Game decision model of emergency reserve management of flood control materials

doi:10.16265/j.cnki.issn1003-3033.2023.05.2184

Abstract

Abstract:

In order to improve the use efficiency of government funds for flood control emergency supplies, combined with the actual flow of flood control supplies reserve and transportation, this paper studies the government-enterprise joint reserve of flood control supplies model of outsourcing or autonomy. Under the condition that the total government and enterprise reserves were fixed, the one-time government subsidy and the proportion of the contracted enterprise's material reserve were taken as decision variables. Respectively, considering the whole supply chain profit optimal, the optimal government cost and supply chain coordination as three objectives, the three flood control and emergency supplies reserves based on option contract models were designed. By deducing the optimal material reserve ratio and the corresponding one-time government subsidy amount under the conditions of different parameters of each model, taking Jiangsu Province as an example, three kinds of flood control materials, namely wood cube, woven bag and block stone, were selected for empirical analysis. The results show that the supply chain coordination model can improve the overall profit of the supply chain effectively, and ensure the optimal government reserve cost and the optimal profit of the contract enterprise to a certain extent. The production cost of entrusted enterprises to reserve materials and the holding cost of government reserve materials have a great impact on the proportion of material reserves.

Key words: flood control supplies, emergency reserve, reserve management, game, decision model, reserve mode, option contract, supply chain coordination

WANG Wei, SONG Yue, CHEN Zhisong, HUANG Li, SHI Yuxin. Game decision model of emergency reserve management of flood control materials[J]. China Safety Science Journal, 2023, 33(5): 191-198.

Figures/Tables 7

Fig.1

Tab.1

Ratio of material reserves in case of the largest profit in supply chain

初始条件	$h v - h g > 0$		$h v - h g < 0$
补充条件	$c v - c g h g - h v > (1 - ρ) + ρ q ∫ 0 q F (x) d x$	$c v - c g h g - h v < (1 - ρ) + ρ q ∫ 0 q F (x) d x$	$c v - c g h g - h v < 1 - ρ$	$c v - c g h g - h v > 1 - ρ + ρ F (q)$	$1 - ρ < c v - c g h g - h v < 1 - ρ + ρ F (q)$
α^* 取值	$α = 1$	$α = 0$	$α = 1$	$α = 0$	$α * = 1 - F - 1 1 + c v - c g (h g - h v) ρ - 1 ρ q$

Tab.1

Tab.2

Proportion of material reserves at lowest cost of government reserves

条件	$α * *$ 取值
$w o < c g + h g - v - ρ (h g + w - v)$	1
$w o > c g + h g - v - ρ (h g - ν + w) {1 - F (q)}$	0
$w o < c g + h g - v - ρ (h g - ν + w) {1 - F (q)} 且 w o > c g + h g - v - ρ (h g + w - v)$	$1 - 1 q F - 1 1 - c g + h g - v - w o ρ (h g - ν + w)$

Tab.2

Tab.3

Ratio of lump-sum subsidy and optimal reserve in case of supply chain coordination

序号	储备模式	参数条件	一次性补贴金额 $w o$	最优储备比例 $α *$
①	混合储备	$1 - ρ < c v - c g h g - h v < 1 - ρ + ρ F (q) 且 h v - h g < 0$	$w o = c g - w + (h g - ν + w) (c v - c g) h g - h v$ 且 $c g + h g - v - ρ (h g + w - v) < w o < c g + h g - v - ρ [1 - F (q)] (h g + w - v)$	$1 - 1 q F - 1 1 + c v - c g (h g - h v) ρ - 1 ρ$
②	协议企业代储	$c v - c g h g - h v > 1 - ρ + ρ q ∫ 0 q F (x) d x 且 h v - h g > 0$	$w o < c g + h g - v - ρ (h g + w - v)$	1
②	协议企业代储	$c v - c g h g - h v < 1 - ρ 且 h v - h g < 0$	$w o < c g + h g - v - ρ (h g + w - v)$	1
③	政府直储	$c v - c g h g - h v < (1 - ρ) + ρ q ∫ 0 q F (x) d x 且 h v - h g > 0$	$w o > c g + h g - v - ρ [1 - F (q)] (h g + w - v)$	0
③	政府直储	$c v - c g h g - h v > 1 - ρ + ρ F (q) 且 h v - h g < 0$	$w o > c g + h g - v - ρ [1 - F (q)] (h g + w - v)$	0

Tab.3

Tab.4

Total supply chain profit, total government cost and profits of agreed enterprise in case of supply chain coordination

序号	供应链总利润	政府总成本	协议企业总利润
①	$E Π s c = χ [c v - c g + (1 - ρ) (h v - h g)] + q [(1 - ρ) (v - h v) - c v] + ρ s q - s U + s ∫ q U F (x) d x + (v - h g) ∫ 0 χ F (x) d x + (v - h v) ∫ χ q F (x) d x$	$E Π g = c g - w + (h g - ν + w) (c v - c g) h g - h v q + (1 - ρ) (h g - v) + w - (h g - ν + w) (c v - c g) h g - h v χ + ρ w α q - s q + s U + (h g - ν) ∫ 0 χ F (x) d x - w ∫ χ q F (x) d x - s ∫ q U F (x) d x$	$E Π s = (1 - ρ) (h v - v) + w - (c v - c g) (h g - ν + w) h g - h v χ + (1 - ρ) (v - h v) - c v + c g - w + (h g - ν + w) (c v - c g) h g - h v q + ρ [(v - h v - w) ∫ χ q F (x) d x + w α q]$
②	$E Π s c = - c v q + (1 - ρ) (v - h v) q + ρ s q - s U + s ∫ q U F (x) d x + (v - h v) ∫ 0 q F (x) d x$	$E Π g = w o q + ρ w q - s q + s U - w ∫ 0 q F (x) d x - s ∫ q U F (x) d x$	$E Π s = q [w o - c v + (1 - ρ) (v - h v)] + ρ {w q + (v - h v - w) ∫ 0 q F (x) d x}$
③	$E Π s c = - c g q + (1 - ρ) (v - h g) q + ρ s q - s U + s ∫ q U F (x) d x + (v - h g) ∫ 0 q F (x) d x$	$E Π g = c g q + (1 - ρ) (h g - v) q + ρ - s q + s U - s ∫ q U F (x) d x + (h g - ν) ∫ 0 q F (x) d x$	$E Π s = 0$

Tab.4

Tab.5

Parameter value

参数符号	参数取值
参数符号	木方		编织袋	块石
q	600		4 600 000	180 000
$ρ$	0.539		0.506	0.493
w	3 906		1.165	29.98
$c g$	2 413		1.675	16.36
$h g$	5 258	0.837		61.43
$c v$	3 565	1.240		74.77
$h v$	3 181	0.433		44.09
$ν$	463	0.050		4.52
s	4 826	3.35		32.73

Tab.5

Tab.6

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物资名称	储备模型	委储比例	一次性补贴	政府总成本	供应链总利润
木方	供应链最优	0.32	3.33×10³	2.77×10⁶	-3.00×10⁶
	政府成本最优	0.00	6.46×10³	3.08×10⁶	-3.08×10⁶
		0.20	4.49×10³	2.95×10⁶	-3.01×10⁶
		0.40	2.90×10³	2.68×10⁶	-3.01×10⁶
		0.60	2.54×10³	2.58×10⁶	-3.02×10⁶
		0.80	2.52×10³	2.57×10⁶	-3.05×10⁶
		1.00	2.52×10³	2.57×10⁶	-3.07×10⁶
	供应链协调	0.32	3.33×10³	2.77×10⁶	-3.00×10⁶
编织袋	供应链最优	1.00	1.47	8.55×10⁶	-6.88×10⁶
	政府成本最优	0.00	2.46	1.01×10⁷	-1.01×10⁷
		0.20	2.46	1.01×10⁷	-9.36×10⁶
		0.40	1.59	8.77×10⁶	-8.64×10⁶
		0.60	1.47	8.55×10⁶	-8.05×10⁶
		0.80	1.47	8.55×10⁶	-7.47×10⁶
		1.00	1.47	8.55×10⁶	-6.88×10⁶
	供应链协调	1.00	1.47	8.55×10⁶	-6.88×10⁶
块石	供应链最优	0.00	66.5	9.72×10⁶	-9.70×10⁶
	政府成本最优	0.00	66.5	9.70×10⁶	-9.70×10⁶
		0.20	56.6	9.51×10⁶	-1.13×10⁷
		0.40	44.6	8.87×10⁶	-1.29×10⁷
		0.60	35.7	8.09×10⁶	-1.46×10⁷
		0.80	31.7	7.61×10⁶	-1.64×10⁷
		1.00	30.4	7.41×10⁶	-1.82×10⁷
	供应链协调	0.00	66.5	9.72×10⁶	-9.72×10⁶

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