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doi: 10.3934/jimo.2020079

## Preserving relational contract stability of fresh agricultural product supply chains

 1 Business School, Hunan Normal University, Changsha 410081, China 2 School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Perth, 6845, Australia

Corresponding author: Honglei Xu

Received  June 2019 Revised  December 2019 Published  April 2020

Since agricultural cooperatives have developed rapidly under the farmland transfer policy in China, they play an important role in the new operation pattern for China's fresh agricultural product supply chains. To enhance current agricultural supply chains' stability, we consider a three-level (farmer-cooperative-retailer) fresh agricultural product supply chain, conduct quantitative analysis of the impact of the quantity flexibility contract, and compare the impact of the relational contract with that of the quantity flexibility contract on the freshness and the profit. Our results show that a suitable relational contract can improve the freshness and increase the profit of the three-level supply chain, but cannot fully guarantee its stability. Furthermore, the government's subsidy policy can improve the relational contract stability of the fresh agricultural product supply chain by providing the protection price contract mechanism of the agricultural product and the cold chain facility subsidy contract.

Citation: Wucheng Zi, Jiayu Zhou, Honglei Xu, Guodong Li, Gang Lin. Preserving relational contract stability of fresh agricultural product supply chains. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020079
##### References:
 [1] J. Blackburn and G. Scudder, Supply chain strategies for perishable products: The case of fresh produce, Produc. Oper. Management, 18 (2009), 129-137.  doi: 10.1111/j.1937-5956.2009.01016.x.  Google Scholar [2] X. Cai, J. Chen, Y. Xiao and X. Xu, Optimization and coordination of fresh product supply chains with freshness-keeping effort, Produc. Oper. Management, 19 (2010), 261-278.  doi: 10.1111/j.1937-5956.2009.01096.x.  Google Scholar [3] J. Chen, Y. W. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, Internat. J. Produc. Res., 55 (2017), 5287-5304.  doi: 10.1080/00207543.2017.1308571.  Google Scholar [4] J. He, X. Cheng, J. He and H. Xu, Cv-CapsNet: Complex-valued capsule network, IEEE Access, 7 (2019), 85492-85499.  doi: 10.1109/ACCESS.2019.2924548.  Google Scholar [5] A. Herbon, E. Levner and T. C. E. Cheng, Perishable inventory management with dynamic pricing using time-temperature indicators linked to automatic detecting devices, Internat. J. Produc. Econ., 147 (2014), 605-613.  doi: 10.1016/j.ijpe.2013.07.021.  Google Scholar [6] S. Hosseiniyekani and M. Zibaei, The choice of feasible commodities for futures trading: A study of Iranian agricultural commodities, African J. Agricultural Res., 4 (2009), 193-199.   Google Scholar [7] Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, Internat. J. Produc. Res., 55 (2016), 202-227.  doi: 10.1080/00207543.2016.1201601.  Google Scholar [8] L. Lin, S. Yang and B. Dan, Three-level supply chain coordination of fresh and live agricultural products by revenue-sharing contracts, J. Systems Engineering, 25 (2010), 484-491.   Google Scholar [9] E. J. Lodree and B. M. Uzochukwu, Production planning for a deteriorating item with stochastic demand and consumer choice, Internat. J. Produc. Econ., 116 (2008), 219-232.  doi: 10.1016/j.ijpe.2008.09.010.  Google Scholar [10] Y. Qin, J. Wang and C. Wei, Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Internat. J. Produc. Econ., 152 (2014), 42-48.  doi: 10.1016/j.ijpe.2014.01.005.  Google Scholar [11] M. Rahdar and A. S. Nookabadi, Coordination mechanism for a deteriorating item in a two-level supply chain system, Appl. Math. Model., 38 (2014), 2884-2900.  doi: 10.1016/j.apm.2013.11.019.  Google Scholar [12] L. Wang and B. Dan, The incentive mechanism for preservation in fresh agricultural supply chain considering consumer utility, J. Industrial Engineering Engineering Management, 29 (2015), 200-206.   Google Scholar [13] Y. B. Xiao, J. Chen and X. Xu, Fresh product supply chain coordination under CIF business model with long distance transportation, Systems Engineering Theory Practice, 28 (2008), 19-34.  doi: 10.1016/S1874-8651(09)60009-0.  Google Scholar [14] X. Xie, X. Liu and H. Xu, Synchronization of delayed coupled switched neural networks: Mode-dependent average impulsive interval, Neurocomputing, 365 (2019), 261-272.  doi: 10.1016/j.neucom.2019.07.045.  Google Scholar [15] X. Xie, H. Xu and X. Cheng, Improved results on exponential stability of discrete-time switched delay systems, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 199-208.  doi: 10.3934/dcdsb.2017010.  Google Scholar [16] F. Xiong, J. Peng, P. Jin, X. Zhang and Y. Qiu, The impact of relational contracts stability about fresh agricultural product supply chain study: From the persepective of cold chain facilities subsidy mode, Chinese J. Management Science, 23 (2015), 102-111.   Google Scholar [17] H. Xu, Y. Zhang, J. Yang, G. Zhou and L. Caccetta, Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria, J. Global Optim., 65 (2016), 109-118.  doi: 10.1007/s10898-015-0339-7.  Google Scholar [18] Y. Yang, T. Fan and L. Zhang, Coordination of fresh agricultural supply chain with asymmetric freshness information, Chinese J. Management Science, 24 (2016), 147-155.   Google Scholar [19] A. Zaheer and N. Venkatraman, Relational governance as an interorganizational strategy: An empirical test of the role of trust in economic exchange, Strategic Management J., 16 (1995), 373-392.  doi: 10.1002/smj.4250160504.  Google Scholar [20] C. Zhang, W. Liu and J. Lai, A model of relational contract of farm produce supply chain based on GNBS $&$ formal fixed price contract, Chinese J. Management Science, 17 (2009), 94-101.   Google Scholar [21] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49.  doi: 10.1016/j.omega.2015.03.004.  Google Scholar [22] X. Zhao and F. Wu, Coordination of agri-food chain with revenue-sharing contract under stochastic output and stochastic demand, Asia-Pac. J. Oper. Res., 28 (2011), 487-510.  doi: 10.1142/S021759591100320X.  Google Scholar [23] S. Zheng, L. Chen and W. Zhuo, Research on the stability of contract relationship among company,cooperative and farmer, J. Fujian Agriculture Forestry University (Philosophy Social Sciences), 16 (2013), 13-17.   Google Scholar

show all references

##### References:
 [1] J. Blackburn and G. Scudder, Supply chain strategies for perishable products: The case of fresh produce, Produc. Oper. Management, 18 (2009), 129-137.  doi: 10.1111/j.1937-5956.2009.01016.x.  Google Scholar [2] X. Cai, J. Chen, Y. Xiao and X. Xu, Optimization and coordination of fresh product supply chains with freshness-keeping effort, Produc. Oper. Management, 19 (2010), 261-278.  doi: 10.1111/j.1937-5956.2009.01096.x.  Google Scholar [3] J. Chen, Y. W. Zhou and Y. Zhong, A pricing/ordering model for a dyadic supply chain with buyback guarantee financing and fairness concerns, Internat. J. Produc. Res., 55 (2017), 5287-5304.  doi: 10.1080/00207543.2017.1308571.  Google Scholar [4] J. He, X. Cheng, J. He and H. Xu, Cv-CapsNet: Complex-valued capsule network, IEEE Access, 7 (2019), 85492-85499.  doi: 10.1109/ACCESS.2019.2924548.  Google Scholar [5] A. Herbon, E. Levner and T. C. E. Cheng, Perishable inventory management with dynamic pricing using time-temperature indicators linked to automatic detecting devices, Internat. J. Produc. Econ., 147 (2014), 605-613.  doi: 10.1016/j.ijpe.2013.07.021.  Google Scholar [6] S. Hosseiniyekani and M. Zibaei, The choice of feasible commodities for futures trading: A study of Iranian agricultural commodities, African J. Agricultural Res., 4 (2009), 193-199.   Google Scholar [7] Y. Hou, F. Wei, S. X. Li, Z. Huang and A. Ashley, Coordination and performance analysis for a three-echelon supply chain with a revenue sharing contract, Internat. J. Produc. Res., 55 (2016), 202-227.  doi: 10.1080/00207543.2016.1201601.  Google Scholar [8] L. Lin, S. Yang and B. Dan, Three-level supply chain coordination of fresh and live agricultural products by revenue-sharing contracts, J. Systems Engineering, 25 (2010), 484-491.   Google Scholar [9] E. J. Lodree and B. M. Uzochukwu, Production planning for a deteriorating item with stochastic demand and consumer choice, Internat. J. Produc. Econ., 116 (2008), 219-232.  doi: 10.1016/j.ijpe.2008.09.010.  Google Scholar [10] Y. Qin, J. Wang and C. Wei, Joint pricing and inventory control for fresh produce and foods with quality and physical quantity deteriorating simultaneously, Internat. J. Produc. Econ., 152 (2014), 42-48.  doi: 10.1016/j.ijpe.2014.01.005.  Google Scholar [11] M. Rahdar and A. S. Nookabadi, Coordination mechanism for a deteriorating item in a two-level supply chain system, Appl. Math. Model., 38 (2014), 2884-2900.  doi: 10.1016/j.apm.2013.11.019.  Google Scholar [12] L. Wang and B. Dan, The incentive mechanism for preservation in fresh agricultural supply chain considering consumer utility, J. Industrial Engineering Engineering Management, 29 (2015), 200-206.   Google Scholar [13] Y. B. Xiao, J. Chen and X. Xu, Fresh product supply chain coordination under CIF business model with long distance transportation, Systems Engineering Theory Practice, 28 (2008), 19-34.  doi: 10.1016/S1874-8651(09)60009-0.  Google Scholar [14] X. Xie, X. Liu and H. Xu, Synchronization of delayed coupled switched neural networks: Mode-dependent average impulsive interval, Neurocomputing, 365 (2019), 261-272.  doi: 10.1016/j.neucom.2019.07.045.  Google Scholar [15] X. Xie, H. Xu and X. Cheng, Improved results on exponential stability of discrete-time switched delay systems, Discrete Contin. Dyn. Syst. Ser. B, 22 (2017), 199-208.  doi: 10.3934/dcdsb.2017010.  Google Scholar [16] F. Xiong, J. Peng, P. Jin, X. Zhang and Y. Qiu, The impact of relational contracts stability about fresh agricultural product supply chain study: From the persepective of cold chain facilities subsidy mode, Chinese J. Management Science, 23 (2015), 102-111.   Google Scholar [17] H. Xu, Y. Zhang, J. Yang, G. Zhou and L. Caccetta, Practical exponential set stabilization for switched nonlinear systems with multiple subsystem equilibria, J. Global Optim., 65 (2016), 109-118.  doi: 10.1007/s10898-015-0339-7.  Google Scholar [18] Y. Yang, T. Fan and L. Zhang, Coordination of fresh agricultural supply chain with asymmetric freshness information, Chinese J. Management Science, 24 (2016), 147-155.   Google Scholar [19] A. Zaheer and N. Venkatraman, Relational governance as an interorganizational strategy: An empirical test of the role of trust in economic exchange, Strategic Management J., 16 (1995), 373-392.  doi: 10.1002/smj.4250160504.  Google Scholar [20] C. Zhang, W. Liu and J. Lai, A model of relational contract of farm produce supply chain based on GNBS $&$ formal fixed price contract, Chinese J. Management Science, 17 (2009), 94-101.   Google Scholar [21] J. Zhang, G. Liu, Q. Zhang and Z. Bai, Coordinating a supply chain for deteriorating items with a revenue sharing and cooperative investment contract, Omega, 56 (2015), 37-49.  doi: 10.1016/j.omega.2015.03.004.  Google Scholar [22] X. Zhao and F. Wu, Coordination of agri-food chain with revenue-sharing contract under stochastic output and stochastic demand, Asia-Pac. J. Oper. Res., 28 (2011), 487-510.  doi: 10.1142/S021759591100320X.  Google Scholar [23] S. Zheng, L. Chen and W. Zhuo, Research on the stability of contract relationship among company,cooperative and farmer, J. Fujian Agriculture Forestry University (Philosophy Social Sciences), 16 (2013), 13-17.   Google Scholar
The relationship between re-transaction costs and incentive coefficients of cooperatives and retailers
Notations
 Variables Meaning $P$ The price of the spot market for the fresh product $P_0$ The price for the payment to a farmer $P_c$ The price paid to a cooperative $P_x$ The spot market price at the time of fulfilling contract $V_x$ Fresh product's value to the retailer $D$ The market demand of fresh product $D_0$ The amount of demand when the farmer and the cooperative sign the contract $D_c$ The amount of demand when the cooperative and the retailer sign the contract $D_x$ The amount of spot market demand when fulfilling the contract $\theta$ The freshness of agricultural products ($0 \le \theta \le 1$) $\theta_1$ The freshness of fresh product provided by the farmer $\theta_2$ The freshness of fresh product provided by the cooperative $C_a$ The variable cost of the farmer to maintain high agricultural product freshness $C_b$ The variable cost of the cooperative to maintain high agricultural product freshness $\pi_f$ The profit function of the farmer $\pi_c$ The profit function of the cooperative $\pi_e$ The profit function of the retailer $\pi_{sx}$ The overall profit function of the supply chain
 Variables Meaning $P$ The price of the spot market for the fresh product $P_0$ The price for the payment to a farmer $P_c$ The price paid to a cooperative $P_x$ The spot market price at the time of fulfilling contract $V_x$ Fresh product's value to the retailer $D$ The market demand of fresh product $D_0$ The amount of demand when the farmer and the cooperative sign the contract $D_c$ The amount of demand when the cooperative and the retailer sign the contract $D_x$ The amount of spot market demand when fulfilling the contract $\theta$ The freshness of agricultural products ($0 \le \theta \le 1$) $\theta_1$ The freshness of fresh product provided by the farmer $\theta_2$ The freshness of fresh product provided by the cooperative $C_a$ The variable cost of the farmer to maintain high agricultural product freshness $C_b$ The variable cost of the cooperative to maintain high agricultural product freshness $\pi_f$ The profit function of the farmer $\pi_c$ The profit function of the cooperative $\pi_e$ The profit function of the retailer $\pi_{sx}$ The overall profit function of the supply chain
Profits of members of the supply chain under different contractual relationships
 $\pi_f$ $\pi_c$ $\pi_e$ $\pi_{sx}$ No contract 1720.33 1071.20 2921.24 5712.77 Flexibility contract 1942.14 1221.72 13752.03 16915.89 Relational contract 2702.69 3949.91 14867.88 21520.48 Government subsidy 5034.03 10221.25 14555.91 29811.19
 $\pi_f$ $\pi_c$ $\pi_e$ $\pi_{sx}$ No contract 1720.33 1071.20 2921.24 5712.77 Flexibility contract 1942.14 1221.72 13752.03 16915.89 Relational contract 2702.69 3949.91 14867.88 21520.48 Government subsidy 5034.03 10221.25 14555.91 29811.19
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