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November  2021, 17(6): 3269-3295. doi: 10.3934/jimo.2020118

Order allocation model in logistics service supply chain with demand updating and inequity aversion: A perspective of two option contracts comparison

Weihua Liu **, , Xinran Shen , , Di Wang and  Jingkun Wang

College of Management and Economics, Tianjin University, No.92, Weijin Road, Nankai District, Tianjin, 300072, China

* Corresponding author

** Co-Corresponding author

Received  August 2019 Revised  January 2020 Published  November 2021 Early access  June 2020

This paper considers an logistics service supply chain consisting of a logistics service integrator (LSI) and a number of functional logistics service providers (FLSPs). In the environment of demand updating, we focus on the inequity aversion among the FLSPs and introduce two option contracts (the reservation option contract and the option guarantee contract), build the multi-objective programming models, to explore effects of the inequity aversion behavior on the order allocation, and whether the two option contracts can mitigate the impact of inequity aversion on order allocation. Three important conclusions are obtained after two option contracts comparisons: first, there is an optimal update time, at which point, the order allocation results reach the optimal value and tend to be stable. Second, two option contracts both can not only increase the total performance of the supply chain, but also mitigate the impact of inequity aversion on the allocation under certain conditions. Third, when demand decreases, the reservation option contract is better than option guarantee contract, in contrast, when demand increases, option guarantee contract is better.

Keywords: Order allocation model, demand updating, option contract, inequity aversion, multi-objective programming.
Mathematics Subject Classification: 91A05, 90C29.
Citation: Weihua Liu, Xinran Shen, Di Wang, Jingkun Wang. Order allocation model in logistics service supply chain with demand updating and inequity aversion: A perspective of two option contracts comparison. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3269-3295. doi: 10.3934/jimo.2020118
References:
[1]

H. V. Arani, M. Rabbani and H. Rafiei, A revenue-sharing option contract toward coordination of supply chains, International Journal of Production Economics, 77 (2016), 42-56. Google Scholar

[2]

K. Bimpikis, D. Crapis and A. Tahbaz-Salehi, Information sale and competition, Management Science, 65 (2019), 2646-2664. doi: 10.1287/mnsc.2018.3068.  Google Scholar

[3]

A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. doi: 10.1287/mnsc.1040.0342.  Google Scholar

[4]

H. Chen, J. Chen and Y. Chen, Coordination mechanism for a supply chain with demand information updating, International Journal of Production Economics, 103 (2006), 347-361. doi: 10.1016/j.ijpe.2005.09.002.  Google Scholar

[5]

X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57.  doi: 10.1016/j.ijpe.2013.12.004.  Google Scholar

[6]

Y. Chen and A. Yano, Improving supply chain performance and managing risk under weather-related demand uncertainty, Management Science, 56 (2010), 1380-1397. doi: 10.1287/mnsc.1100.1194.  Google Scholar

[7]

Y. Chen and X. Zhao, Modeling bounded rationality in capacity allocation games with the quantal response equilibrium, Management Science, 58 (2012), 1952-1962. doi: 10.1287/mnsc.1120.1531.  Google Scholar

[8]

G. B. Dahl, K. V. Loken and M. Mogstad, Peer effects in program participation, American Economic Review, 104 (2014), 2049-2074. doi: 10.3386/w18198.  Google Scholar

[9]

E. A. Demirtas and O. Üstün, An integrated multiobjective decision making process for supplier selection and order allocation, Omega, 36 (2008), 76-90. doi: 10.1016/j.omega.2005.11.003.  Google Scholar

[10]

G. D. Eppen and A. V. Iyer, Backup agreements in fashion buying the value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469.  Google Scholar

[11]

F. Gao, F. Y. Chen and X. Chao, Joint optimal ordering and weather hedging decisions: Mean-CVaR model, Flexible services and manufacturing journal, 23 (2011), 1-25. doi: 10.1007/s10696-011-9078-3.  Google Scholar

[12]

V. R. Ghezavati, M. S. Jabal-Ameli and A. Makui, A new heuristic method for distribution networks considering service level constraint and coverage radius, Expert Systems with Applications, 36 (2009), 5620-5629. doi: 10.1016/j.eswa.2008.06.130.  Google Scholar

[13]

B. Gu and Q. Ye, First step in social media: Measuring the influence of online management responses on customer satisfaction, Production and Operations Management, 23 (2014), 570-582. doi: 10.1111/poms.12043.  Google Scholar

[14]

Z. Guan, X. Zhang, M. Zhou and Y. Dan, Demand information sharing in competing supply chains with manufacturer-provided service, International Journal of Production Economics, 220 (2020). doi: 10.1016/j.ijpe.2019.07.023.  Google Scholar

[15]

Y.-S. Huang, R.-S. Ho and C.-C. Fang, Quantity discount coordination for allocation of purchase orders in Supply Chains with multiple suppliers, International Journal of Production Research, 53 (2015), 6653-6671. doi: 10.1080/00207543.2015.1055345.  Google Scholar

[16]

T.-H. Ho and X. Su, Peer-induced fairness in games, America Economic Reviews, 99 (2009), 2022-2049. doi: 10.1257/aer.99.5.2022.  Google Scholar

[17]

T.-H. Ho, X. Su and Y. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. doi: 10.1111/poms.12064.  Google Scholar

[18]

M.-G. Huang, Real options approach-based demand forecasting method for a range of products with highly volatile and correlated demand, European Journal of Operation Research, 198 (2009), 867-877. doi: 10.1016/j.ejor.2008.10.002.  Google Scholar

[19]

K. Kawamoto, Status-seeking behavior, the evolution of income inequality, and growth, Economic Theory, 39 (2009), 269-289. doi: 10.1007/s00199-007-0318-4.  Google Scholar

[20]

T. D. Klastorin, K. Moinzadeh and J. Son, Coordinating orders in supply chains through price discounts, IIE Transactions, 34 (2002), 679-689. doi: 10.1080/07408170208928904.  Google Scholar

[21]

X. Liu, Q. Gou, L. Alwan and L. Liang, Option contracts: A solution for overloading problems in the delivery service supply chain, Journal of the Operational Research Society, 67 (2016), 187-197. doi: 10.1057/jors.2014.133.  Google Scholar

[22]

W. Liu, X. Liu and X. Li, The two-stage batch ordering strategy of logistics service capacity with demand update, Transportation Research Part E: Logistics and Transportation Review, 83 (2015b), 65-89. doi: 10.1016/j.tre.2015.08.009.  Google Scholar

[23]

W. Liu, X. Shen and D. Wang, The impacts of dual overconfidence behavior and demand updating on the decisions of port service supply chain: A real case study from China, Annals of Operations Research, (2018b), 1-40. doi: 10.1007/s10479-018-3095-5.  Google Scholar

[24]

W. Liu, D. Wang, X. Shen, X. Yan and W. Wei, The impacts of distributional and peer-induced fairness concerns on the decision-making of order allocation in logistics service supply chain, Transportation Research Part E: Logistics and Transportation Review, 116 (2018a), 102-122. doi: 10.1016/j.tre.2018.05.006.  Google Scholar

[25]

W. Liu, M. Wang, D. Zhu and L. Zhou, Service capacity procurement of logistics service supply chain with demand updating and loss-averse preference, Applied Mathematical Modelling, 66 (2019), 486-507. doi: 10.1016/j.apm.2018.09.020.  Google Scholar

[26]

W. Liu, S. Wang, D. Zhu, D. Wang and X. Shen, Order allocation of logistics service supply chain with fairness concern and demand updating: Model analysis and empirical examination, Annals of Operations Research, 268 (2018), 177-213. doi: 10.1007/s10479-017-2482-7.  Google Scholar

[27]

W. Liu, D. Xie, Y. Liu and X. Liu, Service capability procurement decision in logistics service supply chain: A research under demand updating and quality guarantee, International Journal of Production Research, 53 (2015a), 488-510. doi: 10.1080/00207543.2014.955219.  Google Scholar

[28]

K. S. Moghaddam, Supplier selection and order allocation in closed-loop supply chain systems using hybrid Monte Carlo simulation and goal programming, International Journal of Production Research, 53 (2015), 6320-6338. doi: 10.1080/00207543.2015.1054452.  Google Scholar

[29]

K. Nedaiasl, A. F. Bastani and A. Rafiee, A product integration method for the approximation of the early exercise boundary in the American option pricing problem, Mathematical Methods in the Applied Sciences, 42 (2019), 2825-2841. doi: 10.1002/mma.5553.  Google Scholar

[30]

N. K. Nomikos, I. Kyriakou, N. C. Papapostolou and P. K. Pouliasis, Freight options: Price modelling and empirical analysis, Transportation Research Part E: Logistics and Transportation Review, 51 (2013), 82-94. doi: 10.1016/j.tre.2012.12.001.  Google Scholar

[31]

D. Özgen, S. Önüt, B. Gülsün, U. F. Tuzkaya and G. Tuzkaya, A two-phase possibilistic linear programming methodology for multi-objective supplier evaluation and order allocation problems, Information Sciences, 178 (2008), 485-500. doi: 10.1016/j.ins.2007.08.002.  Google Scholar

[32]

F. Perea, J. Puerto and F. R. Fernández, Modeling cooperation on a class of distribution problems, European Journal of Operational Research, 198 (2009), 726-733. doi: 10.1016/j.ejor.2008.09.042.  Google Scholar

[33]

S. P. Sethi, H. Yan, H. Zhang and J. Zhou, Information updated supply chain with service-level constraints, Journal of Industrial and Management Optimization, 1 (2005), 513-31. doi: 10.3934/jimo.2005.1.513.  Google Scholar

[34]

B. Shen, T. M. Choi and S. Minner, A review on supply chain contracting with information considerations: Information updating and informatio asymmetry, International Journal of Production Research, (2018), 1-39. Google Scholar

[35]

S. Spinler, A. Huchzermeier and P. R. Kleindorfer, Risk hedging via options contracts for physical delivery, OR Spectrum, 25 (2003), 379-395. doi: 10.1007/s00291-003-0128-4.  Google Scholar

[36]

C. Wang and X. Chen, Option contracts in fresh produce supply chain with circulation loss, Journal of Industrial Engineering and Management, 6 (2013), 104-112. doi: 10.3926/jiem.667.  Google Scholar

[37]

V. Wadhwa and A. R. Ravindran, Vendor selection in outsourcing, Computers and Operations Research, 34 (2007), 3725-3737. doi: 10.1016/j.cor.2006.01.009.  Google Scholar

[38]

J.-Z. Wu, C.-F. Chien and M. Gen, Coordinating strategic outsourcing decisions for semiconductor assembly using a bi-objective genetic algorithm, International Journal of Production Research, 50 (2012), 235-260. doi: 10.1080/00207543.2011.571457.  Google Scholar

[39]

D. J. Wu, P. R. Kleindorfer and J. E. Zhang, Optimal bidding and contracting strategies for capital-intensive goods, European Journal of Operational Research, 137 (2002), 657-676. doi: 10.1016/S0377-2217(01)00093-5.  Google Scholar

[40]

D. J. Wu and P. R. Kleindorfer, Competitive options, supply contracting, and electronic markets, Management Science, 51 (2005), 452-466. doi: 10.1287/mnsc.1040.0341.  Google Scholar

[41]

J. Wu, H. Wang and J. Shang, Multi-sourcing and information sharing under competition and supply uncertainty, European Journal of Operational Research, 278 (2019), 658-671. doi: 10.1016/j.ejor.2019.04.039.  Google Scholar

[42]

S. Zhang, B. Dan and M. Zhou, After-sale service deployment and information sharing in a supply chain under demand uncertainty, European Journal of Operational Research, 279 (2019), 351-363. doi: 10.1016/j.ejor.2019.05.014.  Google Scholar

[43]

J. Zhang, B. Shou and J. Chen, Postponed product differentiation with demand information update, International Journal of Production Economics, 141 (2013), 529-540. doi: 10.1016/j.ijpe.2012.09.007.  Google Scholar

[44]

Y. Zhao, T.-M. Choi, T. C. E. Cheng and S. Wang, Supply option contracts with spot market and demand information updating, European Journal of Operational Research, 266 (2018), 1062-1071. doi: 10.1016/j.ejor.2017.11.001.  Google Scholar

[45]

Y. Zhao, X. Meng, S. Wang and T. C. E. Cheng, A value-based approach to option pricing: The case of supply chain options, International Journal of Production Economics, 143 (2013), 171-177. Google Scholar

[46]

Y. Zhao, S. Wang, T. C. E. Cheng, X. Wang and Z. Huang, Coordination of supply chains by option contracts: A cooperative game theory approach, European Journal of Operational Research, 207 (2010), 668-675. doi: 10.1016/j.ejor.2010.05.017.  Google Scholar

[47]

M. Zheng, K. Wu and Y. Shu, Newsvendor problems with demand forecast updating and supply constraints, Computers and Operations Research, 67 (2016), 193-206. doi: 10.1016/j.cor.2015.10.007.  Google Scholar

show all references

References:
[1]

H. V. Arani, M. Rabbani and H. Rafiei, A revenue-sharing option contract toward coordination of supply chains, International Journal of Production Economics, 77 (2016), 42-56. Google Scholar

[2]

K. Bimpikis, D. Crapis and A. Tahbaz-Salehi, Information sale and competition, Management Science, 65 (2019), 2646-2664. doi: 10.1287/mnsc.2018.3068.  Google Scholar

[3]

A. Burnetas and P. Ritchken, Option pricing with downward-sloping demand curves: The case of supply chain options, Management Science, 51 (2005), 566-580. doi: 10.1287/mnsc.1040.0342.  Google Scholar

[4]

H. Chen, J. Chen and Y. Chen, Coordination mechanism for a supply chain with demand information updating, International Journal of Production Economics, 103 (2006), 347-361. doi: 10.1016/j.ijpe.2005.09.002.  Google Scholar

[5]

X. Chen, G. Hao and L. Li, Channel coordination with a loss-averse retailer and option contracts, International Journal of Production Economics, 150 (2014), 52-57.  doi: 10.1016/j.ijpe.2013.12.004.  Google Scholar

[6]

Y. Chen and A. Yano, Improving supply chain performance and managing risk under weather-related demand uncertainty, Management Science, 56 (2010), 1380-1397. doi: 10.1287/mnsc.1100.1194.  Google Scholar

[7]

Y. Chen and X. Zhao, Modeling bounded rationality in capacity allocation games with the quantal response equilibrium, Management Science, 58 (2012), 1952-1962. doi: 10.1287/mnsc.1120.1531.  Google Scholar

[8]

G. B. Dahl, K. V. Loken and M. Mogstad, Peer effects in program participation, American Economic Review, 104 (2014), 2049-2074. doi: 10.3386/w18198.  Google Scholar

[9]

E. A. Demirtas and O. Üstün, An integrated multiobjective decision making process for supplier selection and order allocation, Omega, 36 (2008), 76-90. doi: 10.1016/j.omega.2005.11.003.  Google Scholar

[10]

G. D. Eppen and A. V. Iyer, Backup agreements in fashion buying the value of upstream flexibility, Management Science, 43 (1997), 1469-1484. doi: 10.1287/mnsc.43.11.1469.  Google Scholar

[11]

F. Gao, F. Y. Chen and X. Chao, Joint optimal ordering and weather hedging decisions: Mean-CVaR model, Flexible services and manufacturing journal, 23 (2011), 1-25. doi: 10.1007/s10696-011-9078-3.  Google Scholar

[12]

V. R. Ghezavati, M. S. Jabal-Ameli and A. Makui, A new heuristic method for distribution networks considering service level constraint and coverage radius, Expert Systems with Applications, 36 (2009), 5620-5629. doi: 10.1016/j.eswa.2008.06.130.  Google Scholar

[13]

B. Gu and Q. Ye, First step in social media: Measuring the influence of online management responses on customer satisfaction, Production and Operations Management, 23 (2014), 570-582. doi: 10.1111/poms.12043.  Google Scholar

[14]

Z. Guan, X. Zhang, M. Zhou and Y. Dan, Demand information sharing in competing supply chains with manufacturer-provided service, International Journal of Production Economics, 220 (2020). doi: 10.1016/j.ijpe.2019.07.023.  Google Scholar

[15]

Y.-S. Huang, R.-S. Ho and C.-C. Fang, Quantity discount coordination for allocation of purchase orders in Supply Chains with multiple suppliers, International Journal of Production Research, 53 (2015), 6653-6671. doi: 10.1080/00207543.2015.1055345.  Google Scholar

[16]

T.-H. Ho and X. Su, Peer-induced fairness in games, America Economic Reviews, 99 (2009), 2022-2049. doi: 10.1257/aer.99.5.2022.  Google Scholar

[17]

T.-H. Ho, X. Su and Y. Wu, Distributional and peer-induced fairness in supply chain contract design, Production and Operations Management, 23 (2014), 161-175. doi: 10.1111/poms.12064.  Google Scholar

[18]

M.-G. Huang, Real options approach-based demand forecasting method for a range of products with highly volatile and correlated demand, European Journal of Operation Research, 198 (2009), 867-877. doi: 10.1016/j.ejor.2008.10.002.  Google Scholar

[19]

K. Kawamoto, Status-seeking behavior, the evolution of income inequality, and growth, Economic Theory, 39 (2009), 269-289. doi: 10.1007/s00199-007-0318-4.  Google Scholar

[20]

T. D. Klastorin, K. Moinzadeh and J. Son, Coordinating orders in supply chains through price discounts, IIE Transactions, 34 (2002), 679-689. doi: 10.1080/07408170208928904.  Google Scholar

[21]

X. Liu, Q. Gou, L. Alwan and L. Liang, Option contracts: A solution for overloading problems in the delivery service supply chain, Journal of the Operational Research Society, 67 (2016), 187-197. doi: 10.1057/jors.2014.133.  Google Scholar

[22]

W. Liu, X. Liu and X. Li, The two-stage batch ordering strategy of logistics service capacity with demand update, Transportation Research Part E: Logistics and Transportation Review, 83 (2015b), 65-89. doi: 10.1016/j.tre.2015.08.009.  Google Scholar

[23]

W. Liu, X. Shen and D. Wang, The impacts of dual overconfidence behavior and demand updating on the decisions of port service supply chain: A real case study from China, Annals of Operations Research, (2018b), 1-40. doi: 10.1007/s10479-018-3095-5.  Google Scholar

[24]

W. Liu, D. Wang, X. Shen, X. Yan and W. Wei, The impacts of distributional and peer-induced fairness concerns on the decision-making of order allocation in logistics service supply chain, Transportation Research Part E: Logistics and Transportation Review, 116 (2018a), 102-122. doi: 10.1016/j.tre.2018.05.006.  Google Scholar

[25]

W. Liu, M. Wang, D. Zhu and L. Zhou, Service capacity procurement of logistics service supply chain with demand updating and loss-averse preference, Applied Mathematical Modelling, 66 (2019), 486-507. doi: 10.1016/j.apm.2018.09.020.  Google Scholar

[26]

W. Liu, S. Wang, D. Zhu, D. Wang and X. Shen, Order allocation of logistics service supply chain with fairness concern and demand updating: Model analysis and empirical examination, Annals of Operations Research, 268 (2018), 177-213. doi: 10.1007/s10479-017-2482-7.  Google Scholar

[27]

W. Liu, D. Xie, Y. Liu and X. Liu, Service capability procurement decision in logistics service supply chain: A research under demand updating and quality guarantee, International Journal of Production Research, 53 (2015a), 488-510. doi: 10.1080/00207543.2014.955219.  Google Scholar

[28]

K. S. Moghaddam, Supplier selection and order allocation in closed-loop supply chain systems using hybrid Monte Carlo simulation and goal programming, International Journal of Production Research, 53 (2015), 6320-6338. doi: 10.1080/00207543.2015.1054452.  Google Scholar

[29]

K. Nedaiasl, A. F. Bastani and A. Rafiee, A product integration method for the approximation of the early exercise boundary in the American option pricing problem, Mathematical Methods in the Applied Sciences, 42 (2019), 2825-2841. doi: 10.1002/mma.5553.  Google Scholar

[30]

N. K. Nomikos, I. Kyriakou, N. C. Papapostolou and P. K. Pouliasis, Freight options: Price modelling and empirical analysis, Transportation Research Part E: Logistics and Transportation Review, 51 (2013), 82-94. doi: 10.1016/j.tre.2012.12.001.  Google Scholar

[31]

D. Özgen, S. Önüt, B. Gülsün, U. F. Tuzkaya and G. Tuzkaya, A two-phase possibilistic linear programming methodology for multi-objective supplier evaluation and order allocation problems, Information Sciences, 178 (2008), 485-500. doi: 10.1016/j.ins.2007.08.002.  Google Scholar

[32]

F. Perea, J. Puerto and F. R. Fernández, Modeling cooperation on a class of distribution problems, European Journal of Operational Research, 198 (2009), 726-733. doi: 10.1016/j.ejor.2008.09.042.  Google Scholar

[33]

S. P. Sethi, H. Yan, H. Zhang and J. Zhou, Information updated supply chain with service-level constraints, Journal of Industrial and Management Optimization, 1 (2005), 513-31. doi: 10.3934/jimo.2005.1.513.  Google Scholar

[34]

B. Shen, T. M. Choi and S. Minner, A review on supply chain contracting with information considerations: Information updating and informatio asymmetry, International Journal of Production Research, (2018), 1-39. Google Scholar

[35]

S. Spinler, A. Huchzermeier and P. R. Kleindorfer, Risk hedging via options contracts for physical delivery, OR Spectrum, 25 (2003), 379-395. doi: 10.1007/s00291-003-0128-4.  Google Scholar

[36]

C. Wang and X. Chen, Option contracts in fresh produce supply chain with circulation loss, Journal of Industrial Engineering and Management, 6 (2013), 104-112. doi: 10.3926/jiem.667.  Google Scholar

[37]

V. Wadhwa and A. R. Ravindran, Vendor selection in outsourcing, Computers and Operations Research, 34 (2007), 3725-3737. doi: 10.1016/j.cor.2006.01.009.  Google Scholar

[38]

J.-Z. Wu, C.-F. Chien and M. Gen, Coordinating strategic outsourcing decisions for semiconductor assembly using a bi-objective genetic algorithm, International Journal of Production Research, 50 (2012), 235-260. doi: 10.1080/00207543.2011.571457.  Google Scholar

[39]

D. J. Wu, P. R. Kleindorfer and J. E. Zhang, Optimal bidding and contracting strategies for capital-intensive goods, European Journal of Operational Research, 137 (2002), 657-676. doi: 10.1016/S0377-2217(01)00093-5.  Google Scholar

[40]

D. J. Wu and P. R. Kleindorfer, Competitive options, supply contracting, and electronic markets, Management Science, 51 (2005), 452-466. doi: 10.1287/mnsc.1040.0341.  Google Scholar

[41]

J. Wu, H. Wang and J. Shang, Multi-sourcing and information sharing under competition and supply uncertainty, European Journal of Operational Research, 278 (2019), 658-671. doi: 10.1016/j.ejor.2019.04.039.  Google Scholar

[42]

S. Zhang, B. Dan and M. Zhou, After-sale service deployment and information sharing in a supply chain under demand uncertainty, European Journal of Operational Research, 279 (2019), 351-363. doi: 10.1016/j.ejor.2019.05.014.  Google Scholar

[43]

J. Zhang, B. Shou and J. Chen, Postponed product differentiation with demand information update, International Journal of Production Economics, 141 (2013), 529-540. doi: 10.1016/j.ijpe.2012.09.007.  Google Scholar

[44]

Y. Zhao, T.-M. Choi, T. C. E. Cheng and S. Wang, Supply option contracts with spot market and demand information updating, European Journal of Operational Research, 266 (2018), 1062-1071. doi: 10.1016/j.ejor.2017.11.001.  Google Scholar

[45]

Y. Zhao, X. Meng, S. Wang and T. C. E. Cheng, A value-based approach to option pricing: The case of supply chain options, International Journal of Production Economics, 143 (2013), 171-177. Google Scholar

[46]

Y. Zhao, S. Wang, T. C. E. Cheng, X. Wang and Z. Huang, Coordination of supply chains by option contracts: A cooperative game theory approach, European Journal of Operational Research, 207 (2010), 668-675. doi: 10.1016/j.ejor.2010.05.017.  Google Scholar

[47]

M. Zheng, K. Wu and Y. Shu, Newsvendor problems with demand forecast updating and supply constraints, Computers and Operations Research, 67 (2016), 193-206. doi: 10.1016/j.cor.2015.10.007.  Google Scholar

Figure 1(a).  Utility of the LSI when $ \xi<\mu $
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Figure 1(b).  Utility of the LSI when $ \xi>\mu $
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Figure 2(a).  Utility of the FLSPs when $ \xi<\mu $
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Figure 2(b).  Utility of the FLSPs when $ \xi>\mu $
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Figure 3(a).  Total performance when $ \xi<\mu $
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Figure 3(b).  Total performance when $ \xi>\mu $
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Figure 4(a).  Utility of the LSI when $ \xi<\mu $
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Figure 4(b).  Utility of the LSI when $ \xi>\mu $
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Figure 5(a).  Utility of FLSPs when $ \xi<\mu $
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Figure 5(b).  Utility of FLSPs when $ \xi>\mu $
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Figure 6(a).  Total performance when $ \xi<\mu $
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Figure 6(b).  Total performance when $ \xi>\mu $
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Figure 7(a).  $ \Delta\Pi_{LSI}^{1-2} $ in the case of decreased demand
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Figure 7(b).  $ \Delta \Pi_{LSI}^{1-3} $ in the case of decreased demand
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Figure 8(a).  $ \Delta U_{FLSP}^{1-2} $ in the case of decreased demand
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Figure 8(b).  $ \Delta U_{FLSP}^{1-3} $ in the case of decreased demand
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Figure 9(a).  $ \Delta TP^{1-2} $ in the case of decreased demand
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Figure 9(b).  $ \Delta TP^{1-3} $ in the case of decreased demand
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Figure 10(a).  $ \Delta\Pi_{LSI}^{1-2} $ in the case of increased demand
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Figure 10(b).  $ \Delta\Pi_{LSI}^{1-3} $ in the case of increased demand
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Figure 11(a).  $ \Delta\Pi_{FLSP}^{1-2} $ in the case of increased demand
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Figure 11(b).  $ \Delta\Pi_{FLSP}^{1-3} $ in the case of increased demand
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Figure 12(a).  $ \Delta TP^{1-2} $ in the case of increased demand
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Figure 12(b).  $ \Delta TP^{1-3} $ in the case of increased demand
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Table 1.  The differences between the relevant literatures and this paper
Research content [21] [26] [6] This paper
Supply chain structureA single provider and a single retailer Logistics service supply chain with single LSI and multiple FLSPs Agricultural product supply chain with a single manufacturer and a single retailer Logistics service supply chain with single LSI and multiple FLSPs
Demand updating is considered $ \times $ $ \surd $ $ \times $ $ \surd $
Option types Reservation option $ \times $ Derivative option Reservation option and derivative option
Fairness concern is considered $ \times $ $ \surd $ $ \times $ $ \surd $
Research problem Supply chain coordination and performance management Behavioral management in order allocation Supply chain performance and risk management The effect of option and behavior on the performance of order allocation
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Research content [21] [26] [6] This paper
Supply chain structureA single provider and a single retailer Logistics service supply chain with single LSI and multiple FLSPs Agricultural product supply chain with a single manufacturer and a single retailer Logistics service supply chain with single LSI and multiple FLSPs
Demand updating is considered $ \times $ $ \surd $ $ \times $ $ \surd $
Option types Reservation option $ \times $ Derivative option Reservation option and derivative option
Fairness concern is considered $ \times $ $ \surd $ $ \times $ $ \surd $
Research problem Supply chain coordination and performance management Behavioral management in order allocation Supply chain performance and risk management The effect of option and behavior on the performance of order allocation
Table 2.  Notations
Notation Description
$ c_{i, opp} $ Opportunity cost of FLSP $ i $ at the time $ t $
$ C_I $ Demand updating cost of LSI
$ c_i $ The cost of unit logistics capacity for FLSP $ i $
$ d_{i, 0} $ Initial utility of FLSP $ i $
$ d_{i, 1} $ Satisfaction utility of FLSP $ i $ with the reservation option in the second stage
$ d_{i, 2} $ Satisfaction utility of FLSP $ i $ with the option guarantee in the second stage
$ D $ Demand in the first stage, which subjects to the normal distribution $ D\thicksim N(\mu, \sigma^2) $
$ e_i $ Option purchase price of unit logistics capacity for FLSP $ i $ in reservation option contract
$ h_i $ Option executive price of unit logistics capacity for FLSP $ i $ in reservation option contract
$ n $ The total number of FLSPs
$ p_i $ The market price at which the LSI buys the unit logistics capacity from the FLSP $ i $
$ q $ Option purchase quantity for LSI in option guarantee contract
$ d_{i, 2} $ Satisfaction utility of FLSP $ i $ with the option guarantee in the second stage
$ D $ Demand in the first stage, which subjects to the normal distribution $ D\thicksim N(\mu, \sigma^2) $
$ Q $ The updated demand in the second stage, which subjects to the normal distribution $ (Q\mid\xi)\thicksim N(\mu(\xi), \nu^2) $
$ r $ Option purchase price of unit logistics capacity for LSI in option guarantee contract
$ R $ Option compensation price of unit logistics capacity for LSI in option guarantee contract
$ v_{i, 1} $ In the first stage, profit utility of FLSP $ i $ in reservation option contract
$ v_{i, 2} $ In the second stage, profit utility of FLSP $ i $ in reservation option contract
$ w_{i1} $ The weight of satisfaction utility of FLSP $ i $
$ w_{i2} $ The weight of profit utility of FLSP $ i $
$ x_{i, 1} $ In the first stage, logistics service capacity provided by FLSP $ i $ in reservation option contract
$ x_{i, 2} $ In the second stage, logistics service capacity provided by FLSP $ i $ in reservation option contract
$ y_{i, 1} $ In the first stage, logistics service capacity provided by FLSP $ i $ in option guarantee contract
$ y_{i, 2} $ In the second stage, logistics service capacity provided by FLSP $ i $ in option guarantee contract
$ z_1 $ The total profit of the LSI
$ z_2 $ The total utility of the FLSP
$ \alpha_i $ Advantage unfair coefficient of FLSP $ i $
$ \beta_i $ Disadvantage unfair coefficient of FLSP $ i $
$ \lambda $ Unit logistics capacity income
$ \xi $ Based on the demanded sample information collected in the lead time, the estimated mean of the demand (Estimated Demand Average)
$ \tau(t) $ Demand forecast error, reflecting the degree of deviation between demand forecast and the actual needs
$ \theta_i^- $ Minimum logistics capacity provided by FLSP $ i $
$ \theta_i^+ $ Maximum logistics capacity provided by FLSP $ i $
$ \eta $ Compensation threshold in option guarantee
$ TP $ Compensation threshold in option guarantee
$ \Delta LSI $ Change ratio in profit of LSI
$ \Delta FLSP $ Change ratio in profit of FLSP
$ \Delta TP $ Change ratio in total performance of supply chain
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Notation Description
$ c_{i, opp} $ Opportunity cost of FLSP $ i $ at the time $ t $
$ C_I $ Demand updating cost of LSI
$ c_i $ The cost of unit logistics capacity for FLSP $ i $
$ d_{i, 0} $ Initial utility of FLSP $ i $
$ d_{i, 1} $ Satisfaction utility of FLSP $ i $ with the reservation option in the second stage
$ d_{i, 2} $ Satisfaction utility of FLSP $ i $ with the option guarantee in the second stage
$ D $ Demand in the first stage, which subjects to the normal distribution $ D\thicksim N(\mu, \sigma^2) $
$ e_i $ Option purchase price of unit logistics capacity for FLSP $ i $ in reservation option contract
$ h_i $ Option executive price of unit logistics capacity for FLSP $ i $ in reservation option contract
$ n $ The total number of FLSPs
$ p_i $ The market price at which the LSI buys the unit logistics capacity from the FLSP $ i $
$ q $ Option purchase quantity for LSI in option guarantee contract
$ d_{i, 2} $ Satisfaction utility of FLSP $ i $ with the option guarantee in the second stage
$ D $ Demand in the first stage, which subjects to the normal distribution $ D\thicksim N(\mu, \sigma^2) $
$ Q $ The updated demand in the second stage, which subjects to the normal distribution $ (Q\mid\xi)\thicksim N(\mu(\xi), \nu^2) $
$ r $ Option purchase price of unit logistics capacity for LSI in option guarantee contract
$ R $ Option compensation price of unit logistics capacity for LSI in option guarantee contract
$ v_{i, 1} $ In the first stage, profit utility of FLSP $ i $ in reservation option contract
$ v_{i, 2} $ In the second stage, profit utility of FLSP $ i $ in reservation option contract
$ w_{i1} $ The weight of satisfaction utility of FLSP $ i $
$ w_{i2} $ The weight of profit utility of FLSP $ i $
$ x_{i, 1} $ In the first stage, logistics service capacity provided by FLSP $ i $ in reservation option contract
$ x_{i, 2} $ In the second stage, logistics service capacity provided by FLSP $ i $ in reservation option contract
$ y_{i, 1} $ In the first stage, logistics service capacity provided by FLSP $ i $ in option guarantee contract
$ y_{i, 2} $ In the second stage, logistics service capacity provided by FLSP $ i $ in option guarantee contract
$ z_1 $ The total profit of the LSI
$ z_2 $ The total utility of the FLSP
$ \alpha_i $ Advantage unfair coefficient of FLSP $ i $
$ \beta_i $ Disadvantage unfair coefficient of FLSP $ i $
$ \lambda $ Unit logistics capacity income
$ \xi $ Based on the demanded sample information collected in the lead time, the estimated mean of the demand (Estimated Demand Average)
$ \tau(t) $ Demand forecast error, reflecting the degree of deviation between demand forecast and the actual needs
$ \theta_i^- $ Minimum logistics capacity provided by FLSP $ i $
$ \theta_i^+ $ Maximum logistics capacity provided by FLSP $ i $
$ \eta $ Compensation threshold in option guarantee
$ TP $ Compensation threshold in option guarantee
$ \Delta LSI $ Change ratio in profit of LSI
$ \Delta FLSP $ Change ratio in profit of FLSP
$ \Delta TP $ Change ratio in total performance of supply chain
Table 3.  Parameter seeting
FLSP $ p_i $ $ c_i $ $ e_i $ $ h_i $ $ [\theta_i^-, \theta_i^+] $ $ w_{i1} $ $ w_{i2} $ $ r_i $ $ d_{i, 0} $
$ A_1 $ 24 8 10 16 [15,24] 0.6 0.4 0.5 0.3
$ A_2 $ 15 5 6 10 [20,35] 0.6 0.4 0.4 0.35
$ A_3 $ 26 9 11 17 [25,45] 0.7 0.3 0.6 0.35
Note: (i) According to the Assumption1, if $ \xi>\mu $, we set $ \xi = 120 $. If $ \xi<\mu $, we set $ \xi = 80 $. (ii) in this paper, the demand $ D $ before updating is a signal, the LSI would update the information and accordingly estimate the mean value as $ \xi $. Therefore, the estimated value is effected by the updated information, because the actual demand often changes fiercely, the $ \xi $ may be much larger or smaller $ \mu $.
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FLSP $ p_i $ $ c_i $ $ e_i $ $ h_i $ $ [\theta_i^-, \theta_i^+] $ $ w_{i1} $ $ w_{i2} $ $ r_i $ $ d_{i, 0} $
$ A_1 $ 24 8 10 16 [15,24] 0.6 0.4 0.5 0.3
$ A_2 $ 15 5 6 10 [20,35] 0.6 0.4 0.4 0.35
$ A_3 $ 26 9 11 17 [25,45] 0.7 0.3 0.6 0.35
Note: (i) According to the Assumption1, if $ \xi>\mu $, we set $ \xi = 120 $. If $ \xi<\mu $, we set $ \xi = 80 $. (ii) in this paper, the demand $ D $ before updating is a signal, the LSI would update the information and accordingly estimate the mean value as $ \xi $. Therefore, the estimated value is effected by the updated information, because the actual demand often changes fiercely, the $ \xi $ may be much larger or smaller $ \mu $.
Table 4.  Summary of parameter influence laws
Dependent variable Independent variable
Demand update time $ t $ Difference of the fairness Preference among the FLSPs
$ \xi<\mu $ $ \xi>\mu $ $ \xi<\mu $ $ \xi>\mu $
Model 1
reservation option		 Utility of LSI $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \nearrow $ $ \nearrow $
Utility of FLSPs $ \nearrow \longrightarrow $ $ \searrow \longrightarrow $ $ \searrow $ $ \searrow $
Total performance $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \nearrow $ $ \nearrow $
Model 2
Option derivatives		 Utility of LSI $ \uparrow \searrow \longrightarrow $ $ \uparrow \searrow \longrightarrow $ $ \rightarrow $ $ \rightarrow $
Utility of FLSPs $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \searrow $ $ \searrow $
Total performance $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \searrow $ $ \searrow $
Note: $ \nearrow $ indicates with the increase of independent variable, the value of dependent variable will increase, $ \searrow $ indicates with the increase of independent variable, the value of dependent variable will decrease, $ \longrightarrow $ indicates with the increase of independent variable, the value of dependent variable unchanged, $ \uparrow $ indicates with the increase of independent variable, the value of dependent variable will increase suddenly.
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Dependent variable Independent variable
Demand update time $ t $ Difference of the fairness Preference among the FLSPs
$ \xi<\mu $ $ \xi>\mu $ $ \xi<\mu $ $ \xi>\mu $
Model 1
reservation option		 Utility of LSI $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \nearrow $ $ \nearrow $
Utility of FLSPs $ \nearrow \longrightarrow $ $ \searrow \longrightarrow $ $ \searrow $ $ \searrow $
Total performance $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \nearrow $ $ \nearrow $
Model 2
Option derivatives		 Utility of LSI $ \uparrow \searrow \longrightarrow $ $ \uparrow \searrow \longrightarrow $ $ \rightarrow $ $ \rightarrow $
Utility of FLSPs $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \searrow $ $ \searrow $
Total performance $ \searrow \longrightarrow $ $ \nearrow \longrightarrow $ $ \searrow $ $ \searrow $
Note: $ \nearrow $ indicates with the increase of independent variable, the value of dependent variable will increase, $ \searrow $ indicates with the increase of independent variable, the value of dependent variable will decrease, $ \longrightarrow $ indicates with the increase of independent variable, the value of dependent variable unchanged, $ \uparrow $ indicates with the increase of independent variable, the value of dependent variable will increase suddenly.
Table 5.  Application conditions that option can reduce the impact on allocation of inequity aversion
$ \xi<\mu $ Options stype Inequity aversion difference is small Inequity aversion difference is large
$ \Delta\Pi_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $ $ \Delta\Pi_{LSI}^{1-3} $ $ \Delta\ U_{FLSPI}^{1-3} $ $ \Delta\ TP^{1-3} $
Option1 $ Y $ $ Y $ $ Y^* $ $ Y $ $ Y $ $ Y^* $
Option2 $ Y^* $ $ Y^* $ $ Y $ $ Y^* $ $ Y^* $ $ Y $
$ \xi>\mu $ Option1 $ N $ $ Y $ $ Y $ $ N $ $ Y $ $ N $
Option2 $ Y $ $ Y^* $ $ N $ $ Y $ $ Y^* $ $ Y $
Note: $ Y $ indicates that the option contract can weaken the impact of the inequity aversion; $ Y^* $ indicates that the weakening effect is better; $ N $ indicates that option contract cannot diminish the impact of the inequity aversion.
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$ \xi<\mu $ Options stype Inequity aversion difference is small Inequity aversion difference is large
$ \Delta\Pi_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $ $ \Delta\Pi_{LSI}^{1-3} $ $ \Delta\ U_{FLSPI}^{1-3} $ $ \Delta\ TP^{1-3} $
Option1 $ Y $ $ Y $ $ Y^* $ $ Y $ $ Y $ $ Y^* $
Option2 $ Y^* $ $ Y^* $ $ Y $ $ Y^* $ $ Y^* $ $ Y $
$ \xi>\mu $ Option1 $ N $ $ Y $ $ Y $ $ N $ $ Y $ $ N $
Option2 $ Y $ $ Y^* $ $ N $ $ Y $ $ Y^* $ $ Y $
Note: $ Y $ indicates that the option contract can weaken the impact of the inequity aversion; $ Y^* $ indicates that the weakening effect is better; $ N $ indicates that option contract cannot diminish the impact of the inequity aversion.
Table 6.  Allocation data of none option contract ([26])
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
10 528.280 564.390 641.890 0.305 0.306 0.292 0.191 0.188 0.182
15 561.290 596.290 676.780 0.344 0.340 0.319 0.217 0.214 0.207
20 604.580 642.280 748.980 0.356 0.355 0.347 0.224 0.222 0.215
25 621.360 660.270 746.250 0.362 0.359 0.351 0.228 0.225 0.218
30 628.930 668.260 752.570 0.364 0.359 0.354 0.229 0.225 0.219
35 631.240 671.020 753.180 0.364 0.359 0.354 0.229 0.225 0.219
40 631.240 671.850 754.020 0.364 0.363 0.354 0.229 0.225 0.219
45 631.240 671.980 754.380 0.364 0.363 0.354 0.229 0.227 0.219
50 632.240 672.980 755.380 0.364 0.363 0.354 0.229 0.227 0.219
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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
10 528.280 564.390 641.890 0.305 0.306 0.292 0.191 0.188 0.182
15 561.290 596.290 676.780 0.344 0.340 0.319 0.217 0.214 0.207
20 604.580 642.280 748.980 0.356 0.355 0.347 0.224 0.222 0.215
25 621.360 660.270 746.250 0.362 0.359 0.351 0.228 0.225 0.218
30 628.930 668.260 752.570 0.364 0.359 0.354 0.229 0.225 0.219
35 631.240 671.020 753.180 0.364 0.359 0.354 0.229 0.225 0.219
40 631.240 671.850 754.020 0.364 0.363 0.354 0.229 0.225 0.219
45 631.240 671.980 754.380 0.364 0.363 0.354 0.229 0.227 0.219
50 632.240 672.980 755.380 0.364 0.363 0.354 0.229 0.227 0.219
Table 7.  Allocation data of option1 (reservation option contract)
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 5212.604 5214.035 5219.711 0.390 0.390 0.390 0.999 1.000 1.000
10 4989.574 4991.008 4996.698 0.385 0.384 0.384 0.999 1.000 1.000
15 4820.468 4821.904 4827.605 0.380 0.380 0.380 0.999 0.999 1.000
20 4731.125 4732.563 4738.269 0.378 0.378 0.378 0.999 0.999 1.000
25 4692.747 4694.186 4699.894 0.377 0.377 0.377 0.999 0.999 1.000
30 4677.743 4679.182 4684.891 0.376 0.376 0.376 0.999 0.999 1.000
35 4672.095 4673.534 4679.243 0.376 0.376 0.376 0.999 0.999 1.000
40 4669.999 4671.438 4677.148 0.376 0.376 0.376 0.999 0.999 1.000
45 4669.226 4670.665 4676.374 0.376 0.376 0.376 0.999 0.999 1.000
50 4668.941 4670.380 4676.090 0.376 0.376 0.376 0.999 0.999 1.000
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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 5212.604 5214.035 5219.711 0.390 0.390 0.390 0.999 1.000 1.000
10 4989.574 4991.008 4996.698 0.385 0.384 0.384 0.999 1.000 1.000
15 4820.468 4821.904 4827.605 0.380 0.380 0.380 0.999 0.999 1.000
20 4731.125 4732.563 4738.269 0.378 0.378 0.378 0.999 0.999 1.000
25 4692.747 4694.186 4699.894 0.377 0.377 0.377 0.999 0.999 1.000
30 4677.743 4679.182 4684.891 0.376 0.376 0.376 0.999 0.999 1.000
35 4672.095 4673.534 4679.243 0.376 0.376 0.376 0.999 0.999 1.000
40 4669.999 4671.438 4677.148 0.376 0.376 0.376 0.999 0.999 1.000
45 4669.226 4670.665 4676.374 0.376 0.376 0.376 0.999 0.999 1.000
50 4668.941 4670.380 4676.090 0.376 0.376 0.376 0.999 0.999 1.000
Table 8.  Allocation data of option2 (option guarantee contract)
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 3513.128 3513.128 3513.127 1.423 1.423 1.422 0.994 0.995 0.996
10 4473.498 4473.498 4473.498 1.422 1.422 1.422 0.992 0.994 0.995
15 4533.986 4533.986 4533.986 1.422 1.422 1.422 0.991 0.994 0.995
20 4458.996 4458.996 4458.996 1.422 1.422 1.422 0.991 0.993 0.994
25 4426.783 4426.783 4426.783 1.422 1.422 1.421 0.991 0.993 0.994
30 4414.189 4414.189 4414.189 1.422 1.422 1.421 0.991 0.993 0.994
35 4409.448 4409.448 4409.448 1.422 1.422 1.421 0.991 0.993 0.994
40 4407.690 4407.690 4407.689 1.422 1.422 1.421 0.991 0.993 0.994
45 4407.040 4407.040 4407.040 1.422 1.422 1.421 0.991 0.993 0.994
50 4406.801 4406.801 4406.801 1.422 1.422 1.421 0.991 0.993 0.994
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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 3513.128 3513.128 3513.127 1.423 1.423 1.422 0.994 0.995 0.996
10 4473.498 4473.498 4473.498 1.422 1.422 1.422 0.992 0.994 0.995
15 4533.986 4533.986 4533.986 1.422 1.422 1.422 0.991 0.994 0.995
20 4458.996 4458.996 4458.996 1.422 1.422 1.422 0.991 0.993 0.994
25 4426.783 4426.783 4426.783 1.422 1.422 1.421 0.991 0.993 0.994
30 4414.189 4414.189 4414.189 1.422 1.422 1.421 0.991 0.993 0.994
35 4409.448 4409.448 4409.448 1.422 1.422 1.421 0.991 0.993 0.994
40 4407.690 4407.690 4407.689 1.422 1.422 1.421 0.991 0.993 0.994
45 4407.040 4407.040 4407.040 1.422 1.422 1.421 0.991 0.993 0.994
50 4406.801 4406.801 4406.801 1.422 1.422 1.421 0.991 0.993 0.994
Table 9.  Changes in order allocation when inequity aversion difference is small
t $ \Delta\prod_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 6.835$ \% $ 0.029$ \% $ 0.000$ \% $ 1.553$ \% $ 0.019$ \% $ 0.005$ \% $ 0.624$ \% $ 0.012$ \% $ 0.254$ \% $
15 6.236$ \% $ 0.030$ \% $ 0.000$ \% $ 1.553$ \% $ 0.020$ \% $ 0.005$ \% $ 1.279$ \% $ 0.013$ \% $ 0.264$ \% $
20 6.236$ \% $ 0.030$ \% $ 0.000$ \% $ 1.213$ \% $ 0.021$ \% $ 0.005$ \% $ 0.449$ \% $ 0.013$ \% $ 0.238$ \% $
25 6.262$ \% $ 0.031$ \% $ 0.000$ \% $ 1.413$ \% $ 0.021$ \% $ 0.005$ \% $ 0.750$ \% $ 0.013$ \% $ 0.226$ \% $
30 6.253$ \% $ 0.031$ \% $ 0.000$ \% $ 1.625$ \% $ 0.021$ \% $ 0.005$ \% $ 1.442$ \% $ 0.013$ \% $ 0.232$ \% $
35 6.302$ \% $ 0.031$ \% $ 0.000$ \% $ 1.848$ \% $ 0.021$ \% $ 0.005$ \% $ 1.442$ \% $ 0.013$ \% $ 0.230$ \% $
40 6.433$ \% $ 0.031$ \% $ 0.000$ \% $ 1.848$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.232$ \% $
45 6.454$ \% $ 0.031$ \% $ 0.000$ \% $ 0.909$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.234$ \% $
50 6.444$ \% $ 0.031$ \% $ 0.000$ \% $ 0.909$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.225$ \% $
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t $ \Delta\prod_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 6.835$ \% $ 0.029$ \% $ 0.000$ \% $ 1.553$ \% $ 0.019$ \% $ 0.005$ \% $ 0.624$ \% $ 0.012$ \% $ 0.254$ \% $
15 6.236$ \% $ 0.030$ \% $ 0.000$ \% $ 1.553$ \% $ 0.020$ \% $ 0.005$ \% $ 1.279$ \% $ 0.013$ \% $ 0.264$ \% $
20 6.236$ \% $ 0.030$ \% $ 0.000$ \% $ 1.213$ \% $ 0.021$ \% $ 0.005$ \% $ 0.449$ \% $ 0.013$ \% $ 0.238$ \% $
25 6.262$ \% $ 0.031$ \% $ 0.000$ \% $ 1.413$ \% $ 0.021$ \% $ 0.005$ \% $ 0.750$ \% $ 0.013$ \% $ 0.226$ \% $
30 6.253$ \% $ 0.031$ \% $ 0.000$ \% $ 1.625$ \% $ 0.021$ \% $ 0.005$ \% $ 1.442$ \% $ 0.013$ \% $ 0.232$ \% $
35 6.302$ \% $ 0.031$ \% $ 0.000$ \% $ 1.848$ \% $ 0.021$ \% $ 0.005$ \% $ 1.442$ \% $ 0.013$ \% $ 0.230$ \% $
40 6.433$ \% $ 0.031$ \% $ 0.000$ \% $ 1.848$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.232$ \% $
45 6.454$ \% $ 0.031$ \% $ 0.000$ \% $ 0.909$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.234$ \% $
50 6.444$ \% $ 0.031$ \% $ 0.000$ \% $ 0.909$ \% $ 0.021$ \% $ 0.005$ \% $ 0.371$ \% $ 0.013$ \% $ 0.225$ \% $
Table 10.  Changes in order allocation when inequity aversion difference is large
t $ \Delta\prod_{LSI}^{1-3} $ $ \Delta U_{FLSP}^{1-3} $ $ \Delta TP^{1-3} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 21.506$ \% $ 0.143$ \% $ 0.000$ \% $ 4.643$ \% $ 0.078$ \% $ 0.023$ \% $ 4.007$ \% $ 0.062$ \% $ 0.348$ \% $
15 20.576$ \% $ 0.148$ \% $ 0.000$ \% $ 4.484$ \% $ 0.085$ \% $ 0.023$ \% $ 7.386$ \% $ 0.064$ \% $ 0.363$ \% $
20 23.884$ \% $ 0.151$ \% $ 0.000$ \% $ 4.017$ \% $ 0.088$ \% $ 0.023$ \% $ 2.570$ \% $ 0.065$ \% $ 0.350$ \% $
25 20.099$ \% $ 0.152$ \% $ 0.000$ \% $ 4.295$ \% $ 0.090$ \% $ 0.023$ \% $ 2.774$ \% $ 0.066$ \% $ 0.343$ \% $
30 19.659$ \% $ 0.153$ \% $ 0.000$ \% $ 4.356$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.348$ \% $
35 19.318$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.349$ \% $
40 19.451$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
45 19.508$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
50 19.477$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
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t $ \Delta\prod_{LSI}^{1-3} $ $ \Delta U_{FLSP}^{1-3} $ $ \Delta TP^{1-3} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 21.506$ \% $ 0.143$ \% $ 0.000$ \% $ 4.643$ \% $ 0.078$ \% $ 0.023$ \% $ 4.007$ \% $ 0.062$ \% $ 0.348$ \% $
15 20.576$ \% $ 0.148$ \% $ 0.000$ \% $ 4.484$ \% $ 0.085$ \% $ 0.023$ \% $ 7.386$ \% $ 0.064$ \% $ 0.363$ \% $
20 23.884$ \% $ 0.151$ \% $ 0.000$ \% $ 4.017$ \% $ 0.088$ \% $ 0.023$ \% $ 2.570$ \% $ 0.065$ \% $ 0.350$ \% $
25 20.099$ \% $ 0.152$ \% $ 0.000$ \% $ 4.295$ \% $ 0.090$ \% $ 0.023$ \% $ 2.774$ \% $ 0.066$ \% $ 0.343$ \% $
30 19.659$ \% $ 0.153$ \% $ 0.000$ \% $ 4.356$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.348$ \% $
35 19.318$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.349$ \% $
40 19.451$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
45 19.508$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
50 19.477$ \% $ 0.153$ \% $ 0.000$ \% $ 4.573$ \% $ 0.091$ \% $ 0.023$ \% $ 2.791$ \% $ 0.066$ \% $ 0.350$ \% $
Table 11.  Allocation data of none option contract ([26])
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
10 5043.467 5042.428 4890.278 0.141 0.148 0.137 0.505 0.505 0.505
15 5208.289 5190.688 5212.365 0.268 0.267 0.272 0.734 0.734 0.734
20 5305.389 5306.389 5304.389 0.297 0.296 0.291 0.786 0.786 0.786
25 5321.357 5320.357 5325.357 0.311 0.314 0.320 0.804 0.804 0.803
30 5322.357 5321.357 5326.357 0.319 0.325 0.319 0.807 0.806 0.806
35 5323.357 5322.357 5327.357 0.326 0.327 0.327 0.807 0.807 0.807
40 5324.357 5323.357 5328.357 0.328 0.328 0.327 0.807 0.807 0.807
45 5325.357 5324.357 5329.357 0.328 0.328 0.328 0.807 0.807 0.807
50 5326.357 5325.357 5330.357 0.328 0.328 0.328 0.807 0.807 0.807
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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
10 5043.467 5042.428 4890.278 0.141 0.148 0.137 0.505 0.505 0.505
15 5208.289 5190.688 5212.365 0.268 0.267 0.272 0.734 0.734 0.734
20 5305.389 5306.389 5304.389 0.297 0.296 0.291 0.786 0.786 0.786
25 5321.357 5320.357 5325.357 0.311 0.314 0.320 0.804 0.804 0.803
30 5322.357 5321.357 5326.357 0.319 0.325 0.319 0.807 0.806 0.806
35 5323.357 5322.357 5327.357 0.326 0.327 0.327 0.807 0.807 0.807
40 5324.357 5323.357 5328.357 0.328 0.328 0.327 0.807 0.807 0.807
45 5325.357 5324.357 5329.357 0.328 0.328 0.328 0.807 0.807 0.807
50 5326.357 5325.357 5330.357 0.328 0.328 0.328 0.807 0.807 0.807
Table 12.  Allocation data of option1 (reservation option contract)
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 5951.744 5953.379 5959.872 0.410 0.410 0.410 0.999 1.000 1.000
10 6174.774 6176.406 6182.885 0.417 0.416 0.416 1.000 1.000 1.000
15 6343.880 6345.510 6351.978 0.421 0.421 0.421 1.000 1.000 1.000
20 6433.223 6434.851 6441.314 0.424 0.424 0.424 1.000 1.000 1.000
25 6471.601 6473.229 6479.689 0.425 0.425 0.425 1.000 1.000 1.000
30 6486.605 6488.233 6494.693 0.425 0.425 0.425 1.000 1.000 1.000
35 6492.253 6493.880 6500.340 0.425 0.425 0.425 1.000 1.000 1.000
40 6494.349 6495.976 6502.435 0.426 0.425 0.425 1.000 1.000 1.000
45 6495.122 6496.749 6503.209 0.426 0.426 0.425 1.000 1.000 1.000
50 6495.407 6497.034 6503.493 0.426 0.426 0.425 1.000 1.000 1.000
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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 5951.744 5953.379 5959.872 0.410 0.410 0.410 0.999 1.000 1.000
10 6174.774 6176.406 6182.885 0.417 0.416 0.416 1.000 1.000 1.000
15 6343.880 6345.510 6351.978 0.421 0.421 0.421 1.000 1.000 1.000
20 6433.223 6434.851 6441.314 0.424 0.424 0.424 1.000 1.000 1.000
25 6471.601 6473.229 6479.689 0.425 0.425 0.425 1.000 1.000 1.000
30 6486.605 6488.233 6494.693 0.425 0.425 0.425 1.000 1.000 1.000
35 6492.253 6493.880 6500.340 0.425 0.425 0.425 1.000 1.000 1.000
40 6494.349 6495.976 6502.435 0.426 0.425 0.425 1.000 1.000 1.000
45 6495.122 6496.749 6503.209 0.426 0.426 0.425 1.000 1.000 1.000
50 6495.407 6497.034 6503.493 0.426 0.426 0.425 1.000 1.000 1.000
Table 13.  Allocation data of option2 (option guarantee contract)
t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 4123.226 4123.226 4123.226 1.424 1.424 1.423 0.999 0.999 0.999
10 5441.720 5441.720 5441.720 1.424 1.424 1.424 0.999 0.999 0.999
15 5775.426 5775.426 5775.426 1.424 1.424 1.424 1.000 1.000 1.000
20 5845.852 5845.852 5845.852 1.425 1.424 1.424 1.000 1.000 1.000
25 5876.104 5876.104 5876.104 1.425 1.425 1.424 1.000 1.000 1.000
30 5887.931 5887.931 5887.931 1.425 1.425 1.424 1.000 1.000 1.000
35 5892.383 5892.383 5892.383 1.425 1.425 1.424 1.000 1.000 1.000
40 5894.035 5894.035 5894.035 1.425 1.425 1.424 1.000 1.000 1.000
45 5894.645 5894.645 5894.645 1.425 1.425 1.424 1.000 1.000 1.000
50 5894.869 5894.869 5894.869 1.425 1.425 1.424 1.000 1.000 1.000
Table Options

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t $ \prod_{LSI} $ $ U_{FLSP} $ $ TP $
Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3 Scenario1 Scenario2 Scenario3
5 4123.226 4123.226 4123.226 1.424 1.424 1.423 0.999 0.999 0.999
10 5441.720 5441.720 5441.720 1.424 1.424 1.424 0.999 0.999 0.999
15 5775.426 5775.426 5775.426 1.424 1.424 1.424 1.000 1.000 1.000
20 5845.852 5845.852 5845.852 1.425 1.424 1.424 1.000 1.000 1.000
25 5876.104 5876.104 5876.104 1.425 1.425 1.424 1.000 1.000 1.000
30 5887.931 5887.931 5887.931 1.425 1.425 1.424 1.000 1.000 1.000
35 5892.383 5892.383 5892.383 1.425 1.425 1.424 1.000 1.000 1.000
40 5894.035 5894.035 5894.035 1.425 1.425 1.424 1.000 1.000 1.000
45 5894.645 5894.645 5894.645 1.425 1.425 1.424 1.000 1.000 1.000
50 5894.869 5894.869 5894.869 1.425 1.425 1.424 1.000 1.000 1.000
Table 14.  Changes in order allocation when inequity aversion difference is small
t $ \Delta\prod_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 0.020$ \% $ 0.027$ \% $ 0.000$ \% $ 4.977$ \% $ 0.010$ \% $ 0.007$ \% $ 0.020$ \% $ 0.010$ \% $ 0.066$ \% $
15 0.021$ \% $ 0.026$ \% $ 0.000$ \% $ 0.234$ \% $ 0.009$ \% $ 0.006$ \% $ 0.060$ \% $ 0.010$ \% $ 0.034$ \% $
20 0.024$ \% $ 0.026$ \% $ 0.000$ \% $ 0.448$ \% $ 0.008$ \% $ 0.004$ \% $ 0.013$ \% $ 0.009$ \% $ 0.014$ \% $
25 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.964$ \% $ 0.008$ \% $ 0.003$ \% $ 0.025$ \% $ 0.009$ \% $ 0.005$ \% $
30 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 1.970$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.002$ \% $
35 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.233$ \% $ 0.008$ \% $ 0.002$ \% $ 0.015$ \% $ 0.009$ \% $ 0.001$ \% $
40 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.153$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
45 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.139$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
50 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.128$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
Table Options

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t $ \Delta\prod_{LSI}^{1-2} $ $ \Delta U_{FLSP}^{1-2} $ $ \Delta TP^{1-2} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 0.020$ \% $ 0.027$ \% $ 0.000$ \% $ 4.977$ \% $ 0.010$ \% $ 0.007$ \% $ 0.020$ \% $ 0.010$ \% $ 0.066$ \% $
15 0.021$ \% $ 0.026$ \% $ 0.000$ \% $ 0.234$ \% $ 0.009$ \% $ 0.006$ \% $ 0.060$ \% $ 0.010$ \% $ 0.034$ \% $
20 0.024$ \% $ 0.026$ \% $ 0.000$ \% $ 0.448$ \% $ 0.008$ \% $ 0.004$ \% $ 0.013$ \% $ 0.009$ \% $ 0.014$ \% $
25 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.964$ \% $ 0.008$ \% $ 0.003$ \% $ 0.025$ \% $ 0.009$ \% $ 0.005$ \% $
30 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 1.970$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.002$ \% $
35 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.233$ \% $ 0.008$ \% $ 0.002$ \% $ 0.015$ \% $ 0.009$ \% $ 0.001$ \% $
40 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.153$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
45 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.139$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
50 0.019$ \% $ 0.025$ \% $ 0.000$ \% $ 0.128$ \% $ 0.008$ \% $ 0.002$ \% $ 0.011$ \% $ 0.009$ \% $ 0.000$ \% $
Table 15.  Changes in order allocation when inequity aversion difference is large
t $ \Delta\prod_{LSI}^{1-3} $ $ \Delta U_{FLSP}^{1-3} $ $ \Delta TP^{1-3} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 0.037$ \% $ 0.131$ \% $ 0.000$ \% $ 2.841$ \% $ 0.037$ \% $ 0.036$ \% $ 0.040$ \% $ 0.049$ \% $ 0.000$ \% $
15 0.078$ \% $ 0.127$ \% $ 0.000$ \% $ 1.593$ \% $ 0.031$ \% $ 0.029$ \% $ 0.046$ \% $ 0.048$ \% $ 0.000$ \% $
20 0.019$ \% $ 0.126$ \% $ 0.000$ \% $ 2.087$ \% $ 0.028$ \% $ 0.018$ \% $ 0.045$ \% $ 0.047$ \% $ 0.000$ \% $
25 0.075$ \% $ 0.125$ \% $ 0.000$ \% $ 2.785$ \% $ 0.026$ \% $ 0.013$ \% $ 0.037$ \% $ 0.046$ \% $ 0.000$ \% $
30 0.075$ \% $ 0.125$ \% $ 0.000$ \% $ 0.199$ \% $ 0.026$ \% $ 0.011$ \% $ 0.010$ \% $ 0.046$ \% $ 0.000$ \% $
35 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.156$ \% $ 0.026$ \% $ 0.011$ \% $ 0.011$ \% $ 0.046$ \% $ 0.000$ \% $
40 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.109$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
45 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.106$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
50 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.106$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
Table Options

Download as excel

t $ \Delta\prod_{LSI}^{1-3} $ $ \Delta U_{FLSP}^{1-3} $ $ \Delta TP^{1-3} $
None option Option1 Option2 None option Option1 Option2 None option Option1 Option2
10 0.037$ \% $ 0.131$ \% $ 0.000$ \% $ 2.841$ \% $ 0.037$ \% $ 0.036$ \% $ 0.040$ \% $ 0.049$ \% $ 0.000$ \% $
15 0.078$ \% $ 0.127$ \% $ 0.000$ \% $ 1.593$ \% $ 0.031$ \% $ 0.029$ \% $ 0.046$ \% $ 0.048$ \% $ 0.000$ \% $
20 0.019$ \% $ 0.126$ \% $ 0.000$ \% $ 2.087$ \% $ 0.028$ \% $ 0.018$ \% $ 0.045$ \% $ 0.047$ \% $ 0.000$ \% $
25 0.075$ \% $ 0.125$ \% $ 0.000$ \% $ 2.785$ \% $ 0.026$ \% $ 0.013$ \% $ 0.037$ \% $ 0.046$ \% $ 0.000$ \% $
30 0.075$ \% $ 0.125$ \% $ 0.000$ \% $ 0.199$ \% $ 0.026$ \% $ 0.011$ \% $ 0.010$ \% $ 0.046$ \% $ 0.000$ \% $
35 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.156$ \% $ 0.026$ \% $ 0.011$ \% $ 0.011$ \% $ 0.046$ \% $ 0.000$ \% $
40 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.109$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
45 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.106$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
50 0.075$ \% $ 0.124$ \% $ 0.000$ \% $ 0.106$ \% $ 0.026$ \% $ 0.010$ \% $ 0.006$ \% $ 0.046$ \% $ 0.000$ \% $
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