考虑稳定匹配条件的双边满意匹配决策方法

Abstract

Abstract: Two-sided matching problem refers to how to obtain proper matching result from two disjoint sets of agents according to the preference information of each agent for potential partners from the opposite set. It is a research topic with extensive practical backgrounds in the field of economic management and attracts the attention of many scholars. In this paper, a decision analysis method for two-sided satisfied matching considering stable matching condition is proposed to solve the two-sided matching problem, in which the preference ordinal numbers are provided by agents on both sides. Firstly, the related concepts on two-sided matching, stable matching and satisfied matching are given. Then, considering the stable matching condition, a multi-objective two-sided matching optimization model which maximizes the satisfaction degrees of two-sided agents is constructed. Furthermore, the linear weighted method is used to convert the multi-objective optimization model into a single-objective optimization model, and the optimal matching result can be obtained by solving the model. Finally, a numerical example is given to illustrate the practicality and effectiveness of the method proposed in this paper.

Key words: two-sided matching, ordinal number, stable matching, satisfaction degree, satisfied matching, optimization model

CLC Number:

C934

FAN Zhi-ping, LI Ming-yang, YUE Qi. Decision Analysis Method for Two-Sided Satisfied Matching Considering Stable Matching Condition[J]. Chinese Journal of Management Science, 2014, 22(4): 112-118.

References

[1] Gale D, Shapley L. College admissions and the stability of marriage[J]. American Mathematical Monthly, 1962, 69(1): 9-15.

[2] Janssen M, Verbraeck A. Comparing the strengths and weaknesses of Internet-based matching mechanisms for the transport market[J]. Transportation Research Part E, 2008, 44(3): 475-490.

[3] Sarne D, Kraus S. Managing parallel inquiries in agents' two-sided search[J]. Artificial Intelligence, 2008, 172 (4-5): 541-569.

[4] Lin H T. A job placement intervention using fuzzy approach for two-way choice[J]. Expert Systems with Applications, 2009, 36(2): 2543-2553.

[5] Huang D K, Chiu H N, Yeh R H, et al. A fuzzy multi-criteria decision making approach for solving a bi-objective personnel assignment problem[J]. Computers & Industrial Engineering, 2009, 56(1): 1-10.

[6] Kaiser U, Wright J. Price structure in two-sided markets: Evidence from the magazine industry[J]. International Journal of Industrial Organization, 2006, 24(1): 1-28.

[7] Elitzur R, Gavious A. A multi-period game theoretic model of venture capitalists and entrepreneurs[J]. European Journal of Operational Research, 2003, 144(2): 440-453.

[8] Roth A E. Common and conflicting interests in two-sided matching markets[J]. European Economic Review, 1985, 27(1): 75-96.

[9] McVitie D G, Wilson L B. The stable marriage problem[J]. Communications of the Association for Computing Machinery, 1971, 14(7): 486-492.

[10] Mcvitie D G, Wilson L B.Stable marriage assignment for unequal sets[J]. Bit Numerical mathematics, 1970, 10(3): 295-309.

[11] Halldórsson M M, Iwama K, Miyazaki S, et al. Randomized approximation of the stable marriage problem[J]. Theoretical Computer Science, 2004, 325(3), 439-465.

[12] Vate V, John H.Linear programming brings marital bliss[J]. Operations Research Letters, 1989, 8(3): 1-23.

[13] Roth A E, Rothblum U G, John H, et al. Stable matchings, optimal assignments and linear programming[J]. Mathematics of Operations Research, 1993, 18(4): 803-828.

[14] Iwama K, Manlove D, Miyazaki S, et al. Stable marriage with incomplete lists and ties[C]// Giorgio A, Mariangiola D C, Simonetha R. Proceedings ICALP '99: The 26th International Colloquium on Automata, Languages, and Programming, Lecture Notes in Computer Science, Springer, Berlin, 1999, 1644: 443-452.

[15] Manlove D F, Irving R W, Iwama K, et al. Hard variants of stable marriage[J]. Theoretical Computer Science, 2002, 276(1-2): 261-279.

[16] Iwama K, Miyazaki S, Yamauchi N. A (2-c/√N)-approximation algorithm for the stable marriage problem[J]. Algorithmica, 2008, 51(3): 342-356.

[17] Teo C P, Sethuraman J, Tan W P.Gale-Shapley stable marriage problem revisited strategic issues and applications[J]. Management Science, 2001, 47(9): 1252-1267.

[18] Gale D. The two-sided matching problem: Origin, development and current issues[J]. International Game Theory Review, 2001, 3(2-3): 237-252.

[19] Echenique F.What matchings can be stable? The testable implications of matching theory[J]. Mathematics of Operations Research, 2008, 33(3): 757-768.

[20] 党兴华, 贾卫峰. GS匹配算法在企业技术创新网络结构形成中的应用[J]. 系统工程, 2009, 27(4): 31-36.

[21] Clark S, Kanbur R. Stable partnerships, matching, and local public goods[J]. European Economic Review, 2004, 48(4): 905-925.

[22] Alkan A, Gale D. Stable schedule matching under revealed preference[J]. Journal of Economic Theory, 2003, 112(2): 289-306.

[23] Cohon J L. Multiobjective programming and planning[M]// Mustoe L R, Barry M D J. Mathematics in Science and Engineering, New York: Academic Press, 1978.

[24] 钱颂迪.运筹学[M]. 北京:清华大学出版社, 1996.

Decision Analysis Method for Two-Sided Satisfied Matching Considering Stable Matching Condition

PDF (PC)

Knowledge

Cited

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 0

[1]	Yidan He,Zhengwen He,Nengmin Wang,Zhiqiang Ma. Resource-constrained Max-NPV Multi-project Scheduling Optimization under Sharing Economy Environment [J]. Chinese Journal of Management Science, 2024, 32(9): 260-270.
[2]	Jingchun Feng,Yaqi Yan,Ke Zhang,Daisong Hu. Robust Optimization Model of Water Environment Treatment Portfolio of Big Rivers for Maximizing Enterprise Income——Taking Yangtze River Protection as an Example [J]. Chinese Journal of Management Science, 2024, 32(6): 323-334.
[3]	REN Teng, LI Shu-xuan, ZHOU Zhong-bao, LI Si-di, XIAO He-lu. Study on Efficiency Evaluation of Regional Sustainable Development System Based on BLP-DEA and Satisfaction Degree [J]. Chinese Journal of Management Science, 2022, 30(7): 99-109.
[4]	MA Zhi-qiang, XU Xiao-feng, HE Zheng-wen, WANG Neng-min. Robust Scheduling Optimization of Project Resources with Activity Splitting under Complex and Uncertain Environments [J]. Chinese Journal of Management Science, 2022, 30(3): 117-130.
[5]	ZHANG Meng-ling, WANG Jing, HUANG Jun. Research on Robust Optimization of Emergency Resource Allocation Based on Supplier Participation Mechanism under Uncertain Demand [J]. Chinese Journal of Management Science, 2020, 28(7): 102-111.
[6]	MA Yong, HE Zheng-wen, ZHENG Wei-bo. Proactive Project Scheduling Optimization Based on Flexible Resource Constraint [J]. Chinese Journal of Management Science, 2020, 28(7): 220-230.
[7]	CUI Yu-quan, LIU Bing-jie, LIU Cong, QU Jing-jing. Optimization Model Analysis of New Order Agricultural Cooperation Model [J]. Chinese Journal of Management Science, 2020, 28(12): 140-150.
[8]	ZHANG Yao, SUN Meng-yang, GUAN Xin. Method of Selecting Project Risk Response Strategies Considering Total Risk Interdependence [J]. Chinese Journal of Management Science, 2020, 28(1): 32-44.
[9]	ZHANG Ran, RAN Lun, DU Tao, LI Jin-lin. A Fixed Cost Allocation Based on Two-stage DEA and Satisfaction Degree [J]. Chinese Journal of Management Science, 2019, 27(2): 138-149.
[10]	REN Lei, REN Ming-lun. Dynamic Two-sided Matching Method of Cloud Manufacturing Task based on Learning and Synergy Effect [J]. Chinese Journal of Management Science, 2018, 26(7): 63-70.
[11]	WU Zhi-qiao, LU Xiang-yuan, MU Li-feng, TANG Jia-fu. An Optimization Model for System Component Selection to Minimize Cost and Combinational Risk [J]. Chinese Journal of Management Science, 2017, 25(8): 158-165.
[12]	YUE Qi. Two-sided Matching Decision Considering Matching Aspiration under the Intuitionistic Fuzzy Circumstance [J]. Chinese Journal of Management Science, 2017, 25(6): 161-168.
[13]	LIU Xiao-di, ZHU Jian-jun, ZHANG Shi-tao, LIU Si-feng. Hesitant Fuzzy Stochastic Multiple Attribute Decision Making Method Based on Regret Theory and Group Satisfaction Degree [J]. Chinese Journal of Management Science, 2017, 25(10): 171-178.
[14]	LAN Bo-xiong, WANG Tong-shu. Optimization Model and Algorithms for Large-scale Rail Passenger Transport Network Operation [J]. Chinese Journal of Management Science, 2016, 24(6): 159-170.
[15]	LI Gen, LIU Jia-guo, ZHAO Jin-lou. Scenario Analysis of Complete Energy Intensity of Manufacturing Industry in China Based on Input and Output and Non-linear Optimization [J]. Chinese Journal of Management Science, 2016, 24(3): 31-40.