实物与生产能力双储备下的应急物资多源采购模型与采购定价决策研究

doi:10.16381/j.cnki.issn1003-207x.2023.0143

摘要/Abstract

摘要：

政企联合储备应急物资是提升政府突发事件响应能力的必然举措，但企业却要面临应急物资需求不确定性引发的物资积压与利润损失。进而，引导企业积极参与应急物资储备与供应合作成为政府建立社会化应急物资储备体系的关键。对此，本文基于数量柔性契约构建了政府-多家应急物资生产企业的合作模型，分析研究了企业可以通过协调实物储备与生产能力储备降低协议合作成本情境下的政府柔性采购定价决策，及其影响下的企业柔性供给数量决策和实物储备数量决策，以期从协议企业数量、储备类型多样性与合作公平性等角度丰富应急物资采购管理理论研究成果。研究结果表明：在合作公平性原则下，随着政府常规储备量增加，政府会交替提高针对不同企业的柔性采购价格水平；企业需从系统角度出发，依据自身在众多协议合作方中的生产成本/效率水平情况制定决策；即使储备物资被政府采购的可能性很高，协议企业也应该积极利用生产能力储备方式而不是保有过多的实物储备。

关键词: 应急物资, 多源采购, 采购定价, 实物储备, 生产能力储备

Abstract:

Jointly reserving emergency supplies by government and enterprises is an inevitable measure to improve the government's ability to respond to emergencies. In order to implement emergency material reserve and supply agreement cooperation， the government and enterprises need to jointly solve some practical problems. On the one hand， for the government， enterprises participating in emergency material supply agreement cooperation will face risks and cost pressures brought about by demand uncertainty. Correspondingly， guiding enterprises to participate in agreement cooperation has become the primary issue that the government needs to solve. Furthermore， in order to ensure the supply capacity of emergency supplies， government emergency management departments usually establish （or need to establish） cooperative relationships with multiple enterprises. Correspondingly， how to establish cooperative relationships with numerous enterprises in an efficient and fair way has become a key challenge that the government urgently needs to solve.On the other hand， for agreement enterprises， participating in emergency material supply agreements means facing uncertainty in the demand for emergency materials. Correspondingly， how much and in what form （physical products and production capacity） to reserve will inevitably become important decisions for enterprises to reduce the risks and increase the benefits of agreement cooperation. These decisions will also have an impact on the cost and benefits of the government authority when establishing the social emergency material reserve capacity.Aiming to address the above-mentioned issues， a cooperation model between the government and several emergency material production enterprises is built based on quantity flexibility contract. Government flexible procurement pricing decisions are analyzed under the situation that enterprises can reduce the agreement cooperation cost by coordinating the physical reserves and the production capacity reserves. At the same time， the enterprises’ flexible supply quantity decisions and the physical reserve quantity decisions are studied. Based on the Stackelberg game led by the government authority， the enterprises’ decisions are first analyzed， followed by the government’s decisions. Numerical examples are also used to find more properties.Several key findings are proposed. First， under the principle of cooperative fairness， with the increase of the government's regular reserves quantity， the government will alternately increase the level of flexible procurement prices for different enterprises. Second， enterprises need to make decisions based on their production cost/efficiency level among all agreement partners from a system perspective. Third， even if the reserve materials are highly likely to be purchased by the government， the agreement enterprises should actively use the production capacity reserve method instead of maintaining excessive physical reserves.From the theoretical perspective， it enriches the research results of emergency material procurement management from the perspectives of the number of contracted enterprises， the diversity of reserve types and the fairness of cooperation. From the practical perspective， theory-based decisions and managerial insights can be provided for the government authority to economically increase the social reserve capacity from a broader perspective. At the meantime， the enterprises can also learn how to makedecision for decreasing the risks and costs when joining in the social reserve system.

Key words: emergency materials, multiple sourcing, procurement pricing, physical reserves, production capacity reserves

中图分类号:

F273

张琳,田军. 实物与生产能力双储备下的应急物资多源采购模型与采购定价决策研究[J]. 中国管理科学, 2025, 33(12): 214-225.

Lin Zhang,Jun Tian. Research on Multi-sourcing Procurement Model and Procurement Pricing Decision of Emergency Materials under Dual Reserves of Physical Goods and Production Capacity[J]. Chinese Journal of Management Science, 2025, 33(12): 214-225.

图/表 5

表1

政企成本收益组成"

		政府成本	企业 $j$ 收益
固定		$∑ k = 1 N w k φ k Q$	$w j - c r j - h φ j Q - c r j + h R j - h S j$
灾害 $θ$	$0 ≤ x ≤ Q$	$- r (Q - x)$	$r j R j + v S j$
	$Q ≤ x ≤ Q + R j I j ∑ k = 1 N I k$	$∑ k = 1 N p k x - Q I k ∑ k = 1 N I k$	$p j (x - Q) I j ∑ k = 1 N I k + r j R j - (x - Q) I j ∑ k = 1 N I k + v S j$
	$Q + R j I j ∑ k = 1 N I k ≤ x ≤ Q + ∑ k = 1 N I k$	$∑ k = 1 N p k x - Q I k ∑ k = 1 N I k$	$p j x - Q I j ∑ k = 1 N I k - c e j x - Q I j ∑ k = 1 N I k - R j$ $+ v S j - x - Q I j ∑ k = 1 N I k - R j$
	$Q + ∑ k = 1 N I k ≤ x ≤ U$	$∑ k = 1 N p k I k + m x - Q - ∑ k = 1 N I k$	$p j I j - c e j S j$
无灾害 $(1 - θ)$		$- r Q$	$r j R j + v S j$

表1

图1

表2

不同政府常规储备水平下的政企决策与成本收益"

$Q$	$p 1$	$p 2$	$I 1$	$I 2$	$R 1$	$R 2$	$Π 1$	$Π 2$	$C g$
1000	47	59	11056	9242	10844	4098	39847	20857	270725
2000	49	59	11454	7717	11297	3220	60994	30950	301375
3000	49	60	10445	7701	10308	2971	74806	43724	332298
4000	49	61	9437	7681	9322	2692	89010	56484	363580
5000	51	61	9700	6235	9685	1956	109239	67292	394676
6000	51	62	8698	6255	8673	1673	123437	80098	426125
7000	51	63	7692	6293	7651	1350	138024	92934	457979
8000	54	63	8356	4748	8232	725	159020	104196	490012
9000	53	64	6827	5146	6791	430	171939	117355	521765
10000	55	64	6867	4067	6852	0	190575	129323	553984

表2

图2

表3

不同灾害发生概率水平下的政企决策与成本收益"

$θ$	$p 1$	$p 2$	$I 1$	$I 2$	$R 1$	$R 2$	$Π 1$	$Π 2$	$C g$
0.25	54	64	8611	5747	8451	400	103219	66228	372439
0.3	51	61	9700	6235	9685	1956	109239	67292	394676
0.35	48	58	10237	6995	10222	3190	113172	69228	414136
0.4	46	55	11005	7376	10886	4013	118493	70833	431836
0.45	46	52	12722	7175	12110	4207	129937	70854	450344
0.5	46	51	14507	8534	12306	4815	136910	73548	471395

表3

参考文献 36

[1]	李晟，丰景春，吴凯丽，等.政企联合储备应急物资的合作策略研究［J］.中国管理科学，2024，32（11）： 222-232.
	Li S， Feng J C， Wu K L， et al. Study on cooperative strategy of government-enterprise joint reserve of emergency supplies［J］. Chinese Journal of Management Science， 2024， 32（11）： 222-232.
[2]	Chen Y， Zhao Q， Huang K， et al. A bi-objective optimization model for contract design of humanitarian relief goods procurement considering extreme disasters［J］. Socio-Economic Planning Sciences， 2022， 81： 101214.
[3]	Aghajani M， Ali Torabi S， Heydari J. A novel option contract integrated with supplier selection and inventory prepositioning for humanitarian relief supply chains［J］. Socio-Economic Planning Sciences， 2020， 71： 100780.
[4]	Acar M， Kaya O. Inventory decisions for humanitarian aid materials considering budget constraints［J］. European Journal of Operational Research， 2022， 300（1）： 95-111.
[5]	Diehlmann F， Lüttenberg M， Verdonck L， et al. Public-private collaborations in emergency logistics： A framework based on logistical and game-theoretical concepts［J］. Safety Science， 2021， 141： 105301.
[6]	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.
	Zhang L， Tian J， Yang R N， et al. Emergency supplies procurement pricing strategy under quantity flexible contract［J］. Systems Engineering-Theory & Practice， 2016， 36（10）： 2590-2600.
[7]	张琳，田军，冯耕中. 基于柔性契约的政府应急物资采购模型研究［J］. 运筹与管理， 2017， 26（5）： 53-61.
	Zhang L， Tian J， Feng G Z. Government emergency supplies procurement model based on flexible contract［J］. Operations Research and Management Science， 2017， 26（5）： 53-61.
[8]	扈衷权，田军，冯耕中. 基于数量柔性契约的双源应急物资采购定价模型［J］. 中国管理科学， 2019， 27（12）： 100-112.
	Hu Z Q， Tian J， Feng G Z. The pricing model of emergency supplies under quantity flexible contracts with dual purchasing sources［J］. Chinese Journal of Management Science， 2019， 27（12）： 100-112.
[9]	扈衷权，田军，冯耕中，等. 协议企业代储模式下应急物资储备策略及采购定价研究［J］. 系统工程理论与实践， 2020， 40（3）： 605-616.
	Hu Z Q， Tian J， Feng G Z， et al. Research on emergency supplies reserve strategy and procurement pricing under agreement enterprise reserve［J］.Systems Engineering- Theory & Practice，2020，40（3）： 605-616.
[10]	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.
	Hu Z Q， Tian J， Wang P， 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.
[11]	扈衷权，田军，沈奥，等. 生产能力储备模式下应急物资储备与采购定价模型［J］. 管理工程学报， 2021， 35（2）： 200-210.
	Hu Z Q， Tian J， Shen A， et al. The model of emergency supplies storing and purchase pricing based on production capacity reserve［J］. Journal of Industrial Engineering and Engineering Management， 2021， 35（2）： 200-210.
[12]	刘阳，田军，冯耕中. 基于数量柔性契约与Markov链的应急物资采购模型［J］. 系统工程理论与实践， 2020， 40（1）： 119-133.
	Liu Y， Tian J， Feng G Z. Government’s relief supplies procurement model based on quantity flexible contract and Markov chain［J］. Systems Engineering-Theory & Practice， 2020， 40（1）： 119-133.
[13]	刘阳，田军，冯耕中，等. 考虑突发事件状态转移的政府应急物资采购定价模型［J］. 运筹与管理， 2020， 29（4）： 1-11.
	Liu Y， Tian J， Feng G Z， et al. Government’s Emergency supplies procurement pricing model considering emergency’s state transition［J］. Operations Research and Management Science， 2020， 29（4）： 1-11.
[14]	柴亚光，李芃萱. 考虑储备周期的应急物资柔性采购模型［J］. 管理学报， 2021， 18（7）： 1068-1075.
	Chai Y G， Li P X. Flexible procurement model for government’s emergency supplies considering reserve period［J］. Chinese Journal of Management， 2021， 18（7）： 1068-1075.
[15]	张琳，田军，冯耕中. 价格柔性契约下政府应急物资采购协调机制研究［J］. 中国管理科学， 2017， 25（11）： 158-167.
	Zhang L， Tian J， Feng G Z. Coordination mechanism of government emergency supplies procurement under price flexibility contract［J］. Chinese Journal of Management Science， 2017， 25（11）： 158-167.
[16]	Zhang L， Tian J， Fung R Y K， et al. Materials procurement and reserves policies for humanitarian logistics with recycling and replenishment mechanisms［J］. Computers & Industrial Engineering， 2019， 127： 709-721.
[17]	Liang L， Wang X， Gao J. An option contract pricing model of relief material supply chain［J］. Omega， 2012， 40（5）： 594-600.
[18]	Balcik B， Ak D. Supplier selection for framework agreements in humanitarian relief［J］. Production and Operations Management， 2014， 23（6）： 1028-1041.
[19]	Zhang J H， Sun X Q， Zhu R， et al. Solving an emergency rescue materials problem under the joint reserves mode of government and framework agreement suppliers［J］. Plos One 2017，12（10）： e0186747.
[20]	Ali Torabi S， Shokr I， Tofighi S， et al. Integrated relief pre-positioning and procurement planning in humanitarian supply chains［J］.Transportation Research Part E： Logistics and Transportation Review， 2018， 113： 123-146.
[21]	Safaei A S， Farsad S， Paydar M M. Emergency logistics planning under supply risk and demand uncertainty［J］.Operational Research， 2020， 20（3）： 1437-1460.
[22]	Hu S L， Han C F， Meng L P. Stochastic optimization for joint decision making of inventory and procurement in humanitarian relief［J］. Computers & Industrial Engineering， 2017， 111： 39-49.
[23]	Hu S， Dong Z S. Supplier selection and pre-positioning strategy in humanitarian relief［J］. Omega， 2019， 83： 287-298.
[24]	Olanrewaju O G， Dong Z S， Hu S. Supplier selection decision making in disaster response［J］. Computers & Industrial Engineering， 2020， 143： 106412.
[25]	Falasca M， Zobel C W. A two-stage procurement model for humanitarian relief supply chains［J］. Journal of Humanitarian Logistics and Supply Chain Management， 2011， 1（2）： 151-169.
[26]	Bozorgi-Amiri A， Jabalameli M S， Mirzapour Al-e-Hashem S M J. A multi-objective robust stochastic programming model for disaster relief logistics under uncertainty［J］.OR Spectrum，2013，35（4）： 905-933.
[27]	Shamsi G N， Ali Torabi S， Shakouri G H. An option contract for vaccine procurement using the SIR epidemic model［J］. European Journal of Operational Research， 2018， 267（3）： 1122-1140.
[28]	Liu Y， Tian J， Feng G， et al. A relief supplies purchasing model via option contracts［J］. Computers & Industrial Engineering， 2019， 137： 106009.
[29]	刘阳，田军，冯耕中，等.期权契约机制下应急物资储备模型研究［J］.中国管理科学，2022，30（12）： 338-351.
	Liu Y， Tian J， Feng G Z， et al. The model of pre-positioning relief supplies under option contracts［J］. Chinese Journal of Management Science， 2022， 30（12）： 338-351.
[30]	刘阳，田军，冯耕中，等. 基于期权契约的政企联合储备应急物资模型与利润分配机制研究［J］. 中国管理科学， 2020， 28（8）： 162-171.
	Liu Y， Tian J， Feng G Z， et al. The model of joint relief supplies pre-positioning by the government and two suppliers based on option contract sand suppliers’ profits allocation mechanism［J］. Chinese Journal of Management Science， 2020， 28（8）： 162-171.
[31]	陈涛，黄钧，张玲. 协议企业实物储备、生产能力储备模式的协调性研究［J］. 中国管理科学， 2013， 21（5）： 149-156.
	Chen T， Huang J， Zhang L. Research on coordination of the enterprises in-kind agreement physical reserves and production capacity reserves mode［J］. Chinese Journal of Management Science， 2013， 21（5）： 149-156.
[32]	扈衷权，田军，冯耕中. 基于供应方生产能力的应急物资生产模型［J］.运筹与管理，2019，28（4）： 100-108.
	Hu Z Q， Tian J， Feng G Z. An emergency supplies production model based on the production capacity of suppliers［J］. Operations Research and Management Science， 2019， 28（4）： 100-108.
[33]	张琳，田军. 协议企业应急物资生产与原材料预储决策研究［J］. 中国管理科学， 2023， 31（2）： 108-117.
	Zhang L， Tian J. Agreement enterprise’s decisions on the emergency material production and the raw material pre-storage［J］. Chinese Journal of Management Science， 2023， 31（2）： 108-117.
[34]	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.
	Zhang L， Li M T， Tian J. 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.
[35]	Zhang J， Wang Z， Ren F. Optimization of humanitarian relief supply chain reliability： A case study of the Ya’an earthquake［J］. Annals of Operations Research， 2019， 283（1）： 1551-1572.
[36]	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.