May  2022, 18(3): 1723-1735. doi: 10.3934/jimo.2021041

Solutions and characterizations under multicriteria management systems

Department of Applied Mathematics, National Pingtung University, 900 Pingtung, Taiwan

* Corresponding author: Yu-Hsien Liao

Received  January 2020 Revised  October 2020 Published  May 2022 Early access  March 2021

In real situations, agents might take different activity levels to participate; agents might represent administrative areas of different scales. On the other hand, agents always face an increasing need to focus on multiple aims efficiently in their operational processes. Thus, we introduce two solutions to investigate distribution mechanism by applying the maximal level-marginal contributions among activity level (decision) vectors under multicriteria management systems. Based on a specific reduced game and some reasonable properties, we offer some characterizations to analyze the rationality for these two solutions. In order to desire that any utility could be distributed among the players and their activity levels in proportion to related differences, two weighted extensions are also proposed by means of different weight functions.

Citation: Yu-Hsien Liao. Solutions and characterizations under multicriteria management systems. Journal of Industrial and Management Optimization, 2022, 18 (3) : 1723-1735. doi: 10.3934/jimo.2021041
References:
[1]

E. M. BednarczukJ. Miroforidis and P. Pyzel, A multi-criteria approach to approximate solution of multiple-choice knapsack problem, Computational Optimization and Applications, 70 (2018), 889-910.  doi: 10.1007/s10589-018-9988-z.

[2]

R. Branzei, On solution concepts for multi-choice cooperative games, SEIO Bulletin, 24 (2008), 13-19. 

[3]

R. BranzeiN. LlorcaJ. Sanchez-Soriano and S. Tijs, Multi-choice clan games and their core, TOP, 17 (2009), 123-138.  doi: 10.1007/s11750-009-0081-8.

[4]

R. BranzeiN. LlorcaJ. Sanchez-Soriano and S. Tijs, A constrained egalitarian solution for convex multi-choice games, TOP, 22 (2014), 860-874.  doi: 10.1007/s11750-013-0302-z.

[5]

R. BranzeiS. Tijs and J. M. Zarzuelo, Convex multi-choice cooperative games: Characterizations and monotonic allocation schemes, European J. Oper. Res., 198 (2009), 571-575.  doi: 10.1016/j.ejor.2008.09.024.

[6]

S. M. R. Davoodi and A. Goli, An integrated disaster relief model based on covering tour using hybrid Benders decomposition and variable neighborhood search: Application in the Iranian context, Computers and Industrial Engineering, 130 (2019), 370-380.  doi: 10.1016/j.cie.2019.02.040.

[7]

A. Goli, H. K. Zare, R. Tavakkoli–Moghaddam and A. Sadegheih, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry, Computers and Industrial Engineering, 137 (2019), 106090. doi: 10.1016/j. cie. 2019.106090.

[8]

A. GoliH. K. ZareR. Tavakkoli–Moghaddam and A. Sadegheih, Multiobjective fuzzy mathematical model for a financially constrained closed–loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.  doi: 10.1111/coin.12228.

[9]

M. R. GuariniF. Battisti and A. Chiovitti, A methodology for the selection of multi-criteria decision analysis methods in real estate and land management processes, Sustainability, 10 (2018), 507-534.  doi: 10.3390/su10020507.

[10]

S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589-614.  doi: 10.2307/1911054.

[11]

Y. A. Hwang and Y. H. Liao, The unit-level-core for multi-choice games: The replicated core for TU games, Journal of Global Optimization, 47 (2010), 161-171.  doi: 10.1007/s10898-009-9463-6.

[12]

Y. A. Hwang and Y. H. Liao, Reduction and dynamic approach for the multi-choice Shapley value, Journal of Industrial and Management Optimization, 9 (2013), 885-892.  doi: 10.3934/jimo.2013.9.885.

[13]

Y. H. Liao, The maximal equal allocation of nonseparable costs on multi-choice games, Economics Bulletin, 3 (2008), 1-8. 

[14]

Y. H. Liao, The duplicate extension for the equal allocation of nonseparable costs, Operational Research: An International Journal, 13 (2012), 385-397. 

[15]

Y. H. Liao, The precore: Converse consistent enlargements and alternative axiomatic results, TOP, 26 (2018), 146-163.  doi: 10.1007/s11750-017-0463-2.

[16]

Y. H. LiaoP. T. Liu and L. Y. Chung, The normalizations and related dynamic processes for two power indexes, Journal of Control and Decision, 4 (2017), 179-194.  doi: 10.1080/23307706.2017.1319303.

[17]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games, International Journal of Game Theory, 18 (1989), 389-407.  doi: 10.1007/BF01358800.

[18]

H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1985), 303-332.  doi: 10.1111/j.1468-5876.1995.tb00024.x.

[19]

I. MustakerovD. Borissova and E. Bantutov, Multiple-choice decision making by multicriteria combinatorial optimization, Advanced Modeling and Optimization, 14 (2012), 729-737. 

[20]

A. van den NouwelandJ. PottersS. Tijs and J. M. Zarzuelo, Cores and related solution concepts for multi-choice games, ZOR-Mathematical Methods of Operations Research, 41 (1995), 289-311.  doi: 10.1007/BF01432361.

[21] J. S. Ransmeier, The Tennessee Valley Authority, Vanderbilt University Press, Nashville, TN, 1942. 
[22]

A. K. SangaiahE. B. TirkolaeeA. Goli and S. Dehnavi–Arani, Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem, Soft Computing, 24 (2020), 7885-7905.  doi: 10.1007/s00500-019-04010-6.

[23] L. S. Shapley, Discussant's Comment, Joint Cost Allocation, University of Oklahoma Press, Tulsa, 1982. 
[24]

E. B. TirkolaeeA. GoliM. HematianA. K. Sangaiah and T. Han, Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms, Computing, 101 (2019), 547-570.  doi: 10.1007/s00607-018-00693-1.

show all references

References:
[1]

E. M. BednarczukJ. Miroforidis and P. Pyzel, A multi-criteria approach to approximate solution of multiple-choice knapsack problem, Computational Optimization and Applications, 70 (2018), 889-910.  doi: 10.1007/s10589-018-9988-z.

[2]

R. Branzei, On solution concepts for multi-choice cooperative games, SEIO Bulletin, 24 (2008), 13-19. 

[3]

R. BranzeiN. LlorcaJ. Sanchez-Soriano and S. Tijs, Multi-choice clan games and their core, TOP, 17 (2009), 123-138.  doi: 10.1007/s11750-009-0081-8.

[4]

R. BranzeiN. LlorcaJ. Sanchez-Soriano and S. Tijs, A constrained egalitarian solution for convex multi-choice games, TOP, 22 (2014), 860-874.  doi: 10.1007/s11750-013-0302-z.

[5]

R. BranzeiS. Tijs and J. M. Zarzuelo, Convex multi-choice cooperative games: Characterizations and monotonic allocation schemes, European J. Oper. Res., 198 (2009), 571-575.  doi: 10.1016/j.ejor.2008.09.024.

[6]

S. M. R. Davoodi and A. Goli, An integrated disaster relief model based on covering tour using hybrid Benders decomposition and variable neighborhood search: Application in the Iranian context, Computers and Industrial Engineering, 130 (2019), 370-380.  doi: 10.1016/j.cie.2019.02.040.

[7]

A. Goli, H. K. Zare, R. Tavakkoli–Moghaddam and A. Sadegheih, Hybrid artificial intelligence and robust optimization for a multi-objective product portfolio problem Case study: The dairy products industry, Computers and Industrial Engineering, 137 (2019), 106090. doi: 10.1016/j. cie. 2019.106090.

[8]

A. GoliH. K. ZareR. Tavakkoli–Moghaddam and A. Sadegheih, Multiobjective fuzzy mathematical model for a financially constrained closed–loop supply chain with labor employment, Computational Intelligence, 36 (2020), 4-34.  doi: 10.1111/coin.12228.

[9]

M. R. GuariniF. Battisti and A. Chiovitti, A methodology for the selection of multi-criteria decision analysis methods in real estate and land management processes, Sustainability, 10 (2018), 507-534.  doi: 10.3390/su10020507.

[10]

S. Hart and A. Mas-Colell, Potential, value and consistency, Econometrica, 57 (1989), 589-614.  doi: 10.2307/1911054.

[11]

Y. A. Hwang and Y. H. Liao, The unit-level-core for multi-choice games: The replicated core for TU games, Journal of Global Optimization, 47 (2010), 161-171.  doi: 10.1007/s10898-009-9463-6.

[12]

Y. A. Hwang and Y. H. Liao, Reduction and dynamic approach for the multi-choice Shapley value, Journal of Industrial and Management Optimization, 9 (2013), 885-892.  doi: 10.3934/jimo.2013.9.885.

[13]

Y. H. Liao, The maximal equal allocation of nonseparable costs on multi-choice games, Economics Bulletin, 3 (2008), 1-8. 

[14]

Y. H. Liao, The duplicate extension for the equal allocation of nonseparable costs, Operational Research: An International Journal, 13 (2012), 385-397. 

[15]

Y. H. Liao, The precore: Converse consistent enlargements and alternative axiomatic results, TOP, 26 (2018), 146-163.  doi: 10.1007/s11750-017-0463-2.

[16]

Y. H. LiaoP. T. Liu and L. Y. Chung, The normalizations and related dynamic processes for two power indexes, Journal of Control and Decision, 4 (2017), 179-194.  doi: 10.1080/23307706.2017.1319303.

[17]

M. Maschler and G. Owen, The consistent Shapley value for hyperplane games, International Journal of Game Theory, 18 (1989), 389-407.  doi: 10.1007/BF01358800.

[18]

H. Moulin, On additive methods to share joint costs, The Japanese Economic Review, 46 (1985), 303-332.  doi: 10.1111/j.1468-5876.1995.tb00024.x.

[19]

I. MustakerovD. Borissova and E. Bantutov, Multiple-choice decision making by multicriteria combinatorial optimization, Advanced Modeling and Optimization, 14 (2012), 729-737. 

[20]

A. van den NouwelandJ. PottersS. Tijs and J. M. Zarzuelo, Cores and related solution concepts for multi-choice games, ZOR-Mathematical Methods of Operations Research, 41 (1995), 289-311.  doi: 10.1007/BF01432361.

[21] J. S. Ransmeier, The Tennessee Valley Authority, Vanderbilt University Press, Nashville, TN, 1942. 
[22]

A. K. SangaiahE. B. TirkolaeeA. Goli and S. Dehnavi–Arani, Robust optimization and mixed-integer linear programming model for LNG supply chain planning problem, Soft Computing, 24 (2020), 7885-7905.  doi: 10.1007/s00500-019-04010-6.

[23] L. S. Shapley, Discussant's Comment, Joint Cost Allocation, University of Oklahoma Press, Tulsa, 1982. 
[24]

E. B. TirkolaeeA. GoliM. HematianA. K. Sangaiah and T. Han, Multi-objective multi-mode resource constrained project scheduling problem using Pareto-based algorithms, Computing, 101 (2019), 547-570.  doi: 10.1007/s00607-018-00693-1.

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