Abstract
Achieving energy-efficient production has always been a critical issue for the manufacturing industry. In many production systems, the waste of energy mainly results from unbalanced machine efficiency, which brings about a considerable amount of idle time. One of the most important approaches to addressing this problem is to adopt an On/Off control policy on those underutilized machines. In this paper, serial production lines with multiple unreliable machines and finite buffers are considered. All machines are assumed to obey the Bernoulli reliability model, which is commonly used when the machine downtime is relatively short and comparable to the production cycle time (e.g., engine assembly). Besides, considering that in industrial practice, machines usually have to go through a preparation phase during mode switching, a non-negligible warm-up (cool-down) period is taken into account. An On/Off control policy is calculated for lines with two or three machines based on a Markov decision process (MDP) model, then the results are extended to multi-machine lines using a decomposition procedure. Numerical experiments show that the proposed policy achieves better system performance compared to the threshold policy that is commonly used in energy-efficient On/Off control.
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Acknowledgements
We thank the Editor-in-Chief, Associate Editor, and all the anonymous reviewers for their thoughtful comments on an earlier version of this manuscript.
Funding
This work was supported in part by the National Natural Science Foundation of China under Grant 62103042, in part by the Beijing Municipal Natural Science Foundation under Grant 4214076, and in part by the National Key R &D Program of China under Grant 2021YFB1714800.
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Appendices
Appendix A Calculation of the transition matrix
Algorithm for calculating the state transition matrix \(\mathbf {P_{\mathrm {a}}}\) of three-machine lines is shown in Algorithm 1, where idx2state and state2idx are functions that map a state vector \(\left[ h_1,h_2,P_{\mathrm {s}}\right]\) with an index in lexicographical order. \((h_1,h_2)=\Phi _h({\mathbf {h}},{\varvec{\alpha }})\) is defined by 4 equations shown in Eq. (A1).
For two-machine lines, the calculation of \(\mathbf {P_{\mathrm {a}}}\) is shown in Algorithm 2.
Appendix B The policy iteration procedure
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Wang, X., Dai, Y. & Jia, Z. Energy-efficient on/off control in serial production lines with Bernoulli machines. Flex Serv Manuf J 36, 103–128 (2024). https://doi.org/10.1007/s10696-022-09481-8
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DOI: https://doi.org/10.1007/s10696-022-09481-8