Method 2:Rough milling a (180s)-Finish milling b(150s) Rough turning 1- Finish turning 9 Rough milling 1- Finish milling 9 Turning lathe- Turning lathe Milling machine- Milling machine
$ f_{2} $ Method 1:Rough turning c (120s)- Finish turning d(60s)-Grinding e(100s) Rough turning 2- Finish turning 10- Grinding 16 Turning lathe - Turning lathe -Grinding machine
$ f_{3} $ Method 1:Rough turning f (130s)- Finish turning g (50s)- Grinding h (120s) Method 2:Rough milling f(100s)-Finish milling g(40s)- Grinding h (120s) Rough turning 4-Finish turning12-Grinding 18 Rough milling 4-Finish milling 12 -Grinding 18 Turning lathe - Turning lathe -Grinding machine Milling machine - Milling machine -Grinding machine
$ f_{4} $ Method 1:Rough turning i (150s)- Finish turning j (60s)- Grinding k (120s) Rough turning3-Finish turning11 -Grinding 17 Turning lathe - Turning lathe -Grinding machine
$ f_{5} $ Method 1:Rough turning l (150s)- Finish turning m(100s) Method 2:Rough milling l (130s)-Finish milling m(90s) Rough turning 5- Finish turning 13 Rough milling 5-Finish milling 13 Turning lathe - Turning lathe Milling machine - Milling machine
$ f_{6} $ After $ f_{1} $-$ f_{5} $ Method :Drilling n (120s)-Counterboring o (80s) -Reaming p (60s) Drilling 6-Counterboring 7-Reaming14 Drilling machine-Drilling machine -Drilling machine
$ f_{7} $ After $ f_{1} $-$ f_{5} $ Method 1:Drilling q (200s)-Counterboring r (150s) Drilling 8-Counterboring 15 Drilling machine-Drilling machine
Workpiece 2 $ f_{1} $ Method1:Rough milling a (120s)-Semi finish milling b (50s)-Finish milling c (60s) Rough milling 1-Semi finish milling 2-Finish milling 9 Milling machine - Milling machine - Milling machine
$ f_{2} $ Method 1:Milling d (110s) Milling 3 Milling machine
$ f_{3} $ After $ f_{1} $, $ f_{2} $, $ f_{5} $ Method 1:Rough boring e (60s)-Semi boring f (50s) -Finish boring g (60s)-h (0s) Method 2:Drilling e (50s)-Counterboring f (40s) -Rough reaming g (50s)-Finish reaming h (60s) Rough boring 5-Semi boring 7-Finish boring 10-12 Drilling5-Counterboring 7-Rough reaming 10-Finish reaming 12 Boring machine-Boring machine -Boring machine-0 Drilling machine-Drilling machine -Drilling machine -Drilling machine
$ f_{4} $ After $ f_{1} $, $ f_{2} $, $ f_{5} $ Method 1:Rough boring i (60s)-Semi boring j(50s) -Finish boring k(60s)-l(0s) Method 2:Drilling i(50s)-Counterboring j(40s) -Rough reaming k(50s)-Finish reaming l(60s) Rough boring 6-Semi boring 8 -Finish boring 11-13 Drilling 6-Counterboring 8-Rough reaming 11-Finish reaming 13 Boring machine-Boring machine-Boring machine-0 Drilling machine-Drilling machine-Drilling machine-Drilling machine
$ f_{5} $ Method 1:Milling m(110s) Milling 4 Milling machine
Workpiece 3 $ f_{1} $ Method 1:Milling a(120s) Milling 1 Milling machine
$ f_{2} $ Method 1:Rough milling b(100s)- Semi finish milling c(80s) Rough milling 2-Semi finish milling 15 Milling machine-Milling machine
$ f_{3} $ After $ f_{1} $, $ f_{2} $ Method 1;Rough milling d(150s)- Semi finish milling e(130s) Rough milling 3-Semi finish milling 16 Milling machine - Milling machine
$ f_{4} $ After $ f_{1} $, $ f_{2} $ Method 1:Rough turning f(150s)- Semi finish turning g(100s) Method 2;Rough milling f(130s)- Semi finish milling g(100s) Rough turning 4-Semi finish turning17 Turning lathe - Turning lathe
$ f_{5} $ After $ f_{1} $, $ f_{2} $ Method 1;Rough turning h(180s)- Semi finish turning i(100s)- Finish turning j(110s) Rough turning 5-Semi finish turning 6- Finish turning 18 Turning lathe - Turning lathe-Turning lathe
$ f_{6} $ After $ f_{1} $, $ f_{2} $ Method 1:Turning k(100s) Turning 7 Turning lathe
$ f_{7} $ After $ f_{1} $, $ f_{2} $ Method 1:Rough milling l(120s)- Semi finish milling m(100s)-Finish milling n(50s) Rough milling 8-Semi finish milling 9-Finish milling 19 Milling machine - Milling machine - Milling machine
$ f_{8} $ After $ f_{3} $-$ f_{6} $ Method 1;Rough boring o(100s)-Semi boring p(60s)-Finish boring q(110s) Method 2:Rough turning o(120s)-Semi finish turning p(110s)- Finish turning q(80s) Rough boring 10-Semi boring 11-Finish boring 20 Rough turning 10-Semi finish turning 11- Finish turning 20 Boring machine-Boring machine-Boring machine Turning lathe - Turning lathe - Turning lathe
$ f_{9} $ After $ f_{3} $-$ f_{6} $ Method 1:Rough milling r(130s)- Semi finish milling s(90s) Method 2:Rough turning r(150s)- Semi finish turning s(110s) Method 3:Rough boring r(120s)-Semi boring s(70s) Rough milling12-Semi finish milling21 Rough turning 12-Semi finish turning 21 Milling machine- Milling machine Turning lathe- Turning lathe
$ f_{10} $ After $ f_{8} $, $ f_{9} $ Method 1:Drilling t(100s)-Counterboring u(50s) Drilling 13-Counterboring 22 Drilling machine-Drilling machine
$ f_{11} $ After $ f_{8} $, $ f_{9} $ Method 1:Drilling v(120s)-Counterboring w(60s) Drilling 14-Counterboring 23 Drilling machine-Drilling machine
Workpiece Machining features Processing constraints on machining feature Candidate machining methods Process re-coding Machine types
Workpiece 1 $ f_{1} $ Method 1:Rough turning a(200s)-Finish turning b(160s) Method 2:Rough milling a (180s)-Finish milling b(150s) Rough turning 1- Finish turning 9 Rough milling 1- Finish milling 9 Turning lathe- Turning lathe Milling machine- Milling machine
$ f_{2} $ Method 1:Rough turning c (120s)- Finish turning d(60s)-Grinding e(100s) Rough turning 2- Finish turning 10- Grinding 16 Turning lathe - Turning lathe -Grinding machine
$ f_{3} $ Method 1:Rough turning f (130s)- Finish turning g (50s)- Grinding h (120s) Method 2:Rough milling f(100s)-Finish milling g(40s)- Grinding h (120s) Rough turning 4-Finish turning12-Grinding 18 Rough milling 4-Finish milling 12 -Grinding 18 Turning lathe - Turning lathe -Grinding machine Milling machine - Milling machine -Grinding machine
$ f_{4} $ Method 1:Rough turning i (150s)- Finish turning j (60s)- Grinding k (120s) Rough turning3-Finish turning11 -Grinding 17 Turning lathe - Turning lathe -Grinding machine
$ f_{5} $ Method 1:Rough turning l (150s)- Finish turning m(100s) Method 2:Rough milling l (130s)-Finish milling m(90s) Rough turning 5- Finish turning 13 Rough milling 5-Finish milling 13 Turning lathe - Turning lathe Milling machine - Milling machine
$ f_{6} $ After $ f_{1} $-$ f_{5} $ Method :Drilling n (120s)-Counterboring o (80s) -Reaming p (60s) Drilling 6-Counterboring 7-Reaming14 Drilling machine-Drilling machine -Drilling machine
$ f_{7} $ After $ f_{1} $-$ f_{5} $ Method 1:Drilling q (200s)-Counterboring r (150s) Drilling 8-Counterboring 15 Drilling machine-Drilling machine
Workpiece 2 $ f_{1} $ Method1:Rough milling a (120s)-Semi finish milling b (50s)-Finish milling c (60s) Rough milling 1-Semi finish milling 2-Finish milling 9 Milling machine - Milling machine - Milling machine
$ f_{2} $ Method 1:Milling d (110s) Milling 3 Milling machine
$ f_{3} $ After $ f_{1} $, $ f_{2} $, $ f_{5} $ Method 1:Rough boring e (60s)-Semi boring f (50s) -Finish boring g (60s)-h (0s) Method 2:Drilling e (50s)-Counterboring f (40s) -Rough reaming g (50s)-Finish reaming h (60s) Rough boring 5-Semi boring 7-Finish boring 10-12 Drilling5-Counterboring 7-Rough reaming 10-Finish reaming 12 Boring machine-Boring machine -Boring machine-0 Drilling machine-Drilling machine -Drilling machine -Drilling machine
$ f_{4} $ After $ f_{1} $, $ f_{2} $, $ f_{5} $ Method 1:Rough boring i (60s)-Semi boring j(50s) -Finish boring k(60s)-l(0s) Method 2:Drilling i(50s)-Counterboring j(40s) -Rough reaming k(50s)-Finish reaming l(60s) Rough boring 6-Semi boring 8 -Finish boring 11-13 Drilling 6-Counterboring 8-Rough reaming 11-Finish reaming 13 Boring machine-Boring machine-Boring machine-0 Drilling machine-Drilling machine-Drilling machine-Drilling machine
$ f_{5} $ Method 1:Milling m(110s) Milling 4 Milling machine
Workpiece 3 $ f_{1} $ Method 1:Milling a(120s) Milling 1 Milling machine
$ f_{2} $ Method 1:Rough milling b(100s)- Semi finish milling c(80s) Rough milling 2-Semi finish milling 15 Milling machine-Milling machine
$ f_{3} $ After $ f_{1} $, $ f_{2} $ Method 1;Rough milling d(150s)- Semi finish milling e(130s) Rough milling 3-Semi finish milling 16 Milling machine - Milling machine
$ f_{4} $ After $ f_{1} $, $ f_{2} $ Method 1:Rough turning f(150s)- Semi finish turning g(100s) Method 2;Rough milling f(130s)- Semi finish milling g(100s) Rough turning 4-Semi finish turning17 Turning lathe - Turning lathe
$ f_{5} $ After $ f_{1} $, $ f_{2} $ Method 1;Rough turning h(180s)- Semi finish turning i(100s)- Finish turning j(110s) Rough turning 5-Semi finish turning 6- Finish turning 18 Turning lathe - Turning lathe-Turning lathe
$ f_{6} $ After $ f_{1} $, $ f_{2} $ Method 1:Turning k(100s) Turning 7 Turning lathe
$ f_{7} $ After $ f_{1} $, $ f_{2} $ Method 1:Rough milling l(120s)- Semi finish milling m(100s)-Finish milling n(50s) Rough milling 8-Semi finish milling 9-Finish milling 19 Milling machine - Milling machine - Milling machine
$ f_{8} $ After $ f_{3} $-$ f_{6} $ Method 1;Rough boring o(100s)-Semi boring p(60s)-Finish boring q(110s) Method 2:Rough turning o(120s)-Semi finish turning p(110s)- Finish turning q(80s) Rough boring 10-Semi boring 11-Finish boring 20 Rough turning 10-Semi finish turning 11- Finish turning 20 Boring machine-Boring machine-Boring machine Turning lathe - Turning lathe - Turning lathe
$ f_{9} $ After $ f_{3} $-$ f_{6} $ Method 1:Rough milling r(130s)- Semi finish milling s(90s) Method 2:Rough turning r(150s)- Semi finish turning s(110s) Method 3:Rough boring r(120s)-Semi boring s(70s) Rough milling12-Semi finish milling21 Rough turning 12-Semi finish turning 21 Milling machine- Milling machine Turning lathe- Turning lathe
$ f_{10} $ After $ f_{8} $, $ f_{9} $ Method 1:Drilling t(100s)-Counterboring u(50s) Drilling 13-Counterboring 22 Drilling machine-Drilling machine
$ f_{11} $ After $ f_{8} $, $ f_{9} $ Method 1:Drilling v(120s)-Counterboring w(60s) Drilling 14-Counterboring 23 Drilling machine-Drilling machine
Table 4.  Time needed to move a workpiece from one machine to another (/s)
Process/machine Turning Milling Drilling Boring Grinding
M1 M2 M3 M4 M5 M6 M7 M8 M9
Turning M1 0 10 19 40 42 60 62 70 80
M2 10 0 10 40 40 60 60 70 78
M3 19 10 0 40 40 60 60 70 72
Milling M4 40 40 40 0 12 30 30 40 50
M5 42 40 40 12 0 30 30 40 53
Drilling M6 60 60 60 30 30 0 12 20 28
M7 62 60 60 30 30 12 0 20 26
Boring M8 70 70 70 40 40 20 20 0 18
Grinding M9 80 78 72 50 53 28 26 18 0
Process/machine Turning Milling Drilling Boring Grinding
M1 M2 M3 M4 M5 M6 M7 M8 M9
Turning M1 0 10 19 40 42 60 62 70 80
M2 10 0 10 40 40 60 60 70 78
M3 19 10 0 40 40 60 60 70 72
Milling M4 40 40 40 0 12 30 30 40 50
M5 42 40 40 12 0 30 30 40 53
Drilling M6 60 60 60 30 30 0 12 20 28
M7 62 60 60 30 30 12 0 20 26
Boring M8 70 70 70 40 40 20 20 0 18
Grinding M9 80 78 72 50 53 28 26 18 0
Table 5.  The identifiers of clamping method for machining features of workpieces
Workpiece Workpiece 1 Workpiece 2 Workpiece 3
Machining features $ f_{1} $ $ f_{2} $ $ f_{3} $ $ f_{4} $ $ f_{5} $ $ f_{1} $ $ f_{2} $ $ f_{5} $ $ f_{1} $ $ f_{2} $ $ f_{3} $ $ f_{4} $ $ f_{5} $ $ f_{6} $ $ f_{7} $ $ f_{8} $ $ f_{9} $
Machining Turning 1 1 2 2 2 - - - - - - 10 10 10 - 11 11
Milling 3 - 4 - 4 7 8 9 12 12 13 13 - - 13 - 14
methods Grinding - 5 6 5 - - - - - - - - - - - - -
Workpiece Workpiece 1 Workpiece 2 Workpiece 3
Machining features $ f_{1} $ $ f_{2} $ $ f_{3} $ $ f_{4} $ $ f_{5} $ $ f_{1} $ $ f_{2} $ $ f_{5} $ $ f_{1} $ $ f_{2} $ $ f_{3} $ $ f_{4} $ $ f_{5} $ $ f_{6} $ $ f_{7} $ $ f_{8} $ $ f_{9} $
Machining Turning 1 1 2 2 2 - - - - - - 10 10 10 - 11 11
Milling 3 - 4 - 4 7 8 9 12 12 13 13 - - 13 - 14
methods Grinding - 5 6 5 - - - - - - - - - - - - -
Table 6.  Setup times for processing different workpieces on the same machine and times needed to change clamping types (/s)
Workpiece 1 2 3 1 2 3 1 2 3
Machine M1 M2 M3
Workpiece 1 (26) 28 32 (20) 26 30 (20) 26 30
2 30 (0) 40 30 (0) 26 30 (0) 26
3 40 50 (29) 35 30 (22) 35 30 (22)
M4 M5 M6
1 (26) 26 30 (21) 21 30 (0) 58 31
2 30 (22) 26 25 (22) 26 55 (0) 60
3 35 30 (30) 35 30 (30) 25 50 (0)
M7 M8 M9
1 (0) 58 24 (0) 32 40 (18) 29 45
2 55 (0) 60 35 (0) 90 25 (15) 30
3 20 50 (0) 30 80 (28) 40 25 (20)
Workpiece 1 2 3 1 2 3 1 2 3
Machine M1 M2 M3
Workpiece 1 (26) 28 32 (20) 26 30 (20) 26 30
2 30 (0) 40 30 (0) 26 30 (0) 26
3 40 50 (29) 35 30 (22) 35 30 (22)
M4 M5 M6
1 (26) 26 30 (21) 21 30 (0) 58 31
2 30 (22) 26 25 (22) 26 55 (0) 60
3 35 30 (30) 35 30 (30) 25 50 (0)
M7 M8 M9
1 (0) 58 24 (0) 32 40 (18) 29 45
2 55 (0) 60 35 (0) 90 25 (15) 30
3 20 50 (0) 30 80 (28) 40 25 (20)
Table 7.  Powers of machines, usages of coolant and lubricant
Machine
M1 M2 M3 M4 M5 M6 M7 M8 M9
Power (/$ 10^{3}w $) Workpiece 1 9.5 7.6 8 8.5 11.5 12 9.5 9.25 15
2 13.5 9 9.5 9.25 10.6 11.5 10 9.9 15.5
3 9.5 7.5 12 10 9.25 9 9.1 8 15
Idling 1.1 1.4 1.25 0.75 0.9 2.75 2.1 2 2.5
Setup 2.1 2.5 2.3 1.9 2.1 3.8 3.2 3.1 3.6
Coolant Usage(/$ 10^{-3} $$ m^{3} $) 350 360 350 210 200 410 400 300 300
Use cycle(/$ 10^{4}s $) 86 86 86 120 120 90 90 130 100
Lubricant Usage(/$ 10^{-3} $$ m^{3} $) 0.3 0.31 0.33 0.28 0.3 0.33 0.35 0.29 0.32
Use cycle(/$ 10^{4}s $) 41 41 41 46 46 54 54 50 58
Machine
M1 M2 M3 M4 M5 M6 M7 M8 M9
Power (/$ 10^{3}w $) Workpiece 1 9.5 7.6 8 8.5 11.5 12 9.5 9.25 15
2 13.5 9 9.5 9.25 10.6 11.5 10 9.9 15.5
3 9.5 7.5 12 10 9.25 9 9.1 8 15
Idling 1.1 1.4 1.25 0.75 0.9 2.75 2.1 2 2.5
Setup 2.1 2.5 2.3 1.9 2.1 3.8 3.2 3.1 3.6
Coolant Usage(/$ 10^{-3} $$ m^{3} $) 350 360 350 210 200 410 400 300 300
Use cycle(/$ 10^{4}s $) 86 86 86 120 120 90 90 130 100
Lubricant Usage(/$ 10^{-3} $$ m^{3} $) 0.3 0.31 0.33 0.28 0.3 0.33 0.35 0.29 0.32
Use cycle(/$ 10^{4}s $) 41 41 41 46 46 54 54 50 58
Table 8.  Carbon emission factors
Resource Carbon emission factor
Electrical energy 1.8742x$ 10^{-7} $ $ kgCO_{2}/J $
Lubricant 2,850 $ kgCO_{2}/ $$ m^{3} $
coolant 3,050$ kgCO_{2}/ $ $ m^{3} $
Resource Carbon emission factor
Electrical energy 1.8742x$ 10^{-7} $ $ kgCO_{2}/J $
Lubricant 2,850 $ kgCO_{2}/ $$ m^{3} $
coolant 3,050$ kgCO_{2}/ $ $ m^{3} $
Table 9.  A Pareto set of the proposed integrated method of process planning and scheduling
The number of Pareto solutions $ C_{Me} $ $ (kgCO_{2}) $ $ C_{Ie} $ $ (kgCO_{2}) $ $ C_{Ae} $ $ (kgCO_{2}) $ $ C_{t} $ $ (kgCO_{2}) $ $ C_{c} $ $ (kgCO_{2}) $ $ C_{l} $ $ (kgCO_{2}) $ $ C_{p} $ $ (kgCO_{2}) $ $ C_{time} $ (s)
1 8.7531 3.7681 0.095985 0.45655 0.10306 0.19883 13.376 2,796
2 9.0407 3.8443 0.11121 0.52739 0.10387 0.19315 13.821 2,780
3 9.108 3.7814 0.12769 0.53395 0.10151 0.18059 13.833 2,735
... ... ... ... ... ... ... ... ...
27 8.9757 6.1699 0.14854 0.62382 0.10072 0.25358 16.272 2,536
28 8.8894 6.3467 0.2138 0.53723 0.10252 0.22544 16.315 2,530
29 8.8997 6.281 0.27783 0.54117 0.10202 0.22421 16.326 2,525
The number of Pareto solutions $ C_{Me} $ $ (kgCO_{2}) $ $ C_{Ie} $ $ (kgCO_{2}) $ $ C_{Ae} $ $ (kgCO_{2}) $ $ C_{t} $ $ (kgCO_{2}) $ $ C_{c} $ $ (kgCO_{2}) $ $ C_{l} $ $ (kgCO_{2}) $ $ C_{p} $ $ (kgCO_{2}) $ $ C_{time} $ (s)
1 8.7531 3.7681 0.095985 0.45655 0.10306 0.19883 13.376 2,796
2 9.0407 3.8443 0.11121 0.52739 0.10387 0.19315 13.821 2,780
3 9.108 3.7814 0.12769 0.53395 0.10151 0.18059 13.833 2,735
... ... ... ... ... ... ... ... ...
27 8.9757 6.1699 0.14854 0.62382 0.10072 0.25358 16.272 2,536
28 8.8894 6.3467 0.2138 0.53723 0.10252 0.22544 16.315 2,530
29 8.8997 6.281 0.27783 0.54117 0.10202 0.22421 16.326 2,525
Table 10.  Pareto solutions of scheduling after process planning
The number of Pareto solutions $ C_{Me} $ $ (kgCO_{2}) $ $ C_{Ie} $ $ (kgCO_{2}) $ $ C_{Ae} $ $ (kgCO_{2}) $ $ C_{t} $ $ (kgCO_{2}) $ $ C_{c} $ $ (kgCO_{2}) $ $ C_{l} $ $ (kgCO_{2}) $ $ C_{p} $ $ (kgCO_{2}) $ $ C_{time} $ (s)
1 8.5521 4.5633 0.12961 0.4408 0.09917 0.20544 13.966 3,082
2 8.994 4.2145 0.13048 0.44605 0.10144 0.18311 14.169 2,941
3 8.9908 4.4446 0.13095 0.53526 0.1023 0.22189 14.426 2,616
... ... ... ... ... ... ... ... ...
11 9.1172 5.7343 0.072699 0.53526 0.10447 0.21548 15.779 2,545
12 8.9459 6.0728 0.12725 0.47951 0.10216 0.21728 15.945 2,535
13 9.3706 6.1467 0.1115 0.5392 0.10312 0.25379 16.525 2,530
The number of Pareto solutions $ C_{Me} $ $ (kgCO_{2}) $ $ C_{Ie} $ $ (kgCO_{2}) $ $ C_{Ae} $ $ (kgCO_{2}) $ $ C_{t} $ $ (kgCO_{2}) $ $ C_{c} $ $ (kgCO_{2}) $ $ C_{l} $ $ (kgCO_{2}) $ $ C_{p} $ $ (kgCO_{2}) $ $ C_{time} $ (s)
1 8.5521 4.5633 0.12961 0.4408 0.09917 0.20544 13.966 3,082
2 8.994 4.2145 0.13048 0.44605 0.10144 0.18311 14.169 2,941
3 8.9908 4.4446 0.13095 0.53526 0.1023 0.22189 14.426 2,616
... ... ... ... ... ... ... ... ...
11 9.1172 5.7343 0.072699 0.53526 0.10447 0.21548 15.779 2,545
12 8.9459 6.0728 0.12725 0.47951 0.10216 0.21728 15.945 2,535
13 9.3706 6.1467 0.1115 0.5392 0.10312 0.25379 16.525 2,530
[1]

Dariush Mohamadi Zanjirani, Majid Esmaelian. An integrated approach based on Fuzzy Inference System for scheduling and process planning through multiple objectives. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1235-1259. doi: 10.3934/jimo.2018202

[2]

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