考虑层级联盟的需求不确定联合采购成本分摊策略研究

doi:10.16381/j.cnki.issn1003-207x.2022.1858

Abstract

Abstract:

In the procurement of real economic activities， enterprises tend to jointly purchase with other purchasers to reduce procurement costs. When the coalition continues to expand， a larger coalition will be formed， and the coalition structure level is reflected in this formation process. For joint procurement alliances with level coalition structure， the cost allocation problem of such joint procurement is studied with consider the uncertainty of demand in actual procurement， to provide theoretical basis and method support for the selection of joint procurement strategies among players （relationship）. In order to solve the problem of joint procurement cost allocation with level coalition structures and uncertain demand， the interval $τ$ -value allocation solution of cooperative game with coalition structure is defined， which can be expressed as $τ i (v ¯) = [m i + α - (M i - (v) - m i), m i + α + (M i + (v) - m i)]$ . The specific construction process as follows：（1） Firstly， the interval-value is adopted to describe the fuzziness of demand， and the condition of union monotonicity is defined， namely $v + (S) - v - (S) ≥ v + (S \ i) - v - (S \ i)$ . This method to perform interval subtraction can effectively avoid the problem of fuzzy number inversion. （2） Secondly， the condition of union monotonicity is introduced into the classical level coalition structure cooperative game model， and the definition of the interval-value cooperative game of the level coalition structure is given. （3） Then， this game model is introduced into classical cooperative game $τ$ -value model to construct the cooperative game $τ$ -value model of the interval-value with the coalition structure. （4） In addition， the axiomatic of individual rationality and overall effectiveness are proved of this model. （5） Lastly， in order to prove the effectiveness and practicality of the model， the method is applied to the real case of "Beijing-Tianjin-Hebei + Shandong" joint procurement of COVID-19 reagents. The conclusions of this paper are drawn：（1） Compared with real number research， fuzzy number research is more scientific and accurate. （2） The level coalition structure has a significant impact on the cost allocation strategy of joint procurement， that is， when the purchase quantity is the same， the closer the alliance is， the more cost will be saved by joint procurement. Therefore， members can increase their bargaining power by becoming key players to save more procurement costs.

Key words: level coalition structures, uncertain demand, cost allocation, joint procurement, $τ$ -value')"> $τ$ -value

CLC Number:

F273

Jie Yang, Xin Zhang, Dengfeng Li. Cost Allocation Strategy of Joint Procurement with Level Coalition Structures and Uncertain Demand[J]. Chinese Journal of Management Science, 2025, 33(2): 195-206.

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Figures/Tables 5

局中人	$m i$	$M i$	$τ i$
局中人1	27	$[40,42]$	$[35.95,38.25]$
局中人2	27	$[40,42]$	$[35.95,38.25]$
局中人3
局中人4	43	$[54,58]$	$[50.55,54.25]$

$B i$	$m i$	$M i$	$τ i$
${1,2, 3}$	127	$[173,185]$	$[148.16,156.00]$
${4}$	0	$[54,58]$	$[24.84,29.00]$

$B i$	$m i$	$M i$	$τ i$
${1,2}$	$37$	$[148.16,156.00]$	$[92.06,96.50]$
${3}$	0	$[113.16,119.00]$	$[56.10,59.50]$

局中人	$τ i$
局中人1	$[46.03,48.25]$
局中人2	$[46.03,48.25]$
局中人3	$[55.10,59.50]$
局中人4	$[24.84,29.00]$

References 26

1	Young H P. Cost allocation［J］. Handbook of game theory with economic applications， 1994（2）： 1193-1235.
2	Tinoco S V P， Creemers S， Boute R N. Collaborative shipping under different cost-sharing agreements［J］. European Journal of Operational Research， 2017， 263（3）： 827-837.
3	冯海荣，李军，曾银莲. 延期支付下的易腐品联合采购费用分配［J］. 系统工程理论与实践， 2013， 33（6）： 1411-1423.
	Feng H R， Li J， Zeng Y L. Cost allocation for collaborative procurement on perishable products under permissible delay in payments［J］. Systems Engineering-Theory & Practice， 2013， 33（6）： 1411-1423.
4	张云丰，王勇，龚本刚，等.非瞬时补货下改良品联合采购决策［J］. 中国管理科学， 2016， 24（10）： 124-132.
	Zhang Y F， Wang Y， Gong B G， al el. Research of amelioration items joint purchasing decision with non-instantaneous replenishment［J］. Chinese Journal of Management Science， 2016， 24（10）： 124-132.
5	石雪飞，王海燕. 库存容量有限的产品选择及联合采购决策研究［J］. 系统工程学报， 2021， 36（2）： 264-278.
	Shi X F， Wang H Y. Research on product selection and joint replenishment decision based on inventory capacity limitation［J］. Journal of Systems Engineering， 2021， 36（2）： 264-278.
6	冯海荣，曾银莲. 线性数量折扣下零售商合作的联盟稳定性研究［J］. 系统科学与数学， 2018， 38（9）： 989-1004.
	Feng H R， Zeng Y L. Cost allocation and coalition stability for collaborative procurement with Linear quantity discount［J］. Journal of Systems Science and Mathematical Science， 2018， 38（9）： 989-1004.
7	叶银芳，李登峰. 联合订货区间值EOQ模型及成本分摊合作博弈方法［J］. 系统工程理论与实践， 2018， 38（7）： 1819-1829.
	Ye Y F， Li D F. Joint replenishment interval-valued EOQ model and cooperative game method of the cost allocation［J］. Systems Engineering-Theory&Practice， 2018， 38（7）： 1819-1829.
8	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， al el. 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.
9	Yang J， Li D F， Xu Z S. Profit allocations for restricted coalition with hesitation degrees in cooperative game theory［J］. IEEE Access， 2020（8）： 83105-83115.
10	杨洁，赖礼邦. 考虑联盟结构的联合采购合作剩余分配博弈分析［J］. 运筹与管理， 2021， 30（6）： 91-95.
	Yang J， Lai L B. Game analysis of surplus allocation in joint purchasing cooperation considering alliance structure［J］. Operations Research and Management Science， 2021， 30（6）： 91-95.
11	Zou R， Xu G J， Li W Z， et al. A coalitional compromised solution for cooperative games［J］. Social Choice and Welfare， 2020， 55（4）： 735-758.
12	Magaña A， Carreras F. Coalition formation and stability［J］. Group Decision and Negotiation， 2018， 27（3）： 467-502.
13	Winter E. A value for cooperative games with levels structure of cooperation［J］. International Journal of Game Theory， 1989， 18（2）： 227-240.
14	Álvarez-Mozos M， Tejada O. Parallel characterizations of a generalized Shapley value and a generalized Banzhaf value for cooperative games with level structure of cooperation［J］. Decision Support Systems， 2011， 52（1）： 21-27.
15	Hu X F， Li D F. The equal surplus division value for cooperative games with a level structure［J］. Group Decision and Negotiation， 2021， 30（6）： 1315-1341.
16	杨靛青，李登峰. 多层级联盟结构合作对策τ值及其应用［J］. 系统工程学报， 2017， 32（4）： 441-453.
	Yang D Q， Li D F. τ-value for the cooperative game with multi-level coalition structures and application［J］. Journal of Systems Engineering， 2017， 32（4）： 441-453.
17	杨靛青，李登峰，俞裕兰. 模糊联盟图合作对策τ值［J］. 控制与决策， 2017， 32（9）： 1653-1658.
	Yang D Q， Li D F， Yu Y L. τ-values for fuzzy graph cooperative games［J］. Control and Decision， 2017， 32（9）： 1653-1658.
18	Yu X H， Zhang Q. Core for game with fuzzy generalized triangular payoff value［J］. International Journal of Uncertainty， Fuzziness and Knowledge-Based Systems， 2019， 27（5）： 789-813.
19	Zhang X， Sun H， Xu G J， et al. On the core， nucleolus and bargaining sets of cooperative games with fuzzy payoffs［J］. Journal of Intelligent & Fuzzy Systems， 2019， 36（6）： 6129-6142.
20	张莉，胡小建，卢朝东. 模糊需求下的易腐品供应链中零售商决策模型［J］. 中国管理科学， 2016， 24（S1）： 553-557.
	Zhang L， Hu X J， Lu C D. Retailers decision model of perishable supply chain based on fuzzy demand［J］. Chinese Journal of Management Science， 2016， 24（S1）： 553-557.
21	周珍，崔笑颖，张美佳，等. 雾霾治理限制性合作博弈与成本分摊研究［J］. 系统科学与数学， 2019， 39（6）： 875-887.
	Zhou Z， Cui X Y， Zhang M J， al el. The restricted cooperative game and its cost allocation of haze control［J］. Journal of Systems Science and Mathematical Science， 2019，39（6）： 875-887.
22	Basso F， Basso L J， Rönnqvist M， et al. Coalition formation in collaborative production and transportation with competing firms［J］. European Journal of Operational Research， 2021， 289（2）： 569-581.
23	杨洁，李登峰. 一种要素双模糊的限制交流结构合作博弈方法及应用［J］. 控制与决策， 2021， 36（2）： 475-482.
	Yang J， Li D F. An allocation model of limited communication structure cooperative game with dual fuzzy elements［J］. Control and Decision， 2021， 36（2）： 475-482.
24	Tijs S. Bounds for the core of a game and the t-value［C］//Proceedings of the Seminar on Game Theory， Hagen， Germany， October 7-10， 1980.
25	Moore R E. Methods and applications of interval analysis［M］. Philadelphia：Society for Industrial and Applied Mathematics， 1979.
26	Stefanini L. A generalization of hukuhara difference and division for interval and fuzzy arithmetic［J］. Fuzzy Sets and Systems， 2010， 161（11）： 1564-1584.

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Cost Allocation Strategy of Joint Procurement with Level Coalition Structures and Uncertain Demand

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