针对生产和维修计划共享生产设备的问题，建立了经济生产批量和设备状态监测维修的联合优化模型.运用随机系数增长模型描述设备的退化状态，每完成一个生产批量就对设备进行状态监测.监测到的设备状态由设备的实际状态和监测误差构成，当监测状态达到或超过预防性维修阈值时，需要对设备进行预防性维修并更新，当实际状态达到故障阈值时，设备故障停机，需对设备进行故障维修并更新.基于两种更新情况，建立了更新周期内的费用和周期长度模型，并进一步运用更新回报定理建立了单位时间期望费用模型，通过对模型进行优化，可得到预防性更新状态阈值和每个批量的生产时间两个决策变量的最优取值.最后，通过国内某钢厂轧钢设备的数据资料对模型进行了数值分析，分析结果和实际情况相符合.
Abstract
A joint optimization model of economic production quantity and condition-based maintenance policy is proposed in this paper, considering the situation that the production plan and maintenance schedule share the same machine. Using the random coefficient growth model to describe the degenerated condition, the condition monitoring is carried out when a lot is finished. The observed condition composed of two parts, the actual deterioration condition and the random error, once the condition information observed is equal to or higher than the preventive maintenance level, or the actual condition is equal to the failure level, the machine should be renewed. The cost and the length model in the renewal cycle are proposed, then the expected cost per unit time is modeled based on the renewal reward theory. The optimal condition of preventive maintenance level and production time of one lot can be calculated by minimizing the expected cost per unit time. Numerical examples are presented based on the data collected from a steel mill, the results are consistent with the actual situation.
关键词
状态监测维修 /
经济生产批量 /
随机系数增长模型 /
更新回报定理
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Key words
condition-based maintenance /
economic production quantity /
the random coefficient growth model /
renewal reward theory
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中图分类号：
TB114.3
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参考文献
[1] 刘学娟, 赵斐, 马晓洋. 多产品生产计划与非周期预防维修整合优化模型[J]. 中国管理科学, 2017, 25(11):189-196.Liu X J, Zhao F, Ma X Y. Joint optimal multi-product and non-cyclical preventive maintenance planning model[J]. Chinese Journal of Management Science, 2017, 25(11):189-196.
[2] 祝颖, 冷乔, 王丽亚, 等. 带缓冲多阶段系统的生产批量与维护计划集成优化[J]. 工业工程与管理, 2015, 20(6):48-53.Zhu Y, Leng Q, Wang L Y, et al. Joint optimization of production lot and maintenance planning in a multi-stage system with intermediate buffers[J]. Industrial Engineering and Management, 2015, 20(6):48-53.
[3] Liu X, Wang W, Peng R. An integrated preventive maintenance and production planning model with sequence-dependent setup costs and times[J]. Quality and Reliability Engineering International, 2017, 33:2452-2461.
[4] 卢震, 郭巧顺, 徐健. 基于周期性不完全预防性维修的最优经济生产批量决策[J]. 系统工程理论与实践, 2017, 37(10):2621-2629.Lu Z, Guo Q S, Xu J. The decision of optimal economic production lot based on periodic imperfect preventive maintenance[J]. Systems Engineering-Theory & Practice, 2017, 37(10):2621-2629.
[5] Peng H, Houtum G. Joint optimization of condition-based maintenance and production lot-sizing[J]. European Journal of Operational Research, 2016, 253:94-107.
[6] 廖雯竹. 基于设备衰退机制的预知性维护策略及生产排程集成研究[D]. 上海:上海交通大学, 2011.Liao W. Research of predictive maintenance policy and integrated production scheduling model based on machine degradation[D]. Shanghai:Shanghai Jiao Tong University, 2011.
[7] 王建军, 刘晓盼, 刘锋, 等. 随机机器故障下加工时间可控的并行机鲁棒调度[J]. 中国管理科学, 2017, 25(3):137-146.Wang J J, Liu X P, Liu F, et al. Robust scheduling of unrelated parallel machines subject to stochastic breakdowns and controllable processing times[J]. Chinese Journal of Management Science, 2017, 25(3):137-146.
[8] Giri B C, Dohi T. Exact formulation of stochastic EMQ model for an unreliable production system[J]. Journal of the Operational Research Society, 2005, 56(5):563-575.
[9] Kim C H, Hong Y. An optimal production run length in deteriorating production processes[J]. International Journal of Production Economics, 1999, 58:183-189.
[10] El-Ferik S. Economic production lot-sizing for an unreliable machine under imperfect age-based maintenance policy[J]. European Journal of Operational Research, 2008, 186:150-163.
[11] Bouslah B, Gharbi A, Pellerin R. Joint optimal lot sizing and production control policy in an unreliable and imperfect manufacturing system[J]. International Journal of Production Economics, 2013, 144:143-156.
[12] Chen YC. An optimal production and inspection strategy with preventive maintenance error and rework[J]. Journal of Manufacturing Systems, 2013, 32:99-106.
[13] Wang W. Condition-based maintenance modeling[M]//Complex System Maintenance Handbook. Springer, 2008:111-131.
[14] Jafari L, Makis V. Joint optimal lot sizing and preventive maintenance policy for a production facility subject to condition monitoring[J]. Int J Production Economics, 2015, 169:156-168.
[15] Jafari L, Makis V. Optimal lot-sizing and maintenance policy for a partially observable production system[J]. Computers & Industrial Engineering, 2016, 93:88-98.
[16] Bouslah B, Gharbi A, Pellerin R. Joint economic design of production, continuous sampling inspection and preventive maintenance of a deteriorating production system[J]. International Journal of Production Economics, 2016, 173:184-198.
[17] Cheng G, Zhou B, Li L. Joint optimization of lot sizing and condition-based maintenance for multi-component production systems[J]. Computers and Industrial Engineering, 2017, 110:538-549.
[18] 成国庆, 周炳海, 李玲. 复杂生产系统经济生产批量与视情维护策略模型[J]. 计算机集成制造系统, 2018, 24(9):2270-2278. Cheng G Q, Zhou B H, Li L. Modelling economic production quantity and condition-based maintenance policy for a complex production system[J]. Computer Integrated Manufacturing Systems, 2018, 24(9):2270-2278.
[19] Wang W. A model to determine the optimal critical level and the monitoring intervals in condition-based maintenance[J]. International Journal of Production Research, 2000, 38(6):1425-1436.
[20] Lu C, Meeker W. Using degradation measures to estimate a time-to failure distribution[J]. Technometrics, 1993, 35(2):161-173.
[21] Ross S M. Stochastic processes[M]. New York:Wiley, 1983.
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脚注
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基金
国家自然科学基金（71601019）；教育部人文社会科学研究项目（16YJC630174）
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