设备故障条件下生产计划的鲁棒性分析
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摘要
以有限产能批量问题为背景,假定生产过程受到泊松分布的设备故障影响,引入与故障相关的鲁棒性约束,并建立生产计划决策的模型.首先将这一随机规划问题转换为确定性模型,然后用优化软件Lingo求解.算例结果表明,基于故障期望的计划模型中各个周期满足产能约束的一致性较差,而新模型能达到较高的鲁棒性水平,对应的生产成本会有一定程度的上升,而随着鲁棒性水平的降低,生产成本呈阶段性下降趋势,并与基于故障期望的模型趋近;同时发现与后者相比,新模型在增加有限的生产成本(高约1.0%)条件下,可以获得较高(85%)的鲁棒性水平.
In this paper,based on the Capacitated Lot-sizing Problem,it is assumed that the production process is affected by the Poisson distribution equipment failure,and the fault-related robustness constraints are introduced and the production planning decision model is established.This stochastic programming problem is first converted into a deterministic model and further solved by the optimization software Lingo.The results of the example show that the consistency of the capacity constraints in each cycle of the planning model based on the failure expectation is poor and the new model can achieve a higher level of robustness,and the corresponding production cost will increase to a certain extent.With the decrease of the level of robustness,the production cost shows a downward trend and approaches to the model that is based on failure expectation.At the same time,compared with the latter,the new model is capable of accomplishing a higher level of robustness(85%) with increase of a limited production cost(about 1.0% higher).
In this paper,based on the Capacitated Lot-sizing Problem,it is assumed that the production process is affected by the Poisson distribution equipment failure,and the fault-related robustness constraints are introduced and the production planning decision model is established.This stochastic programming problem is first converted into a deterministic model and further solved by the optimization software Lingo.The results of the example show that the consistency of the capacity constraints in each cycle of the planning model based on the failure expectation is poor and the new model can achieve a higher level of robustness,and the corresponding production cost will increase to a certain extent.With the decrease of the level of robustness,the production cost shows a downward trend and approaches to the model that is based on failure expectation.At the same time,compared with the latter,the new model is capable of accomplishing a higher level of robustness(85%) with increase of a limited production cost(about 1.0% higher).
引文
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[14]Leung S C H,Tsang S O S,Ng W L,et al.A robust optimization model for multi-site production planning problem in an uncertain environment[J].European Journal of Operational Research,2007,181(1):224-238.
[15]Zanjani M K,Ait-Kadi D,Nourelfath M.Robust production planning in a manufacturing environment with random yield:A case in sawmill production planning[J].European Journal of Operational Research,2010,201(3):882-891.
[16]Zanjani M K,Nourelfath M,Ait-Kadi D.A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand[J].International Journal of Production Research,2010,48(16):4701-4723.
[17]Nourelfath M.Service level robustness in stochastic production planning under random machine breakdowns[J].European Journal of Operational Research,2011,212(1):81-88.
[18]刘学娟,赵斐.多产品生产计划与设备维修整合优化模型[J].工业工程与管理,2015,20(4):23-28.
[19]Savsar M.Modelling of multi-stage production lines with maintenance operations[J].International Journal of Computer Integrated Manufacturing,2008,21(4):396-406.
[2]Weinstein L,Chung C H.Integrating maintenance and production decisions in a hierarchical production planning environment[J].Computers and Operations Research,1999,26(10/11):1059-1074.
[3]Aghezzaf E H,Jamali M A,Ait-Kadi D.An integrated production and preventive maintenance planning mode[J].European Journal of Operational Research,2007,181(2):679-685.
[4]Najid M N,Alaoui-Selsouli M,Mohafid A.An integrated production and maintenance planning model with time windows and shortage cost[J].International Journal of Production Research,2011,49(8):2265-2283.
[5]Fitouhi M C,Nourelfath M.Integrating noncyclical preventive maintenance scheduling and production planning for a single machine[J].International Journal of Production Economics,2012,136(2):344-351.
[6]张岳君,陆志强.一种基于设备运行的预防性维护与生产批量联合决策模型[J].计算机集成制造系统,2014,20(7):1737-1742.
[7]张博文,陆志强,张岳君.并行机系统生产计划与预防性维护联合建模[J].上海交通大学学报(自然版),2015,49(4):564-571.
[8]胡家文,蒋祖华,侯文瑞,等.批量生产模式下考虑设备运行负荷的预防维护策略[J].上海交通大学学报(自然版),2018,52(3):332-339.
[9]赵世雄.基于加工失效情形下生产批量计划与设备维护集成优化研究[D].上海:上海交通大学,2014.
[10]冷乔,王丽亚,赵世雄,等.多机串行系统的生产批量与维护计划集成优化[J].计算机集成制造系统,2016,22(8):1945-1952.
[11]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.
[12]Leung S C H,Wu Y.A robust optimization model for stochastic aggregate production planning[J].Production Planning and Control,2004,15(5):502-514.
[13]Wu Y.Robust optimization applied to uncertain production loading problems with import quota limits under the global supply chain management environment[J].International Journal of Production Research,2006,44(5):849-882.
[14]Leung S C H,Tsang S O S,Ng W L,et al.A robust optimization model for multi-site production planning problem in an uncertain environment[J].European Journal of Operational Research,2007,181(1):224-238.
[15]Zanjani M K,Ait-Kadi D,Nourelfath M.Robust production planning in a manufacturing environment with random yield:A case in sawmill production planning[J].European Journal of Operational Research,2010,201(3):882-891.
[16]Zanjani M K,Nourelfath M,Ait-Kadi D.A multi-stage stochastic programming approach for production planning with uncertainty in the quality of raw materials and demand[J].International Journal of Production Research,2010,48(16):4701-4723.
[17]Nourelfath M.Service level robustness in stochastic production planning under random machine breakdowns[J].European Journal of Operational Research,2011,212(1):81-88.
[18]刘学娟,赵斐.多产品生产计划与设备维修整合优化模型[J].工业工程与管理,2015,20(4):23-28.
[19]Savsar M.Modelling of multi-stage production lines with maintenance operations[J].International Journal of Computer Integrated Manufacturing,2008,21(4):396-406.