Abstract
Green low carbon flexible job shop problems have been extensively studied in recent decades, while most of them ignore the influence of workers. In this paper, we take workers into account and consider the effects of their learning abilities on the processing time and energy consumption. And then a new low carbon flexible job shop scheduling problem considering worker learning (LFJSP-WL) is investigated. To reduce carbon emission (CE), a novel CE assessment of machines is presented which combines the production scheduling strategies based on worker learning. A memetic algorithm (MA) is tailored to solve the LFJSP-WL with objectives of minimizing the makespan, total CE and total cost of workers. In LFJSP-WL, a three-layer chromosome encoding method is adopted and several approaches considering the problem characteristics are designed in population initialization, crossover and mutation. Besides, four effective neighborhood structures are developed to enhance the exploitation and exploration capacities, and the elite pool strategy is presented to reserve elite solutions along each iteration. The Taguchi method of DOE is used to obtain the best combination of the key parameters used in MA. Computational experiments conducted show that the MA is able to easily obtain better solutions for most of the tested 22 challenging problem instances compared to two other well-known algorithms, demonstrating its superior performance for the proposed LFJSP-WL.
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Abbreviations
- n :
-
Total number of jobs
- m :
-
Total number of machines
- l :
-
Total number of workers
- p i :
-
Total number of operations of job i
- i, h :
-
Index of jobs, i, h = 1,2,…, n
- j, g :
-
Index of operations
- k, q :
-
Index of machines, k, q = 1,2,…, m
- r :
-
Index of workers, r = 1,2,…, l
- Oij(Ohg):
-
The jth(gth) operation of job i(h)
- tij(thg):
-
The basic processing time of operation Oij(Ohg) (s)
- aij(ahg):
-
The actual processing time of operation Oij(Ohg) (s)
- e kr :
-
The basic efficiency of worker r when operating machine k
- e ir :
-
The basic efficiency of worker r when processing job i
- b r :
-
The learning coefficient of worker r
- dk(dq):
-
The limiting efficiency of machine k(q)
- L :
-
A large enough number
- W ijkr :
-
The cost of Oij on machine k operated by worker r
- S ij :
-
The starting time of operation Oij (s)
- Cij(Chg):
-
The completion time of operation Oij(Ohg) (s)
- C k :
-
The completion time of machine k (s)
- CE i :
-
The CE of job i (kg CO2—e)
- e k s :
-
The CE of machine k during one unit time when in the standby state (kg CO2—e)
- CE k s :
-
The CE of machine k when in the stand-by state (kg CO2—e)
- CE i p :
-
The CE of job i when in the processing state (kg CO2—e)
- CE i t :
-
The CE of job i related to tool wear (kg CO2—e)
- CE i a :
-
The CE of job i related to coolant and lubricant oil (kg CO2—e)
- V ij :
-
The removal volume of materials
- T c k :
-
The mean interval time of the renewal of coolant on machine k (s)
- T t k :
-
The life of tool used on machine k before regrinding (s)
- T l k :
-
The mean interval time of the renewal of lubricant oil on machine k (s)
- TQ kc(TQ kl):
-
The initial coolant(lubricant oil) quantity of machine k before updating (L)
- TL k t :
-
The energy consumption for regrinding tool once (kJ)
- EF ijkc(EF ijkl):
-
The emission factor of coolant(lubricant oil) on machine k (kg CO2—e/kg)
- EF e :
-
The emission factor of electric energy (kg CO2—e/kg)
- μ ijk a :
-
The carbon emission coefficient of auxiliary materials on machine k (kg CO2—e/s)
- μ ijk t :
-
The carbon emission coefficient of tool on machine k (kg CO2—e/s)
- C max :
-
The max completion time of all machines k(q) (s)
- A ijkr :
-
The cumulative time of worker r operating machine k before Oij (s)
- B ijr :
-
The cumulative time of worker r processing job i before Oij (s)
- X ijkr :
-
Xijkr = 1 If Oij is processed on machine k operated by worker l; otherwise, Xijkr = 0
- X ijk :
-
Xijk = 1 If Oij is processed on machine k; otherwise Xijk = 0
- X igr :
-
Xijr = 1 If Oig is operated by worker r; otherwise Xigr = 0
- X ij−hg :
-
Xij−hg = 1 If the completion time of Oij is greater than the starting time of Ohg; otherwise Xij−hg = 0
- X ig−ij :
-
Xij−ig = 1 If Oig is processed before Oij; otherwise Xig−ij = 0
- X hgk−ijk :
-
Xhgk−ijk = 1 If operation Ohg is prior to Oij adjacently on machine k; otherwise Xhgk−ijk = 0
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Acknowledgements
The authors are grateful to the editor and anonymous referees for their valuable comments and suggestions. This work is financially supported by the National Key R&D Program of China (2018YFB1701400), the National Natural Science Foundation of China (71473077), the State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body (71775004).
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Zhu, H., Deng, Q., Zhang, L. et al. Low carbon flexible job shop scheduling problem considering worker learning using a memetic algorithm. Optim Eng 21, 1691–1716 (2020). https://doi.org/10.1007/s11081-020-09494-y
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DOI: https://doi.org/10.1007/s11081-020-09494-y