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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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[1] 如何降低零售业的缺货率[Online], 下载地址: http://www.chinawuliu.com.cn, May 6, 2016.How to reduce the retail shortage rate[Online], available: http://www.chinawuliu.com.cn, May 6, 2016. [2] 应对高退货率唯品会逆势提价物流[Online], 下载地址: http://www.chinawuliu.com.cn, May 6, 2016.To cope with high return rates vipshop contrarian price logistics[Online], available: http://www.chinawuliu.com.cn, May 6, 2016. [3] Snyder L V, Atan Z, Peng P, Rong Y, Schmitt A J, Sinsoysal B. OR/MS models for supply chain disruptions:a review. ⅡE Transactions, 2016, 48 (2):89-109 https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID1689882_code983952.pdf?abstractid=1689882&mirid=3 [4] Gerchak Y, Parlar M. Yield randomness, cost tradeoffs, and diversification in the EOQ model. Naval Research Logistics, 1990, 37 (3):341-354 doi: 10.1002/nav.v37.3 [5] Tomlin B. On the value of mitigation and contingency strategies for managing supply chain disruption risks. Management Science, 2006, 52 (5):639-657 doi: 10.1287/mnsc.1060.0515 [6] Qi L, Lee K. Supply chain risk mitigations with expedited shipping. Omega, 2015, 57 (12):98-113 https://www.sciencedirect.com/science/article/pii/S0305048314001492 [7] 田军, 张海青, 汪应洛.基于能力期权契约的双源应急物资采购模型.系统工程理论与实践, 2013, 33 (9):2212-2219 doi: 10.12011/1000-6788(2013)9-2212Tian Jun, Zhang Hai-Qing, Wang Ying-Luo. Emergency supplies purchasing model based on capacity option contract with dual purchasing sources. Systems Engineering-Theory & Practice, 2013, 33 (9):2212-2219 doi: 10.12011/1000-6788(2013)9-2212 [8] Silbermayr L, Minner S. A multiple sourcing inventory model under disruption risk. International Journal of Production Economics, 2014, 149 (1):37-46 https://econpapers.repec.org/RePEc:eee:proeco:v:149:y:2014:i:c:p:37-46 [9] Zhu S X. Analysis of dual sourcing strategies under supply disruptions. International Journal of Production Economics, 2015, 170 (1):191-203 https://www.sciencedirect.com/science/article/pii/S0925527315003576 [10] Silbermayr L, Minner S. Dual sourcing under disruption risk and cost improvement through learning. European Journal of Operational Research, 2016, 250 (1):226-238 doi: 10.1016/j.ejor.2015.09.017 [11] Parlar M, Perry D. Inventory models of future supply uncertainty with single and multiple suppliers. Naval Research Logistics, 1996, 43 (2):191-210 doi: 10.1002/(ISSN)1520-6750 [12] Gürler Ü, Parlar M. An inventory problem with two randomly available suppliers. Operations Research, 1997, 45 (6):904-918 doi: 10.1287/opre.45.6.904 [13] Harrison J M, Sellke T M, Taylor A J. Impulse control of Brownian motion. Mathematics of Operations Research, 1983, 8 (3):454-466 doi: 10.1287/moor.8.3.454 [14] Dai J G, Yao D C. Brownian inventory models with convex holding cost, Part 1:average-optimal controls. Stochastic Systems, 2013, 3 (2):442-499 doi: 10.1287/11-SSY041 [15] Yao D C, Chao X L, Wu J C. Optimal control policy for a Brownian inventory system with concave ordering cost. Journal of Applied Probability, 2015, 52 (4):909-925 doi: 10.1239/jap/1450802743 [16] Benkherouf L, Bensoussan A. Optimality of an (s, S) policy with compound Poisson and diffusion demands:a quasi-variational inequalities approach. SIAM Journal on Control and Optimization, 2009, 48 (2):756-762 doi: 10.1137/080715883 [17] Li X D, Tang D, Wang Y J, Yang X W. Optimal processing rate and buffer size of a jump-diffusion processing system. Annals of Operations Research, 2014, 217 (1):319-335 doi: 10.1007/s10479-013-1521-2 [18] 宋春跃, 李平.含扩散项不可靠生产系统最优生产控制的数值求解.控制理论与应用, 2009, 26 (7):709-714 http://www.oalib.com/paper/4747515Song Chun-Yue, Li Ping. Numerical solution for optimal production control of unreliable production systems with diffusion terms. Control Theory & Applications, 2009, 26 (7):709-714 http://www.oalib.com/paper/4747515 [19] Muthuraman K, Seshadri S, Wu Q. Inventory management with stochastic lead times. Mathematics of Operations Research, 2015, 40 (2):302-327 doi: 10.1287/moor.2014.0671 [20] 娄山佐, 田新诚.随机供应中断和退货环境下库存问题的建模与控制.自动化学报, 2014, 40 (11):2436-2444 http://www.aas.net.cn/CN/abstract/abstract18520.shtmlLou Shan-Zuo, Tian Xin-Cheng. Modeling and control for inventory with stochastic supply disruptions and returns. Acta Automatica Sinica, 2014, 40 (11):2436-2444 http://www.aas.net.cn/CN/abstract/abstract18520.shtml [21] 娄山佐, 田新诚.随机供应中断和退货环境下库存的应急控制.自动化学报, 2015, 41 (1):94-103 http://www.aas.net.cn/CN/abstract/abstract18520.shtmlLou Shan-Zuo, Tian Xin-Cheng. Contingent control of inventory under stochastic supply disruptions and returns. Acta Automatica Sinica, 2015, 41 (1):94-103 http://www.aas.net.cn/CN/abstract/abstract18520.shtml [22] Kella O, Boxma O. Useful martingales for stochastic storage processes with Lëvy-type input. Journal of Applied Probability, 2013, 50 (2):439-449 doi: 10.1239/jap/1371648952 [23] Brill P H. Level Crossing Methods in Stochastic Models. New York, USA:Springer, 2008. 48-110 -
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