政府补贴下应急医疗物资政企协议储备决策研究

doi:10.16381/j.cnki.issn1003-207x.2020.2437

摘要/Abstract

摘要：

政企协议储备是完善应急物资保障体系，提高应急物资储备能力的一种有效方式。政府作为合作主导方，应给予政府补贴以鼓励协议企业进行实物和生产能力两种形式的储备。本文基于全球新冠肺炎疫情的现实背景，引入疫情发生概率因素，构建协议企业应急医疗物资储备决策模型，探讨协议采购价格、疫情发生概率和政府补贴三种因素对协议企业储备决策的影响，最后运用算例对所得结论进行验证。

关键词: 政府补贴, 应急医疗物资, 实物储备, 生产能力储备, 疫情发生概率

Abstract:

As the COVID-19 has spreaded globally since last year， all countries suffered severely. China took active responses to the disease when it first appeared， and first-level responses to public health emergencies have been initiated across the country. However， for a long time， the government’s emergency medical supplies reserve couldn’t meet the huge demand after the outbreak. It exposed our country’s weaknesses that we are inexperienced in managing emergency medical supplies reserve. For now， there are three main problems. Fristly， the major department of the reserve is government， while society and enterprises rarely participate in. Secondly， there are few forms of reserves， most of them are physical reserves， and production capacity reserves takes a small portion. Thirdly， the enthusiasm of enterprises participating in normalized emergency medical supplies reserve is not high due to the lack of government incentives. Therefore， in order to improve our country’s emergency medical supplies reserve system， besides government’s own reserves， the government should also entrust enterprises to reserve both physical and production capacity. At the same time， government should provide subsidies to the agreement enterprises， in order to encourage them to keep the production lines， what kind of reserve form the agreement enterprise should choose and how government subsidies will affect their reserve decisions have become the urgent problems. This article focuses on agreement enterprises which provide emergency medical supplies reserve， supposing that government subsidizes their production capacity reserve. Aiming at maximizing the benefits of the agreement enterprises and considering the actual probability of the outbreak of the epidemic， a model of coordination between physical reserve and production capacity reserve of agreement enterprises is constructed and the government-led Stackelberg game theory is used to solve it. The optimal strategy of reserve in different situations is given based on the analysis about the impact of government subsidies， the probability of outbreaks， and agreed purchase prices on the optimal reserve decision of agreement enterprises. Finally， combining the realistic background， the conclusions are verified by calculation examples. The specific research results obtained are as follows. Fristly， the agreement enterprises will choose not to cooperate with government for its own interests when the probability of outbreaks or the amount of government subsidies is low. Secondly， the agreement enterprises will choose to cooperate with government when the probability of outbreaks is high， and they will decide whether to choose a single or a mixed reserve form in view of the combined influence of the agreed purchase price， the probability of outbreaks， and government subsidies. The problem of emergency medical supplies reserve of agreement enterprises is studied， and a scientific guidance and basis for the cooperation between government and enterprises is provided to carry out them. In the future， the government can be the main body of research to discuss its pricing decisions and subsidy strategies.

Key words: government subsidies, emergency medical supplies, physical reserves, production capacity reserves, probability of outbreak

中图分类号:

F252.3

魏洁,郑迎迎,刘畅,张瑞. 政府补贴下应急医疗物资政企协议储备决策研究[J]. 中国管理科学, 2023, 31(11): 1-11.

Jie WEI,Ying-ying ZHENG,Chang LIU,Rui ZHANG. Research on the Decision-making of Emergency Eedical Supplies under Government-Subsidized Government-Enterprise Agreement Reserve[J]. Chinese Journal of Management Science, 2023, 31(11): 1-11.

图/表 7

图1

表1

变量符号及说明"

变量符号	符号说明	变量符号	符号说明
$x$	某种应急医疗物资的随机需求量	$F (x)$	需求 $x$ 的概率分布函数
$Q$	应急医疗物资的实物储备量	$q$	应急医疗物资的生产能力储备量
$C p r$	实物储备形式下单位产品生产成本以及储备成本	$C p c$	生产能力储备形式下单位原材料储备成本及生产线建造维护成本
$v$	实物储备形式下单位产品剩余价值	$r$	生产能力储备形式下单位原材料剩余价值
$p a$	政府与企业协议采购价格	$p m$	单位物资现货市场采购价格
$p b$	实物储备和生产能力储备均衡价格	$W 0$	政府给予企业的单位物资补贴
$s$	政府补贴上限	$m$	紧急加工成本
$α$	疫情发生概率	$U$	企业生产能力约束

表1

表2

不同储备决策下的最优储备量"

储备决策	最优实物储备量（ $Q *$ ）	最优生产能力储备量（ $q *$ ）
①	$0$	$0$
②	$F - 1 (1 - v - C p r α (v - p a))$	$0$
③	$0$	$F - 1 [1 - r - C p c + W 0 α (r - p a + m)]$
④	$F - 1 [1 - v - r + C p c - W 0 - C p r α (v - m - r)]$	$F - 1 [1 - r - C p c + W 0 α (r - p a + m) + v - r + C p c - W 0 - C p r α (v - m - r)]$

表2

表3

不同协议采购价格下企业最优储备决策"

协议采购价格（ $p a$ ）	疫情发生概率（ $α$ ）	政府补贴（ $W 0$ ）	决策类型	情形
$C p c + m < p a ≤$ $s v + m C p r + r C p r - m v - C p c v s + C p r - v - C p c + r$	$0 < α ≤ C p r - v p a - v$	$0 ≤ W 0 ≤ s$	①	1
	$C p r - v p a - v < α < 1$	$0 ≤ W 0 ≤ s$	②	2
$s v + m C p r + r C p r - m v - C p c v s + C p r - v - C p c + r <$ $p a ≤ m C p r + r C p r - m v - C p c v C p r - v - C p c + r$	$0 < α ≤ C p c - r - s p a - m - r$	$0 ≤ W 0 ≤ s$	①	3
	$C p c - r - s p a - m - r < α ≤ C p r - v p a - v$	$0 ≤ W 0 ≤ α (r - p a + m) + C p c - r$	①	4
	$C p c - r - s p a - m - r < α ≤ C p r - v p a - v$	$α (r - p a + m) + C p c - r < W 0 ≤ s$	$③$	5
	$C p r - v p a - v < α ≤$ $C p r - C p c + r - v + s r + m - v$	$0 ≤ W 0 ≤$ $C p r (r + m) - v (m + C p c) - p a (r + C p r - C p c - v) p a - v$	$②$	6
		$C p r (r + m) - v (m + C p c) - p a (r + C p r - C p c - v) p a - v <$ $W 0 ≤ α (r + m - v) - C p r + C p c - r + v$	④	7
		$α (r + m - v) - C p r + C p c - r + v < W 0 ≤ s$	$③$	8
	$C p r - C p c + r - v + s r + m - v < α < 1$	$0 ≤ W 0 ≤$ $C p r (r + m) - v (m + C p c) - p a (r + C p r - C p c - v) p a - v$	$②$	9
	$C p r - C p c + r - v + s r + m - v < α < 1$	$C p r (r + m) - v (m + C p c) - p a (r + C p r - C p c - v) p a - v <$ $W 0 ≤ s$	④	10
$m C p r + r C p r - m v - C p c v C p r - v - C p c + r <$ $p a < p m$	$0 < α ≤ C p c - r - s p a - m - r$	$0 ≤ W 0 ≤ s$	①	11
	$C p c - r - s p a - m - r < α ≤ C p c - r p a - m - r$	$0 ≤ W 0 ≤ α (r - p a + m) + C p c - r$	①	12
	$C p c - r - s p a - m - r < α ≤ C p c - r p a - m - r$	$α (r - p a + m) + C p c - r < W 0 ≤ s$	$③$	13
	$C p c - r p a - m - r < α ≤$ $C p r - C p c + r - v r + m - v$	$0 ≤ W 0 ≤ s$	$③$	14
	$C p r - C p c + r - v r + m - v < α ≤$ $C p r - C p c + r - v + s r + m - v$	$0 ≤ W 0 ≤ α (r + m - v) - C p r + C p c - r + v$	④	15
		$α (r + m - v) - C p r + C p c - r + v < W 0 ≤ s$	$③$	16
	$C p r - C p c + r - v + s r + m - v < α < 1$	$0 ≤ W 0 ≤ s$	④	17

表3

表4

pa=85时企业最优储备决策"

协议采购价格（ $p a$ ）	疫情发生概率（ $α$ ）	政府补贴（ $W 0$ ）	实物储备量（ $Q *$ ）	生产能力储备量（ $q *$ ）
$p a = 85$	$0 < α ≤ 0.545$	$0 ≤ W 0 ≤ 5$
$p a = 85$	$0.545 < α < 1$	$0 ≤ W 0 ≤ 5$

表4

表5

pa=115时企业最优储备决策"

协议采购价格（ $p a$ ）	疫情发生概率（ $α$ ）	政府补贴（ $W 0$ ）
$p a = 115$	$0 < α ≤ 0.273$	$0 ≤ W 0 ≤ 5$
	$0.273 < α ≤ 0.353$
	$0.353 < α ≤ 0.5$
	$0.5 < α < 1$

表5

表6

pa=140时企业最优储备决策"

协议采购价格（ $p a$ ）	疫情发生概率（ $α$ ）	政府补贴（ $W 0$ ）
$p a = 140$	$0 < α ≤ 0.188$	$0 ≤ W 0 ≤ 5$
	$0.188 < α ≤ 0.25$
	$0.25 < α ≤ 0.333$
	$0.333 < α ≤ 0.5$
	$0.5 < α < 1$

表6

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