考虑等待时间约束的不完美生产系统的产出优化

周炳海; 刘玉旺

doi:10.13700/j.bh.1001-5965.2016.0824

考虑等待时间约束的不完美生产系统的产出优化

doi: 10.13700/j.bh.1001-5965.2016.0824

周炳海^,,
刘玉旺

同济大学机械与能源工程学院, 上海 201804

基金项目:

国家自然科学基金 71471135

详细信息

通讯作者:
周炳海, E-mail:bhzhou@tongji.edu.cn

中图分类号: TP391
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- 被引次数: 0
出版历程
- 收稿日期: 2016-10-26
- 录用日期: 2016-12-09
- 网络出版日期: 2017-10-20

Throughput optimization for an imperfect production system with queue time constraints

ZHOU Binghai^,,
LIU Yuwang

School of Mechanical and Energy Engineering, Tongji University, Shanghai 201804, China

Funds:

National Natural Science Foundation of China 71471135

More Information

Corresponding author: ZHOU Haibin, E-mail:bhzhou@tongji.edu.cn

摘要

摘要:
针对某些生产系统存在等待时间约束及设备劣化引起产品质量损失这2个问题，构建了系统的缓冲区控制和预防性维护的联合优化模型。首先，利用伽马过程对下游瓶颈工作站的劣化过程进行建模，并考虑由于其状态劣化引起的产品质量损失；其次，在此基础上，将工件的到达、中间缓冲区及下游工作站的加工过程视为一排队系统，引入M/G/1/K排队模型分别求解了在制品（WIP）被阻塞和超出等待时间约束的概率；最后，以最大化系统的“有效产出”为目标，对系统的预防性维护和缓冲区控制作了联合优化。数值实例表明：本文所提模型是切实、有效的，对带等待时间约束的生产系统的缓冲区控制、预防性维护以及产出提高具有一定的指导意义。
- 设备劣化 /
- 伽马过程 /
- 质量损失 /
- 等待时间约束 /
- 缓冲
Abstract:
To efficiently solve the problems of queue time constraints and quality loss caused by machine degradation during production activities, a joint optimization mathematical model considering both preventive maintenance and the control of the buffer capacity was constructed in this paper. First, gamma process was introduced to model the degradation of the downstream bottleneck station, and the quality loss caused by its degradation was also considered. Second, based on the model mentioned above, we treated the arrival of workpieces, the intermediate buffer and the working process of downstream station as a queuing system and obtained the probability of work in process (WIP) blocking and exceeding the queue time constraints using M/G/1/K queuing model. Finally, with the objective function of maximizing the "effective throughput", we jointly explored the optimization of the threshold of preventive maintenance and the capacity of the intermediate buffer. Numerical example shows that the proposed model is practical and effective, which has certain instructive significance to the buffer capacity control, preventive maintenance and throughput improvement for those imperfect production systems with queue time constraints.
- machine degradation /
- gamma process /
- quality loss /
- queue time constraints /
- buffer

HTML全文

图 1 带等待时间约束的串行生产系统

Figure 1. A serial production system with queue time constraints

下载: 全尺寸图片幻灯片

图 2 “有效产出”示意图

Figure 2. Schematic diagram of "effective throughput"

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图 3 排队系统的状态转移示意图

Figure 3. Schematic diagram of state transition for queuing systems

下载: 全尺寸图片幻灯片

图 4 工作站2达到D_P经历时间的CDF和PDF

Figure 4. CDF and PDF of service time of station 2 until D_P

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图 5 不同维护周期里失效率函数随时间的变化

Figure 5. Variation of failure rate function with time in different maintenance periods

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图 6 不同D_P下各维护周期的期望运行时间

Figure 6. Expected service time of each maintenance period under different D_P

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图 7 不同D_P对应的的总期望产出及质量损失

Figure 7. Expected total throughput and quality loss under different D_P

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图 8 P_B、P_S随缓冲区容量的变化

Figure 8. Variation of P_B and P_S with buffer capacity

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表 1 不同的[D_P, K]对应的系统有效产出

Table 1. Effective throughput of systems under different combinations of [D_P, K]

K/个	有效产出/个
K/个	D_P=110μm	D_P=115μm	D_P=120μm	D_P=125μm	D_P=130μm	D_P=135μm
6	3365	3378	3386	3393	3400	3393
7	3378	3390	3398	3405	3412	3406
8	3365	3377	3386	3393	3399	3392
9	3346	3358	3367	3373	3380	3372
10	3328	3340	3348	3355	3361	3353
11	3312	3324	3332	3338	3344	3336
12	3299	3311	3319	3325	3331	3323
13	3290	3301	3309	3316	3321	3313
14	3283	3295	3303	3309	3314	3306

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