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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.Abstract: Supply disruptions and returns may lead to stock shortage and fluctuation. So it is a very difficult problem for today's managers to mitigate their influence. Under the condition that a dual-sourcing strategy is utilized to tackle the stock shortage and a jump-diffusion process is adopted to express the inventory level process, the stationary distribution of the inventory level, as well as the expected cycle cost and time functions are derived by applying continuous-time Markov chain, level-crossing and martingale theorems. Subsequently, the functions are employed to develop a long-run average cost rate model. Finally, numerical results show that the suppliers' reliability and the nature of the disruptions have a big impact on the optimal policy and cost. Moreover, the dual-sourcing strategy can mitigate the influence of supply disruptions on inventory effectively, in particular, when the suppliers' reliability are lower or their disruptions are rare and long in nature.
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Key words:
- Inventory control /
- supply disruption /
- dual sourcing /
- jump-diffusion /
- level-crossing
1) 本文责任编委 赵千川 -
表 1 供应商的状态参数及可靠性
Table 1 Status parameters and reliability of the suppliers
${\rm Data sets}$ $\gamma_{_1}$ $\theta_{_1}$ $\zeta_{_1}$ $\gamma_{_2}$ $\theta_{_2}$ $\zeta_{_2}$ 1 0.1 0.9 90% 0.1 0.9 90% 2 0.1 0.9 90% 0.9 0.1 10% 3 0.9 0.1 10% 0.1 0.9 90% 4 0.9 0.1 10% 0.9 0.1 10% 5 0.1 0.1 50% 0.1 0.1 50% 6 0.1 0.1 50% 0.9 0.9 50% 7 0.9 0.9 50% 0.1 0.1 50% 8 0.9 0.9 50% 0.9 0.9 50% 
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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$ $\hat{s}^\ast$ $q_2^\ast$ 1 167.20 66.07 320.62 208.54 42.43 413.29 176.01 13.38 0.02 300.46 2 167.20 66.07 320.62 954.20 672.16 818.15 172.10 15.09 55.72 318.50 3 782.66 863.70 734.29 208.54 42.43 413.29 372.19 129.38 42.40 397.65 4 782.66 863.70 734.29 954.20 672.16 818.15 807.48 497.81 477.67 628.89 5 521.72 617.14 668.31 680.49 458.17 746.25 397.92 86.62 249.19 520.71 6 521.72 617.14 668.31 343.75 120.58 469.85 246.93 178.79 98.37 409.08 7 282.38 156.98 372.86 680.49 458.17 746.25 302.60 27.99 93.65 362.88 8 282.38 156.98 372.86 343.75 120.58 469.85 280.89 37.72 65.46 349.77
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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 $k_2$
${\rm Data sets}$ $K_2$ $k_2$ $q_1^\ast$ $q_2^\ast$ $s^\ast$ $TC^\ast$ ${\rm Data sets}$ $K_2$ $k_2$ $q_1^\ast$ $q_2^\ast$ $s^\ast$ $TC^\ast$ 1 10 1 64.37 64.38 0.02 278.26 5 10 1 164.49 164.49 309.42 484.27 1 20 1 69.91 83.81 0.01 284.57 5 20 1 178.70 204.41 296.06 486.25 1 10 2 149.85 9.15 0.01 292.41 5 10 2 365.99 57.85 263.66 517.44 2 10 1 150.47 96.24 58.19 315.42 6 10 1 55.29 219.90 112.42 345.07 2 20 1 153.27 101.63 57.02 315.97 6 20 1 59.03 232.38 109.23 347.91 2 10 2 166.51 10.45 57.64 317.63 6 10 2 237.05 168.66 100.91 406.52 3 10 1 96.24 150.47 58.19 315.42 7 10 1 219.90 55.29 112.42 345.07 3 20 1 103.89 184.59 47.65 320.26 7 20 1 227.02 76.32 109.73 347.99 3 10 2 369.12 94.19 52.14 391.58 7 10 2 287.76 19.47 97.17 358.48 4 10 1 594.16 594.16 540.50 584.85 8 10 1 130.69 130.69 76.31 318.80 4 20 1 596.67 596.72 539.55 585.32 8 20 1 138.34 142.08 74.03 321.89 4 10 2 805.28 495.42 478.41 628.44 8 10 2 268.52 27.29 68.03 345.65
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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 $\pi$
${\rm Data sets}$ $h$ $\pi$ $q_1^\ast$ $q_2^\ast$ $s^\ast$ $TC^\ast$ ${\rm Data sets}$ $h$ $\pi$ $q_1^\ast$ $q_2^\ast$ $s^\ast$ $TC^\ast$ 1 0.5 15 112.18 12.29 0.01 322.00 5 0.5 15 209.61 66.36 64.11 587.97 1 0.3 20 181.34 13.54 0.03 302.35 5 0.3 20 430.06 93.10 359.65 563.13 2 0.5 15 122.44 15.01 16.97 349.22 6 0.5 15 134.57 131.19 73.58 462.69 2 0.3 20 177.91 15.33 79.66 327.36 6 0.3 20 255.38 196.17 119.99 421.08 3 0.5 15 217.71 111.45 3.78 429.74 7 0.5 15 219.00 27.00 62.95 418.30 3 0.3 20 375.88 135.10 66.37 407.22 7 0.3 20 311.18 28.03 117.58 372.49 4 0.5 15 509.68 349.63 359.37 769.16 8 0.5 15 184.58 36.74 52.13 396.55 4 0.3 20 866.85 558.40 577.86 677.04 8 0.3 20 289.44 39.20 78.93 356.50
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