防汛物资应急储备管理博弈决策模型

doi:10.16265/j.cnki.issn1003-3033.2023.05.2184

中国安全科学学报 ›› 2023, Vol. 33 ›› Issue (5): 191-198.doi: 10.16265/j.cnki.issn1003-3033.2023.05.2184

防汛物资应急储备管理博弈决策模型

王伟¹^,²(), 宋月¹, 陈志松³, 黄莉⁴^,^**(), 石雨欣¹

¹ 河海大学港口海岸与近海工程学院,江苏南京 210098
² 天津大学水利工程仿真与安全国家重点实验室,天津 300072
³ 南京师范大学商学院,江苏南京 210000
⁴ 河海大学公共管理学院,江苏南京 211100

收稿日期:2022-12-21 修回日期:2023-03-15 出版日期:2023-05-28
通讯作者:
** 黄莉(1982—),女,陕西汉中人,博士,副教授,主要从事水灾害应急管理方面的研究。E-mail:lily8214@126.com。
作者简介:
王伟 (1979—),男,湖北天门人,博士,教授,主要从事水灾害应急物流、港口物流等方面的研究。E-mail:13813826667@163.com。
陈志松，教授。
黄莉，副教授
基金资助:
国家重点研发计划课题(2021YFC3001002); 国家自然科学基金面上项目资助(71974052); 中央高校基本科研业务费项目(B210205012); 江苏省水利科技计划项目(2020023)

Game decision model of emergency reserve management of flood control materials

WANG Wei¹^,²(), SONG Yue¹, CHEN Zhisong³, HUANG Li⁴^,^**(), SHI Yuxin¹

¹ College of Harbour, Coastal and Offshore Engineering, Hohai University, Nanjing Jiangsu 210098, China
² State Key Laboratory of Hydraulic Engineering Simulation and Safety, Tianjin University, Tianjin 300072, China
³ Business School, Nanjing Normal University, Nanjing Jiangsu 210000, China
⁴ College of Public Administration, Hohai University, Nanjing Jiangsu 211100, China

Received:2022-12-21 Revised:2023-03-15 Published:2023-05-28

摘要/Abstract

摘要：

为提高政府防汛应急物资资金使用效率,结合实际防汛物资储备调运流程,研究外包还是自主的防汛物资政企联合储备模式,在政企双方总储备量一定的情况下,以政府一次性补贴和委储物资储备比例为决策变量,分别考虑供应链整体利润最优、政府成本最优、供应链协调3种目标,设计3个基于期权契约的防汛应急物资储备模型。通过推导得到各模型不同参数条件下,协议企业的最优物资储备比例和相应的政府一次性补贴金额。以江苏省为例,选取木方、编织袋、块石3种防汛物资进行实证分析,并给出建议的物资储备模式。结果表明:供应链协调模型可以有效提高供应链整体利润,同时一定程度上保证政府储备成本最优和协议企业利润最优;委储物资生产成本和政府直储物资持有成本对物资储备比例具有较大影响。

关键词: 防汛物资, 应急储备, 储备管理, 博弈, 决策模型, 储备模式, 期权契约, 供应链协调

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

王伟, 宋月, 陈志松, 黄莉, 石雨欣. 防汛物资应急储备管理博弈决策模型[J]. 中国安全科学学报, 2023, 33(5): 191-198.

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.

图/表 7

图1

表1

供应链利润最大下物资储备比例

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	$α = 1$	$α = 0$	$α = 1$	$α = 0$	$α * = 1 - F - 1 1 + c v - c g (h g - h v) ρ - 1 ρ q$

表1

表2

政府储备成本最小下物资储备比例

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

表2

表3

供应链协调下的一次性补贴与最优储备比例

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

表3

表4

供应链协调下的供应链总利润、政府总成本及协议企业总利润

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	$E Π s c = - c g q + (1 - ρ) (v - h g) q + ρ s q - s U + s ∫ q U F (x) d x + (v - h g) ∫ 0 q F (x) d x$	$E Π g = c g q + (1 - ρ) (h g - v) q + ρ - s q + s U - s ∫ q U F (x) d x + (h g - ν) ∫ 0 q F (x) d x$	$E Π s = 0$

表4

表5

参数取值

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

表5

表6

参考文献 14

[1]	戢晓峰, 杨春丽, 郝京京, 等. 国内外应急物流研究热点对比与展望[J]. 中国安全科学学报, 2021, 31(12):144-152. doi: 10.16265/j.cnki.issn 1003-3033.2021.12.019
	JI Xiaofeng, YANG Chunli, HAO Jingjing, et al. Research prospects and hotspot comparison for emergency logistics in China and foreign countries[J]. China Safety Science Journal, 2021, 31(12):144-152. doi: 10.16265/j.cnki.issn 1003-3033.2021.12.019
[2]	陈长坤, 赵冬月. 社会经济视角下新冠肺炎疫情危机推演与防控分析[J]. 中国安全科学学报, 2020, 30(12):24-29. doi: 10.16265/j.cnki.issn 1003-3033.2020.12.004
	CHEN Changkun, ZHAO Dongyue. Analysis of crisis deduction and prevention and control during COVID-19 pandemic from asocio-economic perspective[J]. China Safety Science Journal, 2020, 30(12):24-29. doi: 10.16265/j.cnki.issn 1003-3033.2020.12.004
[3]	ZHANG Yongling, CHEN Lu. Emergency materials reserve of government for natural disasters[J]. Natural Hazards, 2016, 81(1):1-14.
[4]	罗静, 李从东. 基于演化博弈的应急物资生产能力储备策略[J]. 工业工程, 2015, 18(2):15-19.
	LUO Jing, LI Congdong. Capacity Reserve strategy of emergency materials based on evolutionary game[J]. Industrial Engineering Journal, 2015, 18(2):15-19.
[5]	艾云飞, 吕靖, 王军, 等. 应急物资政企联合储备合作机理研究[J]. 运筹与管理, 2015, 24(5):126-131. doi: 10.12005/orms.2015.0168
	AI Yunfei, LYU Jing, WANG Jun, et al. The study of cooperation mechanism between government and enterprises in emergency supplies reserve[J]. Operations Research and Management Science, 2015, 24(5):126-131. doi: 10.12005/orms.2015.0168
[6]	MAHMOUDI R, RASTI-BARZOKI M. Sustainable supply chains under government intervention with a real-world case study: an evolutionary game theoretic approach[J]. Computers & Industrial Engineering, 2018, 116(2):130-143. doi: 10.1016/j.cie.2017.12.028
[7]	雷洋, 黄承锋. 基于演化博弈的非耐用型应急物资储备策略分析[J]. 财会月刊, 2017, 21(17):104-108.
	LEI Yang, HUANG Chengfeng. Analysis of non-durable emergency material reserve strategy based on evolutionary game[J]. Finance and Accounting Monthly, 2017, 21(17):104-108.
[8]	张琳, 田军, 党创寅, 等. 企业应急物资轮换更新行为与政府监管博弈分析[J]. 系统工程理论与实践, 2018, 38(10):2611-2619. doi: 10.12011/1000-6788(2018)10-2611-09
	ZHANG Lin, TIAN Jun, DANG Chuangyin, et al. Game analysis of enterprises' replacement of emergency supplies and government's monitoring[J]. Systems Engineering-Theory & Practice, 2018, 38(10):2611-2619.
[9]	NIKKHOO F, BOZORGI-AMIRI A, HEYDARI J. Coordination of relief items procurement in humanitarian logistic based on quantity flexibility contract[J]. International Journal of Disaster Risk Reduction, 2018, 31: 331-340. doi: 10.1016/j.ijdrr.2018.05.024
[10]	张琳, 田军, 杨瑞娜, 等. 数量柔性契约中的应急物资采购定价策略研究[J]. 系统工程理论与实践, 2016, 36(10):2590-2600. doi: 10.12011/1000-6788(2016)10-2590-11
	ZHANG Lin, TIAN Jun, YANG Ruina, et al. Emergency supplies procurement pricing strategy under quantity flexible contract[J]. Systems Engineering-Theory & Practice, 2016, 36(10):2590-2600.
[11]	张琳, 李孟涛, 田军. 考虑灾后现货市场采购的应急物资供应协议企业实物与原材料储备策略研究[J]. 系统工程理论与实践, 2022, 42(4):1001-1012. doi: 10.12011/SETP2021-1621
	ZHANG Lin, LI Mengtao, TIAN Jun. Research on physical reserve and raw material reserve strategy of emergency material supply agreement enterprises considering post-disaster spot market procurement[J]. Systems Engineering-Theory & Practice, 2022, 42(4):1001-1012.
[12]	刘阳, 田军, 冯耕中, 等. 供应商风险规避下基于期权契约的政企联合储备应急物资模型[J]. 运筹与管理, 2020, 29(11):102-111.
	LIU Yang, TIAN Jun, FENG Gengzhong, et al. The model of joint relief supplies reserves of the governmentand a risk-averse supplier based on an option contract[J]. Operations Research and Management Science, 2020, 29(11):102-111.
[13]	扈衷权, 田军, 冯耕中. 基于期权采购的政企联合储备应急物资模型[J]. 系统工程理论与实践, 2018, 38(8):2033-2044.
	HU Zhongquan, TIAN Jun, FENG Gengzhong. The model of joint emergency supplies reserves of governments and enterprises based on option procurement[J]. Systems Engineering-Theory & Practice, 2018, 38(8):2033-2044.
[14]	扈衷权, 田军, 王鹏, 等. 政企联合储备模式下应急物资储备及采购定价研究[J]. 系统工程理论与实践, 2020, 40(12):3181-3193. doi: 10.12011/SETP2020-0057
	HU Zhongquan, TIAN Jun, WANG Peng, et al. A research on emergency supplies reserve and purchase pricing under the mode of joint reserve of governments and enterprises[J]. Systems Engineering-Theory & Practice, 2020, 40(12):3181-3193.

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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防汛物资应急储备管理博弈决策模型

Game decision model of emergency reserve management of flood control materials

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