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; Jingkun Wang

doi:10.3934/jimo.2020118

Article Contents

2021, Volume 17, Issue 6: 3269-3295. Doi: 10.3934/jimo.2020118

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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

^* Corresponding author
^* Corresponding author

^** Co-Corresponding author

Received: July 31, 2019

Revised: December 31, 2019

Early access: June 2020

Published: November 2021

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Abstract

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.

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Mathematics Subject Classification: 91A05, 90C29.

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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 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	$ \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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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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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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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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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
	Options stype	$ \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 $
$ \xi>\mu $	*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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Table 6. Allocation data of none option contract ([26])

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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Table 7. Allocation data of option1 (reservation option contract)

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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Table 8. Allocation data of option2 (option guarantee contract)

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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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} $
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$ \% $

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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} $
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$ \% $

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Table 11. Allocation data of none option contract ([26])

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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Table 12. Allocation data of option1 (reservation option contract)

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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Table 13. Allocation data of option2 (option guarantee contract)

t	$ \prod_{LSI} $			$ U_{FLSP} $			$ TP $
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

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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} $
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$ \% $

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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} $
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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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.