Figure 1(a).
Utility of the LSI when $ \xi<\mu $
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Channel leadership and recycling channel in closed-loop supply chain: The case of recycling price by the recycling party
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
College of Management and Economics, Tianjin University, No.92, Weijin Road, Nankai District, Tianjin, 300072, China |
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 and 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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
| [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. |
Figure 1(b).
Utility of the LSI when $ \xi>\mu $
Figure 2(a).
Utility of the FLSPs when $ \xi<\mu $
Figure 2(b).
Utility of the FLSPs when $ \xi>\mu $
Figure 3(a).
Total performance when $ \xi<\mu $
Figure 3(b).
Total performance when $ \xi>\mu $
Figure 4(a).
Utility of the LSI when $ \xi<\mu $
Figure 4(b).
Utility of the LSI when $ \xi>\mu $
Figure 5(a).
Utility of FLSPs when $ \xi<\mu $
Figure 5(b).
Utility of FLSPs when $ \xi>\mu $
Figure 6(a).
Total performance when $ \xi<\mu $
Figure 6(b).
Total performance when $ \xi>\mu $
Figure 7(a).
$ \Delta\Pi_{LSI}^{1-2} $ in the case of decreased demand
Figure 7(b).
$ \Delta \Pi_{LSI}^{1-3} $ in the case of decreased demand
Figure 8(a).
$ \Delta U_{FLSP}^{1-2} $ in the case of decreased demand
Figure 8(b).
$ \Delta U_{FLSP}^{1-3} $ in the case of decreased demand
Figure 9(a).
$ \Delta TP^{1-2} $ in the case of decreased demand
Figure 9(b).
$ \Delta TP^{1-3} $ in the case of decreased demand
Figure 10(a).
$ \Delta\Pi_{LSI}^{1-2} $ in the case of increased demand
Figure 10(b).
$ \Delta\Pi_{LSI}^{1-3} $ in the case of increased demand
Figure 11(a).
$ \Delta\Pi_{FLSP}^{1-2} $ in the case of increased demand
Figure 11(b).
$ \Delta\Pi_{FLSP}^{1-3} $ in the case of increased demand
Figure 12(a).
$ \Delta TP^{1-2} $ in the case of increased demand
Figure 12(b).
$ \Delta TP^{1-3} $ in the case of increased demand
Table 1.
The differences between the relevant literatures and this paper
| Research content | [21] | [26] | [6] | This paper |
| Supply chain structure | A 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 | ||||
| Option types | Reservation option | Derivative option | Reservation option and derivative option | |
| Fairness concern is considered | ||||
| 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 |
| Research content | [21] | [26] | [6] | This paper |
| Supply chain structure | A 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 | ||||
| Option types | Reservation option | Derivative option | Reservation option and derivative option | |
| Fairness concern is considered | ||||
| 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 |
| Opportunity cost of FLSP |
|
| Demand updating cost of LSI | |
| The cost of unit logistics capacity for FLSP |
|
| Initial utility of FLSP |
|
| Satisfaction utility of FLSP |
|
| Satisfaction utility of FLSP |
|
| Demand in the first stage, which subjects to the normal distribution |
|
| Option purchase price of unit logistics capacity for FLSP |
|
| Option executive price of unit logistics capacity for FLSP |
|
| The total number of FLSPs | |
| The market price at which the LSI buys the unit logistics capacity from the FLSP |
|
| Option purchase quantity for LSI in option guarantee contract | |
| Satisfaction utility of FLSP |
|
| Demand in the first stage, which subjects to the normal distribution |
|
| The updated demand in the second stage, which subjects to the normal distribution |
|
| Option purchase price of unit logistics capacity for LSI in option guarantee contract | |
| Option compensation price of unit logistics capacity for LSI in option guarantee contract | |
| In the first stage, profit utility of FLSP |
|
| In the second stage, profit utility of FLSP |
|
| The weight of satisfaction utility of FLSP |
|
| The weight of profit utility of FLSP |
|
| In the first stage, logistics service capacity provided by FLSP |
|
| In the second stage, logistics service capacity provided by FLSP |
|
| In the first stage, logistics service capacity provided by FLSP |
|
| In the second stage, logistics service capacity provided by FLSP |
|
| The total profit of the LSI | |
| The total utility of the FLSP | |
| Advantage unfair coefficient of FLSP |
|
| Disadvantage unfair coefficient of FLSP |
|
| Unit logistics capacity income | |
| Based on the demanded sample information collected in the lead time, the estimated mean of the demand (Estimated Demand Average) | |
| Demand forecast error, reflecting the degree of deviation between demand forecast and the actual needs | |
| Minimum logistics capacity provided by FLSP |
|
| Maximum logistics capacity provided by FLSP |
|
| Compensation threshold in option guarantee | |
| Compensation threshold in option guarantee | |
| Change ratio in profit of LSI | |
| Change ratio in profit of FLSP | |
| Change ratio in total performance of supply chain |
| Notation | Description |
| Opportunity cost of FLSP |
|
| Demand updating cost of LSI | |
| The cost of unit logistics capacity for FLSP |
|
| Initial utility of FLSP |
|
| Satisfaction utility of FLSP |
|
| Satisfaction utility of FLSP |
|
| Demand in the first stage, which subjects to the normal distribution |
|
| Option purchase price of unit logistics capacity for FLSP |
|
| Option executive price of unit logistics capacity for FLSP |
|
| The total number of FLSPs | |
| The market price at which the LSI buys the unit logistics capacity from the FLSP |
|
| Option purchase quantity for LSI in option guarantee contract | |
| Satisfaction utility of FLSP |
|
| Demand in the first stage, which subjects to the normal distribution |
|
| The updated demand in the second stage, which subjects to the normal distribution |
|
| Option purchase price of unit logistics capacity for LSI in option guarantee contract | |
| Option compensation price of unit logistics capacity for LSI in option guarantee contract | |
| In the first stage, profit utility of FLSP |
|
| In the second stage, profit utility of FLSP |
|
| The weight of satisfaction utility of FLSP |
|
| The weight of profit utility of FLSP |
|
| In the first stage, logistics service capacity provided by FLSP |
|
| In the second stage, logistics service capacity provided by FLSP |
|
| In the first stage, logistics service capacity provided by FLSP |
|
| In the second stage, logistics service capacity provided by FLSP |
|
| The total profit of the LSI | |
| The total utility of the FLSP | |
| Advantage unfair coefficient of FLSP |
|
| Disadvantage unfair coefficient of FLSP |
|
| Unit logistics capacity income | |
| Based on the demanded sample information collected in the lead time, the estimated mean of the demand (Estimated Demand Average) | |
| Demand forecast error, reflecting the degree of deviation between demand forecast and the actual needs | |
| Minimum logistics capacity provided by FLSP |
|
| Maximum logistics capacity provided by FLSP |
|
| Compensation threshold in option guarantee | |
| Compensation threshold in option guarantee | |
| Change ratio in profit of LSI | |
| Change ratio in profit of FLSP | |
| Change ratio in total performance of supply chain |
Table 3.
Parameter seeting
| FLSP | |||||||||
| 24 | 8 | 10 | 16 | [15,24] | 0.6 | 0.4 | 0.5 | 0.3 | |
| 15 | 5 | 6 | 10 | [20,35] | 0.6 | 0.4 | 0.4 | 0.35 | |
| 26 | 9 | 11 | 17 | [25,45] | 0.7 | 0.3 | 0.6 | 0.35 | |
| Note: (i) According to the Assumption1, if | |||||||||
| FLSP | |||||||||
| 24 | 8 | 10 | 16 | [15,24] | 0.6 | 0.4 | 0.5 | 0.3 | |
| 15 | 5 | 6 | 10 | [20,35] | 0.6 | 0.4 | 0.4 | 0.35 | |
| 26 | 9 | 11 | 17 | [25,45] | 0.7 | 0.3 | 0.6 | 0.35 | |
| Note: (i) According to the Assumption1, if | |||||||||
Table 4.
Summary of parameter influence laws
| Dependent variable | Independent variable | ||||
| Demand update time |
Difference of the fairness Preference among the FLSPs | ||||
| Model 1 reservation option |
Utility of LSI | ||||
| Utility of FLSPs | |||||
| Total performance | |||||
| Model 2 Option derivatives |
Utility of LSI | ||||
| Utility of FLSPs | |||||
| Total performance | |||||
| Note: | |||||
| Dependent variable | Independent variable | ||||
| Demand update time |
Difference of the fairness Preference among the FLSPs | ||||
| Model 1 reservation option |
Utility of LSI | ||||
| Utility of FLSPs | |||||
| Total performance | |||||
| Model 2 Option derivatives |
Utility of LSI | ||||
| Utility of FLSPs | |||||
| Total performance | |||||
| Note: | |||||
Table 5.
Application conditions that option can reduce the impact on allocation of inequity aversion
| Options stype | Inequity aversion difference is small | Inequity aversion difference is large | |||||
| Option1 | |||||||
| Option2 | |||||||
| Option1 | |||||||
| Option2 | |||||||
| Note: | |||||||
| Options stype | Inequity aversion difference is small | Inequity aversion difference is large | |||||
| Option1 | |||||||
| Option2 | |||||||
| Option1 | |||||||
| Option2 | |||||||
| Note: | |||||||
| t | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 |
| t | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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 | |||||||||
| 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 |
| t | |||||||||
| 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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