不完备质量下带有风险厌恶的库存决策模型

doi:10.16381/j.cnki.issn1003-207x.2021.0339

Abstract

Abstract:

Quality uncertainty is one of the most important risk sources of the inventory system， which has a negative correlation with the supply capacity on the supply side. Meanwhile， the corresponding linkage effect induced by the quality uncertainty has a disturbing effect on the decision-making behavior of the inventory system， and then affects the risk preference of decision-makers. Therefore， based on the uncertainty of supply capacity， purchase price， wholesale price， residual value and other factors caused by quality imperfection， an inventory decision model with risk aversion under imperfect quality is proposed by Markov process. According to the results of the new model and numerical simulation， the following important conclusions and management implications can be drawn：Firstly， the effect of quality level and supply capacity on optimal expected order quantity and expected profit of inventory system has consistent attribute， that is， the effect of quality level and supply capacity on both have a positive correlation. When the quality level and supply capacity are in the optimal state， the optimal expected order quantity and expected profit reach the optimal value， otherwise vice versa. In addition， if the quality process ${Z k}$ meets ergodicity and irreducibility， the inventory system has a good robustness， and the decision maker can obtain relatively stable expected profits as long as he takes a robust ordering strategy.Secondly， under the multiple random decision environment which is formed by the quality level， supply ability， pleased， wholesale price， the salvage value and demand， the transmission mechanism of risk aversion factor has an invariance property to the decision making mechanism， that is， the attribute of relationships （positive correlation） between risk aversion factor $η$ and optimal expected order quantity and expected profit is not affected by exogenous random factors. This further verifies an important conclusion in behavioral science， that is， in different decision-making environments， the higher the degree of risk aversion of decision makers， the more conservative they will adopt strategies.Thirdly， the relevant conclusion shows that the post-decision information set has certain advantages which is derived from incorporating Markov process into the theoretical framework of the classic risk-averse newsboy model， that is， based on the statistical regularity of Markov process， the traditional post-decision information can be extended from two dimensions to five， and then enrich the ideological connotation of the post-decision information set， to describe the movement mechanism for the optimal expected order quantity， expected profit， order quantity robustness， expected profit stability， return expected profit and other elements of the inventory system. Obviously， Multi- dimensionalization of post-decision information set is more conducive to revealing the statistical structure of stochastic inventory system and perfecting the evaluation mechanism of reliability and performance of inventory system.

Key words: imperfect quality, Markov chain, CVaR criterion, inventory decision

CLC Number:

O211.62

Jie Chen,Lingbo Xing,Weisheng Li,Zhixiang Chen,Chongping Chen. A risk-Averse Inventory Decision-making Model with Quality Incompleteness[J]. Chinese Journal of Management Science, 2024, 32(2): 54-64.

Figures/Tables 6

模型符号	定义
$k = 0,1, 2, ?, K$	多产品库存系统的周期
$S = {1,2, ?, S}$	产品质量的状态集,即根据产品的质量缺陷率的大小,将其划分为 $S$ 个状态以描述产品质量水平的高低(状态 $i$ 的取值越大,质量水平就越高)
${Z k = i, i ∈ S}$	产品的马氏质量波动过程
$P = (p i j) S × S$	产品随机质量过程的转移概率矩阵,其中 $p i j$ 表产品的质量水平从状态 $i$ 转移到 $j$ 的概率
$C k j i$	在第 $k$ 周期,当产品质量水平从状态 $i$ 转移到 $j$ 时的进货价格
$V k j i$	在第 $k$ 周期,当产品质量水平从状态 $i$ 转移到 $j$ 时的单位残值(Salvage value)
$P k j i$	产品在第 $k$ 周期,当产品质量水平从状态 $i$ 转移到 $j$ 时的销售价
$X k$	产品在第 $k$ 周期的随机需求变量
$W k j i$	当产品质量水平从状态 $i$ 转移到 $j$ 时,该产品于第 $k$ 周期的供应能力
$f X k (x)$ , $F X k (x)$	产品在第 $k$ 周期随机需求变量的密度函数和分布函数
$? W k j i (w)$ , $Φ W k j i (w)$	当产品质量水平从状态 $i$ 转移到 $j$ 时,该产品于第 $k$ 周期供应能力的密度函数和分布函数

质量状态	状态1	状态2	状态3
密度函数	$? W k + 1 (1 i 0) (w) = γ 1 2 w Γ (2) e γ 1 w, w ≥ 0 0, ????????????????? w < 0$	$? W k + 1 (2 i 0) (w) = γ 2 2 w Γ (2) e γ 2 w, w ≥ 0 0, ????????????????? w < 0$	$? W k + 1 (3 i 0) (w) = γ 3 2 w Γ (2) e γ 3 w, w ≥ 0 0, ????????????????? w < 0$

模型参数	转移概率矩阵 $P$				其他参数
模型参数	$P = p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 p 33 = 0.50 0.30 0.20 0.10 0.40 0.50 0.05 0.15 0.80$			$V k + 1 1 i 0 = 10$ , $V k + 1 2 i 0 = 20$ , $V k + 1 3 i 0 = 30$ $P k + 1 1 i 0 = 300$ , $P k + 1 2 i 0 = 260$ , $P k + 1 3 i 0 = 220$ $C k + 1 1 i 0 = 150$ , $C k + 1 2 i 0 = 130$ , $C k + 1 3 i 0 = 110$ $η = 0.90$ , $λ = 0.030$ , $γ 1 = 0.025$ ; $γ 2 = 0.035$ $γ 3 = 0.045$
后决策信息	$Q ˉ k + 1 * (i 0)$	$E [Ω k + 1 (Q ˉ k + 1 * (i 0))]$	$E [Ω 再返 (Q * (i ˉ i ˉ))]$		$E [Ω 再返 (Q * (i ? i ?))]$	$Q ˉ 平稳 * (i 0)$	$E 平稳 (i 0)$
初始状态 $i 0 = 1$	72.1	6610.0	6690.1		/	67.3	6497.8
初始状态 $i 0 = 2$	68.2	6523.5	/		/	67.3	6497.8
初始状态 $i 0 = 3$	66.2	6470.6	/		6433.7	67.3	6497.8

模型参数	转移概率矩阵 $P$						其他参数
模型参数	$P = p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 p 33 = 0.50 0.30 0.20 0.10 0.40 0.50 0.05 0.15 0.80$					$V k + 1 12 = 10$ , $V k + 1 22 = 20$ , $V k + 1 32 = 30$ $P k + 1 12 = 300$ , $P k + 1 22 = 260$ , $P k + 1 32 = 220$ $C k + 1 12 = 150$ , $C k + 1 22 = 130$ , $C k + 1 32 = 110$ $λ = 0.030$ , $γ 1 = 0.025$ ; $γ 2 = 0.035$ $γ 3 = 0.045$
厌恶因子 $η$	0.15	0.25	0.35	0.45	0.55		0.65	0.75	0.85	0.95
$Q ˉ k + 1 * (2)$	16.2	22.0	27.4	32.8	38.5		44.8	52.1	61.7	77.4
$E [Ω k + 1 (Q ˉ k + 1 * (2))]$	1901.6	2474.5	2939.2	3336.5	3684.2		3991.0	4260.4	4491.0	4669.4

模型参数	转移概率矩阵 $P$						其他参数
模型参数	$P = p 11 p 12 p 13 p 21 p 22 p 23 p 31 p 32 p 33 = 0.50 0.30 0.20 0.10 0.40 0.50 0.05 0.15 0.80$					$n = 2$ , $η = 0.50$ , $λ = 0.030$ $V k + 1 12 = 10$ , $V k + 1 22 = 20$ , $V k + 1 32 = 30$ $P k + 1 12 = 300$ , $P k + 1 22 = 260$ , $P k + 1 32 = 220$ $C k + 1 12 = 150$ , $C k + 1 22 = 130$ , $C k + 1 32 = 110$
$γ 1$	0.012	0.014	0.016	0.018	0.020		0.022	0.024	0.026	0.028
$γ 2$	0.016	0.018	0.020	0.022	0.024		0.026	0.028	0.030	0.032
$γ 3$	0.020	0.022	0.024	0.026	0.028		0.030	0.032	0.034	0.036
$Q ˉ k + 1 * (2)$	52.1	50.3	48.6	46.9	45.3		43.7	42.1	40.7	39.3
$E [Ω k + 1 (Q ˉ k + 1 * (2))]$	5158.8	4976.2	4796.6	4621.4	4451.9		4288.5	4131.7	3981.8	3838.8

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A risk-Averse Inventory Decision-making Model with Quality Incompleteness

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