需求侧带有多重泊松流的报童模型

doi:10.16381/j.cnki.issn1003-207x.2022.2331

摘要/Abstract

摘要：

由需求侧的超预期因素形成不同属性的多重泊松流，对供应链的优化决策问题具有重要的影响。在泊松流正负属性分类的基础上，为了刻画需求侧中的随机性，本文以泊松过程为理论导向，提出了各泊松流在决策机制中的传导机理，进而构建需求侧带有多重泊松流的报童模型，并导出该模型的最优解。相关结论及数值实验结果表明：正向和负向泊松流分别对决策机制所产生的作用机理具有互反的关系属性，其中决策机制与正向泊松流之间具有正向的关联性，而与负向泊松流形成反向的关联性。然而，随着多重泊松流对需求侧干预次数的增多，最优期望订购量和期望利润逐步趋于平稳化，由此说明“黑天鹅”事件对决策机制所产生的作用机理具有一定的局部性。

关键词: 需求侧, 多重泊松流, 报童模型

Abstract:

Under the background of interweaving and overlapping events such as the great changes of the century， the epidemic of the century， the science and technology war， the trade war， the inflation of major western economies， and the conflict between Russia and Ukraine， many unexpected factors are induced， which have a great impact on the capital flow， technology flow， service flow， logistics and other branches of the supply chain. Then it evolves into the positive and negative intervention effects of various Poisson flows on the demand side with different attributes. Therefore， the randomness on the demand side based on Poisson process is described， and then its statistical regularity is integrated into the theoretical framework of the classic newsboy model， and a new model and its decision mechanism is proposed. Based on the relevant theories of the new model and its numerical experimental results， the following important conclusions and management implications can be further drawn：① The intervention mechanism of multiple Poisson flows formed by unexpected factors on the decision-making mechanism has positive and negative properties， that is， when Poisson flows are positive， there is a positive correlation between the intervention intensity $λ i (i = 1,2, ⋯, n)$ and the decision-making mechanism， which means that when the intervention intensity increases， the optimal order quantity and expected profit have an upward trend. When Poisson flow is negative， there is a reverse correlation between intervention intensity and decision-making mechanism. It is shown that the positive and negative properties of Poisson flow determine the motion trend of the optimal order quantity and the expected profit curve. Therefore， it is necessary to identify the relationship properties between random factors and demand side， so as to reveal the conduction mechanism of each Poisson flow in the decision-making mechanism， and then provide theoretical support for the formulation of decision-making criteria.② When the total number of Poisson flow interventions on market demand remains unchanged， the randomness induced by scale parameter $λ$ has a negative effect the decision-making mechanism， that is， when $λ$ increases， the optimal order quantity and expected profit have a downward trend. Therefore， an important management implication can be drawn from this， namely： Decision makers should take the scale parameter $λ$ as the core element， build a database for risk identification and monitoring， which is used to measure the potential risks loaded by the inventory system， strengthen the awareness of risk prevention and resolution of “seeing the danger in the intangible， seeing the disaster in the unknown”.③ The number of interventions generated by the Poisson flow $Z i$ on the demand side is mapped to the negative effect of the decision-making mechanism， which also depends on the positive and negative properties of the Poisson flow $Z i$ ， that is， the more the number of interventions of the positive Poisson flow on the demand side， the greater the optimal order quantity and expected profit， otherwise the vice versa. It can be seen that in the case of multiple Poisson flows on the demand side， the identification of positive and negative attributes of Poisson flows is helpful to improve the operation and management level of supply chain.In conclusion， decision makers can make full use of the essential characteristics of multiple Poisson flows to build a risk prevention and resolution mechanism with integrated risk data monitoring， risk identification， risk pre-warning， risk response strategy and other elements， so as to improve the ability and decision-making level of risk management in the process of risk decision-making， and to achieve the purpose of optimizing the performance of operation and management.

Key words: demand side, multiple Poisson flows, newsboy model

中图分类号:

O211.62

陈杰,邢灵博,曹娟, 等. 需求侧带有多重泊松流的报童模型[J]. 中国管理科学, 2025, 33(10): 176-186.

Jie Chen,Lingbo Xing,Juan Cao, et al. Newsboy Model under Demand Side with the Multiple Poisson Flows[J]. Chinese Journal of Management Science, 2025, 33(10): 176-186.

图/表 7

图1

表1

泊松分布的近似正则数A(ε=0.0001)"

强度参数 $λ$	0.10	0.12	0.14	0.16	0.18	0.20	0.22	0.24	0.26	0.28
近似正则数 $A (ε)$	3	3	3	3	3	4	4	4	4	4
强度参数 $λ$	0.30	0.32	0.34	0.36	0.38	0.40	0.42	0.44	0.46	0.48
近似正则数 $A (ε)$	4	4	4	4	4	5	5	5	5	5
强度参数 $λ$	0.50	0.52	0.54	0.56	0.58	0.60	0.62	0.64	0.66	0.68
近似正则数 $A (ε)$	5	5	5	5	5	5	6	6	6	6

表1

表2

参数给定下模型的最优解"

模型参数	周期时长: $t = 1$ ; $X 0$ 密度函数参数: $θ = 3$ , $λ = 0.01$ ; 近似正则数: $A (ε) = 4$ ;多重风险流的强度参数: $λ 1 = 0.10$ , $λ 2 = 0.26$ , $λ 3 = 0.16$ ;价格和成本参数: $R = 300$ , $C = 200$ , $V = 20$ ;效益值: $L 1 = 0.90$ , $L 2 = 1.15$ , $L 3 = 0.85$
$N (t)$	0	1	2	3	4	$Q *$	$E [Π (Q *)]$
$Q m *$	126.1	83.5	16.7	2.9	0.4	229.6	/
$E Ω Q m *$	8279.3	5486.1	1094.9	186.9	23.9	/	15071.1

表2

图2

图3

图4

图5

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