Low carbon flexible job shop scheduling problem considering worker learning using a memetic algorithm
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Low carbon flexible job shop scheduling problem considering worker learning using a memetic algorithm Huan Zhu1 · Qianwang Deng1 · Like Zhang1 · Xiang Hu1 · Wenhui Lin1 Received: 13 July 2019 / Revised: 20 February 2020 / Accepted: 20 February 2020 © Springer Science+Business Media, LLC, part of Springer Nature 2020
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. Keywords Carbon emission · Flexible job shop scheduling problem · Worker learning · Memetic algorithm List of symbols n Total number of jobs m Total number of machines l Total number of workers pi Total number of operations of job i * Qianwang Deng [email protected] 1
State Key Laboratory of Advanced Design and Manufacturing for Vehicle Body, Hunan University, Changsha 410082, China
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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) ekr The basic efficiency of worker r when operating machine k eir The basic efficiency of worker r when processing job i br The learning coefficient of worker r dk(dq) The limiting efficiency of machine k(q) L A large enough number Wijkr The cost of Oij on machine k operated by worker r Sij The starting time of operation Oij (s) Cij(Chg) The completion time of operation Oij(Ohg) (s) Ck The completion time of machine k (s) CEi The CE of job i (kg CO2—e) e ks The CE of machine k during one unit time when in t
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