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双源采购跳跃-扩散库存控制模型

娄山佐 田新诚 吴颖颖

娄山佐, 田新诚, 吴颖颖. 双源采购跳跃-扩散库存控制模型. 自动化学报, 2018, 44(2): 270-279. doi: 10.16383/j.aas.2018.c160514
引用本文: 娄山佐, 田新诚, 吴颖颖. 双源采购跳跃-扩散库存控制模型. 自动化学报, 2018, 44(2): 270-279. doi: 10.16383/j.aas.2018.c160514
LOU Shan-Zuo, TIAN Xin-Cheng, WU Ying-Ying. A Jump-diffusion Inventory Control Model with Dual-sourcing. ACTA AUTOMATICA SINICA, 2018, 44(2): 270-279. doi: 10.16383/j.aas.2018.c160514
Citation: LOU Shan-Zuo, TIAN Xin-Cheng, WU Ying-Ying. A Jump-diffusion Inventory Control Model with Dual-sourcing. ACTA AUTOMATICA SINICA, 2018, 44(2): 270-279. doi: 10.16383/j.aas.2018.c160514

双源采购跳跃-扩散库存控制模型

doi: 10.16383/j.aas.2018.c160514
基金项目: 

山东省重大科技创新工程 2017CXGC0601

国家自然科学基金 61703241

山东省重点研究计划 2016ZDJS02B03

详细信息
    作者简介:

    田新诚   山东大学控制科学与工程学院教授.主要研究方向为运动控制, 机电一体化, 智能控制和优化.E-mail:txch@sdu.edu.cn

    吴颖颖  山东大学控制科学与工程学院讲师.主要研究方向为自动拣选系统调度优化, 物流系统规划、设计和仿真.E-mail:Sophia.wu@sdu.edu.cn

    通讯作者:

    娄山佐   山东大学控制科学与工程学院副教授.主要研究方向为复杂系统建模与仿真, 库存控制, 优化算法.本文通信作者.E-mail:Lshanzuo@163.com

A Jump-diffusion Inventory Control Model with Dual-sourcing

Funds: 

Major Science and Technology Innovation Project of Shandong Province 2017CXGC0601

ational Natural Science Foundation of China 61703241

Key Research and Development Project of Shandong Province 2016ZDJS02B03

More Information
    Author Bio:

     Professor at the School of Control Science and Engineering, Shandong University. His research interest covers motion control, mechatronics, intelligent control and optimization

     Lecturer at the School of Control Science and Engineering, Shandong University. Her research interest covers scheduling optimization of automatic picking system, logistics system planning, design and simulation

    Corresponding author: WU Ying-Ying   Lecturer at the School of Control Science and Engineering, Shandong University. Her research interest covers scheduling optimization of automatic picking system, logistics system planning, design and simulation
  • 摘要: 供应中断和退货会引发库存短缺和剧烈波动,所以,如何缓解它们的影响,成为当前企业管理者亟待解决的难题.在采用双源采购策略防御库存短缺和跳跃-扩散过程描述库存水平变化条件下,利用连续时间Markov链、水平穿越和鞅理论,分别确定了库存水平分布及循环的期望费用和时间函数,在此基础上,构建了系统长程平均费用率模型.最后,仿真结果表明,供应商的可靠性和中断类型,对最优控制策略和系统费用产生较大影响.另外,双源采购策略能够有效缓解供应中断对库存的影响,尤其是,当供应商的可靠性较低或中断类型均为频率低持续时间长时.
    1)  本文责任编委 赵千川
  • 图  1  一次循环库存水平典型的样本路径

    Fig.  1  A typical sample path of the inventory level in one cycle

    表  1  供应商的状态参数及可靠性

    Table  1  Status parameters and reliability of the suppliers

    ${\rm Data sets}$$\gamma_{_1}$$\theta_{_1}$$\zeta_{_1}$$\gamma_{_2}$$\theta_{_2}$$\zeta_{_2}$
    10.10.990%0.10.990%
    20.10.990%0.90.110%
    30.90.110%0.10.990%
    40.90.110%0.90.110%
    50.10.150%0.10.150%
    60.10.150%0.90.950%
    70.90.950%0.10.150%
    80.90.950%0.90.950%
    下载: 导出CSV

    表  2  单源和双源采购对应的最优控制策略和费用

    Table  2  Optimal control policy and cost for single and dual sourcing

    ${\rm Data sets}$
    $\vec{q}^\ast$
    $S_1$
    $\overrightarrow{TC}^\ast$

    $\hat{q}^\ast$
    $S_2$
    $\widehat{TC}^\ast$

    $q_1^\ast$
    $S_1 {\rm and} S_2$
    $s^\ast$

    $TC^\ast$
    $\vec{s}^\ast$ $\hat{s}^\ast$ $q_2^\ast$
    1167.2066.07320.62208.5442.43413.29176.0113.380.02300.46
    2167.2066.07320.62954.20672.16818.15172.1015.0955.72318.50
    3782.66863.70734.29208.5442.43413.29372.19129.3842.40397.65
    4782.66863.70734.29954.20672.16818.15807.48497.81477.67628.89
    5521.72617.14668.31680.49458.17746.25397.9286.62249.19520.71
    6521.72617.14668.31343.75120.58469.85246.93178.7998.37409.08
    7282.38156.98372.86680.49458.17746.25302.6027.9993.65362.88
    8282.38156.98372.86343.75120.58469.85280.8937.7265.46349.77
    下载: 导出CSV

    表  3  $K_2$和$k_2$变化对应的最优控制策略和费用

    Table  3  Optimal control policy and cost for varying $K_2$ and $k_2$

    ${\rm Data sets}$$K_2$$k_2$$q_1^\ast$$q_2^\ast$$s^\ast$$TC^\ast$${\rm Data sets}$$K_2$$k_2$$q_1^\ast$$q_2^\ast$$s^\ast$$TC^\ast$
    110164.3764.380.02278.265101164.49164.49309.42484.27
    120169.9183.810.01284.575201178.70204.41296.06486.25
    1102149.859.150.01292.415102365.9957.85263.66517.44
    2101150.4796.2458.19315.42610155.29219.90112.42345.07
    2201153.27101.6357.02315.97620159.03232.38109.23347.91
    2102166.5110.4557.64317.636102237.05168.66100.91406.52
    310196.24150.4758.19315.427101219.9055.29112.42345.07
    3201103.89184.5947.65320.267201227.0276.32109.73347.99
    3102369.1294.1952.14391.587102287.7619.4797.17358.48
    4101594.16594.16540.50584.858101130.69130.6976.31318.80
    4201596.67596.72539.55585.328201138.34142.0874.03321.89
    4102805.28495.42478.41628.448102268.5227.2968.03345.65
    下载: 导出CSV

    表  4  $h$和$\pi$变化对应的最优控制策略和费用

    Table  4  Optimal control policy and cost for varying $h$ and $\pi$

    ${\rm Data sets}$$h$$\pi$$q_1^\ast$$q_2^\ast$$s^\ast$$TC^\ast$${\rm Data sets}$$h$$\pi$$q_1^\ast$$q_2^\ast$$s^\ast$$TC^\ast$
    10.515112.1812.290.01322.0050.515209.6166.3664.11587.97
    10.320181.3413.540.03302.3550.320430.0693.10359.65563.13
    20.515122.4415.0116.97349.2260.515134.57131.1973.58462.69
    20.320177.9115.3379.66327.3660.320255.38196.17119.99421.08
    30.515217.71111.453.78429.7470.515219.0027.0062.95418.30
    30.320375.88135.1066.37407.2270.320311.1828.03117.58372.49
    40.515509.68349.63359.37769.1680.515184.5836.7452.13396.55
    40.320866.85558.40577.86677.0480.320289.4439.2078.93356.50
    下载: 导出CSV
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  • 收稿日期:  2016-07-07
  • 录用日期:  2016-11-28
  • 刊出日期:  2018-02-20

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