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September  2021, 17(5): 2505-2518. 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  September 2021 Early access  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, 2021, 17 (5) : 2505-2518. doi: 10.3934/jimo.2020079
##### References:

show all references

##### References:
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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