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May  2021, 17(3): 1485-1504. doi: 10.3934/jimo.2020031

## Coordination contracts for a dual-channel supply chain under capital constraints

 1 School of Management, Nanjing University of Posts and Telecommunications, Nanjing, 210003, Jiangsu, China 2 School of Economics & Managements, Southeast University, Nanjing, 210089, Jiangsu, China

* Corresponding author: Chong Zhang

Received  May 2019 Revised  July 2019 Published  May 2021 Early access  February 2020

Fund Project: The paper is supported by the Humanity and Social Science Youth Foundation of Ministry of Education of China (18YJC630235), the National Natural Science Foundation of China(71531004, 71803088) and the Scientific Research Foundation of Nanjing University of Posts and Telecommunications (NY219117)

Manufacturers often face capital constraints when opening up online channel, at this time external financing and internal financing are usually considered. Previous literature has shown that internal financing, turns out to be a better option. To figure out how trade credit financing discount contract affects operations and performances of supply chain, this paper studies the pricing decision of a retailer-dominant dual-channel supply chain with manufacturer's capital constraints. The Stackelberg game models under centralized decision and decentralized decision are constructed. Moreover, this paper conducts research about the effects of revenue-sharing (RS) contract, direct channel price discount (DP) contract and retail channel price discount (RP) contract on the performance of supply chain. Numerical examples are provided to explore the comparison of the optimal pricing strategies and total profits under different contracts. The results show that the retailer prefers RS and DP contracts to RP contract. Among them, RS contract has a broader scope of coordination, while DP contract can achieve a higher profit. The results can serve as insights for decision-makers to choose the most appropriate financial discount contract.

Citation: Chong Zhang, Yaxian Wang, Ying Liu, Haiyan Wang. Coordination contracts for a dual-channel supply chain under capital constraints. Journal of Industrial and Management Optimization, 2021, 17 (3) : 1485-1504. doi: 10.3934/jimo.2020031
##### References:
 [1] A. Aslani and J. Heydari, Transshipment contract for coordination of a green dual-channel supply chain under channel disruption, Journal of Cleaner Production, 223 (2019), 596-609.  doi: 10.1016/j.jclepro.2019.03.186. [2] M. Ayyagari, A. Demirguc-Kunt and J. Maksimovic, SME Finance, Working Paper, Washington, D.C.: World Bank Group, 2017. Available at http://documents.worldbank.org/curated/en/860711510585220714/SME-finance, Accessed date: 8 April 2018. [3] B. Barkley, C. K. Mille, M. C. Recto, E. Terry and E. Wavering, Small Business Credit Survey: Report on Employer Firms, Report, Federal Reserve Banks of New York, Atlanta, Boston, Cleveland, Philadelphia, Richmond, St. Louis, 2015. Available at https://www.newyorkfed.org/smallbusiness/small-business-credit-survey-employer-firms-2015, Accessed date: 8 April 2018. [4] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, European Journal of Operational Research, 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [5] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583.  doi: 10.1016/j.omega.2011.11.005. [6] S. C. Chen and J. T. Teng, Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash flow analysis, European Journal of Operational Research, 243 (2015), 566-575.  doi: 10.1016/j.ejor.2014.12.007. [7] D. Dzyabura and S. Jagabathula, Offline assortment optimization in the presence of an online channel, Management Science, 64 (2017), 2767-2786. [8] S. Hua, J. Liu, T. C. E. Cheng and X. Zhai, Financing and ordering strategies for a supply chain under the option contract, International Journal of Production Economics, 208 (2019), 100-121.  doi: 10.1016/j.ijpe.2018.10.008. [9] W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279.  doi: 10.1016/j.ejor.2007.11.041. [10] L. Jiang and Z. Hao, Alleviating supplier's capital restriction by two-order arrangement, Operations Research Letters, 42 (2014), 444-449.  doi: 10.1016/j.orl.2014.07.009. [11] W. Jin, Q. Zhang and J. Luo, Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints, Omega, 88 (2018), 210-222.  doi: 10.1016/j.omega.2018.04.001. [12] P. Kouvelis and W. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2015), 2341-2357.  doi: 10.1287/mnsc.2015.2248. [13] M. Lai, H. Yang, E. Cao, D. Qiu and J. Qiu, Optimal decisions for a dual-channel supply chain under information asymmetry, Journal of Industrial & Management Optimization, 14 (2018), 1023-1040.  doi: 10.3934/jimo.2017088. [14] C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European Journal of Operational Research, 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004. [15] G. Li, H. Wu and S. Xiao, Financing strategies for a capital-constrained manufacturer in a dual-channel supply chain, International Transactions in Operational Research, 2019. doi: 10.1111/itor.12653. [16] Y. Li, X. Zhen, X. Qi and G. G. Cai, Penalty and financial assistance in a supply chain with supply disruption, Omega, 61 (2016), 167-181.  doi: 10.1016/j.omega.2015.12.011. [17] M. Liu, E. Cao and C. K. Salifou, Pricing strategies of a dual-channel supply chain with risk aversion, Transportation Research Part E, 90 (2016), 108-120.  doi: 10.1016/j.tre.2015.11.007. [18] Q. Lu and N. Liu, Effects of e-commerce channel entry in a two-echelon supply chain: A comparative analysis of single-and dual-channel distribution systems, International Journal of Production Economics, 165 (2015), 100-111.  doi: 10.1016/j.ijpe.2015.03.001. [19] I. Moon, X. H. Feng and K. Y. Ryu, Channel coordination for multi-stage supply chains with revenue-sharing contracts under budget constraints, International Journal of Production Research, 53 (2015), 4819-4836.  doi: 10.1080/00207543.2014.993438. [20] H. J. Peng and T. Pang, Financing strategies for a capital-constrained supplier under yield uncertainty, Journal of Industrial and Management Optimization, 2018. doi: 10.3934/jimo.2018183. [21] C. Tang, H. Yang, E. Cao and K. K. Lai, Channel competition and coordination of a dual-channel supply chain with demand and cost disruptions, Applied Economics, 50 (2018), 4999-5016.  doi: 10.1080/00036846.2018.1466989. [22] C. S. Tang, S. A. Yang and J. Wu, Sourcing from suppliers with financial constraints and performance risk, Manufacturing & Service Operations Management, 20 (2017), 70-84. [23] L. Wang, H. Song, D. Zhang and H. Yang, Pricing decisions for complementary products in a fuzzy dual-channel supply chain, Journal of Industrial & Management Optimization, 15 (2019), 343-364. [24] D. D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. [25] S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005. [26] T. Xiao and J. J. Shi, Pricing and supply priority in a dual-channel supply chain, European Journal of Operational Research, 254 (2016), 813-823.  doi: 10.1016/j.ejor.2016.04.018. [27] Y. Xiao and J. Zhang, Preselling to a retailer with cash flow shortage on the manufacturer, Omega, 80 (2018), 43-57.  doi: 10.1016/j.omega.2017.09.004. [28] J. Xie, L. Liang, L. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, International Journal of Production Economics, 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026. [29] L. Xu, C. Wang and J. Zhao, Decision and coordination in the dual-channel supply chain considering cap-and-trade regulation, Journal of Cleaner Production, 197 (2018), 551-561.  doi: 10.1016/j.jclepro.2018.06.209. [30] B. Yan, T. Wang, Y. P. Liu and Y. Liu, Decision analysis of retailer-dominated dual-channel supply chain considering cost misreporting, International Journal of Production Economics, 178 (2016), 34-41.  doi: 10.1016/j.ijpe.2016.04.020. [31] N. Yan and B. Sun, Comparative analysis of supply chain financing strategies between different financing modes, Journal of Industrial and Management Optimization, 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073. [32] H. Yang, F. Sun, J. Chen and B. Chen, Financing decisions in a supply chain with a capital-constrained manufacturer as new entrant, International Journal of Production Economics, 216 (2019), 321-332.  doi: 10.1016/j.ijpe.2019.06.014. [33] H. Yang, W. Zhuo and L. Shao, Equilibrium evolution in a two-echelon supply chain with financially constrained retailers: The impact of equity financing, International Journal of Production Economics, 185 (2017), 139-149. [34] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2017), 3667-3689. [35] W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 29-41.  doi: 10.1287/mksc.1100.0586. [36] B. Zhang, D. D. Wu and L. Liang, Trade credit model with customer balking and asymmetric market information, Transportation Research Part E: Logistics and Transportation Review, 110 (2018), 31-46.  doi: 10.1016/j.tre.2017.10.006.

show all references

##### References:
 [1] A. Aslani and J. Heydari, Transshipment contract for coordination of a green dual-channel supply chain under channel disruption, Journal of Cleaner Production, 223 (2019), 596-609.  doi: 10.1016/j.jclepro.2019.03.186. [2] M. Ayyagari, A. Demirguc-Kunt and J. Maksimovic, SME Finance, Working Paper, Washington, D.C.: World Bank Group, 2017. Available at http://documents.worldbank.org/curated/en/860711510585220714/SME-finance, Accessed date: 8 April 2018. [3] B. Barkley, C. K. Mille, M. C. Recto, E. Terry and E. Wavering, Small Business Credit Survey: Report on Employer Firms, Report, Federal Reserve Banks of New York, Atlanta, Boston, Cleveland, Philadelphia, Richmond, St. Louis, 2015. Available at https://www.newyorkfed.org/smallbusiness/small-business-credit-survey-employer-firms-2015, Accessed date: 8 April 2018. [4] J. Chen, L. Liang, D. Q. Yao and S. Sun, Price and quality decisions in dual-channel supply chains, European Journal of Operational Research, 259 (2017), 935-948.  doi: 10.1016/j.ejor.2016.11.016. [5] J. Chen, H. Zhang and Y. Sun, Implementing coordination contracts in a manufacturer Stackelberg dual-channel supply chain, Omega, 40 (2012), 571-583.  doi: 10.1016/j.omega.2011.11.005. [6] S. C. Chen and J. T. Teng, Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash flow analysis, European Journal of Operational Research, 243 (2015), 566-575.  doi: 10.1016/j.ejor.2014.12.007. [7] D. Dzyabura and S. Jagabathula, Offline assortment optimization in the presence of an online channel, Management Science, 64 (2017), 2767-2786. [8] S. Hua, J. Liu, T. C. E. Cheng and X. Zhai, Financing and ordering strategies for a supply chain under the option contract, International Journal of Production Economics, 208 (2019), 100-121.  doi: 10.1016/j.ijpe.2018.10.008. [9] W. Huang and J. M. Swaminathan, Introduction of a second channel: Implications for pricing and profits, European Journal of Operational Research, 194 (2009), 258-279.  doi: 10.1016/j.ejor.2007.11.041. [10] L. Jiang and Z. Hao, Alleviating supplier's capital restriction by two-order arrangement, Operations Research Letters, 42 (2014), 444-449.  doi: 10.1016/j.orl.2014.07.009. [11] W. Jin, Q. Zhang and J. Luo, Non-collaborative and collaborative financing in a bilateral supply chain with capital constraints, Omega, 88 (2018), 210-222.  doi: 10.1016/j.omega.2018.04.001. [12] P. Kouvelis and W. Zhao, Supply chain contract design under financial constraints and bankruptcy costs, Management Science, 62 (2015), 2341-2357.  doi: 10.1287/mnsc.2015.2248. [13] M. Lai, H. Yang, E. Cao, D. Qiu and J. Qiu, Optimal decisions for a dual-channel supply chain under information asymmetry, Journal of Industrial & Management Optimization, 14 (2018), 1023-1040.  doi: 10.3934/jimo.2017088. [14] C. H. Lee and B. D. Rhee, Trade credit for supply chain coordination, European Journal of Operational Research, 214 (2011), 136-146.  doi: 10.1016/j.ejor.2011.04.004. [15] G. Li, H. Wu and S. Xiao, Financing strategies for a capital-constrained manufacturer in a dual-channel supply chain, International Transactions in Operational Research, 2019. doi: 10.1111/itor.12653. [16] Y. Li, X. Zhen, X. Qi and G. G. Cai, Penalty and financial assistance in a supply chain with supply disruption, Omega, 61 (2016), 167-181.  doi: 10.1016/j.omega.2015.12.011. [17] M. Liu, E. Cao and C. K. Salifou, Pricing strategies of a dual-channel supply chain with risk aversion, Transportation Research Part E, 90 (2016), 108-120.  doi: 10.1016/j.tre.2015.11.007. [18] Q. Lu and N. Liu, Effects of e-commerce channel entry in a two-echelon supply chain: A comparative analysis of single-and dual-channel distribution systems, International Journal of Production Economics, 165 (2015), 100-111.  doi: 10.1016/j.ijpe.2015.03.001. [19] I. Moon, X. H. Feng and K. Y. Ryu, Channel coordination for multi-stage supply chains with revenue-sharing contracts under budget constraints, International Journal of Production Research, 53 (2015), 4819-4836.  doi: 10.1080/00207543.2014.993438. [20] H. J. Peng and T. Pang, Financing strategies for a capital-constrained supplier under yield uncertainty, Journal of Industrial and Management Optimization, 2018. doi: 10.3934/jimo.2018183. [21] C. Tang, H. Yang, E. Cao and K. K. Lai, Channel competition and coordination of a dual-channel supply chain with demand and cost disruptions, Applied Economics, 50 (2018), 4999-5016.  doi: 10.1080/00036846.2018.1466989. [22] C. S. Tang, S. A. Yang and J. Wu, Sourcing from suppliers with financial constraints and performance risk, Manufacturing & Service Operations Management, 20 (2017), 70-84. [23] L. Wang, H. Song, D. Zhang and H. Yang, Pricing decisions for complementary products in a fuzzy dual-channel supply chain, Journal of Industrial & Management Optimization, 15 (2019), 343-364. [24] D. D. Wu, L. Yang and D. L. Olson, Green supply chain management under capital constraint, International Journal of Production Economics, 215 (2019), 3-10. [25] S. Xiao, S. P. Sethi, M. Liu and S. Ma, Coordinating contracts for a financially constrained supply chain, Omega, 72 (2017), 71-86.  doi: 10.1016/j.omega.2016.11.005. [26] T. Xiao and J. J. Shi, Pricing and supply priority in a dual-channel supply chain, European Journal of Operational Research, 254 (2016), 813-823.  doi: 10.1016/j.ejor.2016.04.018. [27] Y. Xiao and J. Zhang, Preselling to a retailer with cash flow shortage on the manufacturer, Omega, 80 (2018), 43-57.  doi: 10.1016/j.omega.2017.09.004. [28] J. Xie, L. Liang, L. Liu and P. Ieromonachou, Coordination contracts of dual-channel with cooperation advertising in closed-loop supply chains, International Journal of Production Economics, 183 (2017), 528-538.  doi: 10.1016/j.ijpe.2016.07.026. [29] L. Xu, C. Wang and J. Zhao, Decision and coordination in the dual-channel supply chain considering cap-and-trade regulation, Journal of Cleaner Production, 197 (2018), 551-561.  doi: 10.1016/j.jclepro.2018.06.209. [30] B. Yan, T. Wang, Y. P. Liu and Y. Liu, Decision analysis of retailer-dominated dual-channel supply chain considering cost misreporting, International Journal of Production Economics, 178 (2016), 34-41.  doi: 10.1016/j.ijpe.2016.04.020. [31] N. Yan and B. Sun, Comparative analysis of supply chain financing strategies between different financing modes, Journal of Industrial and Management Optimization, 11 (2015), 1073-1087.  doi: 10.3934/jimo.2015.11.1073. [32] H. Yang, F. Sun, J. Chen and B. Chen, Financing decisions in a supply chain with a capital-constrained manufacturer as new entrant, International Journal of Production Economics, 216 (2019), 321-332.  doi: 10.1016/j.ijpe.2019.06.014. [33] H. Yang, W. Zhuo and L. Shao, Equilibrium evolution in a two-echelon supply chain with financially constrained retailers: The impact of equity financing, International Journal of Production Economics, 185 (2017), 139-149. [34] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, 64 (2017), 3667-3689. [35] W. S. Yoo and E. Lee, Internet channel entry: A strategic analysis of mixed channel structures, Marketing Science, 30 (2011), 29-41.  doi: 10.1287/mksc.1100.0586. [36] B. Zhang, D. D. Wu and L. Liang, Trade credit model with customer balking and asymmetric market information, Transportation Research Part E: Logistics and Transportation Review, 110 (2018), 31-46.  doi: 10.1016/j.tre.2017.10.006.
Model structure of the supply chain
Sequences of event and decisions
Effects of on optimal solutions
Effects of ${I_m}$ on optimal solutions
Effects of $\xi$ on optimal solutions
Effects of $\mu$ on optimal solutions
Effects of $\kappa$ on optimal solutions
Comparison of the total profit of the three contracts
Notations and descriptions used in the paper
 Parameters $c$ The unit production cost of products, ＄/unit. $w$ The unit wholesale price of products, ＄/unit. $I_i$ The interest charged per dollar per year, ＄/year, $i = m, r$ refer to the manufacturer and the retailer. $N$ The length of advance payment period offered by the retailer in years. $a$ Market primary demand, $a > 0$ $\lambda$ The cross price sensitivity and $0 < \lambda < 1$, which can reveal that the effect of ownership price is greater than that of cross-price. $s$ The degree of customer loyalty to the retail channel and $0 < s < 1$, and $1 - s$ represents the degree of customer loyalty to the direct channel. $L$ Retailer's advance payment to manufacturer as a function of >$c$, ${D_r}$, ${D_d}$ and $B$. $L = c({D_r}{{ + }}{D_d}) - B$, where $B \le c({D_r} + {D_d})$ $\le w{D_r}{ + }B$. ${\pi _i}$ The supply chain member's annual profit, $i = m, r, sc$ refer to the manufacturer, the retailer and the supply chain separately. $*$ Represents the optimal value of a decision variable. Decision variables ${p_d}$ Direct price decided by the manufacturer, ＄/unit, with ${p_d} > w > c$. ${p_r}$ Retail price decided by the retailer, ＄/unit, with ${p_r} > w > c$. Superscript $S$ The Stackelberg game with the retailer as the leader $C$ The centralized decision $RS$ The revenue-sharing contract $DP$ The retail channel price discount contract $PR$ The case with green products in the dual-channel supply chain Subscript $m$ Manufacturer $r$ Retailer $sc$ Supply chain
 Parameters $c$ The unit production cost of products, ＄/unit. $w$ The unit wholesale price of products, ＄/unit. $I_i$ The interest charged per dollar per year, ＄/year, $i = m, r$ refer to the manufacturer and the retailer. $N$ The length of advance payment period offered by the retailer in years. $a$ Market primary demand, $a > 0$ $\lambda$ The cross price sensitivity and $0 < \lambda < 1$, which can reveal that the effect of ownership price is greater than that of cross-price. $s$ The degree of customer loyalty to the retail channel and $0 < s < 1$, and $1 - s$ represents the degree of customer loyalty to the direct channel. $L$ Retailer's advance payment to manufacturer as a function of >$c$, ${D_r}$, ${D_d}$ and $B$. $L = c({D_r}{{ + }}{D_d}) - B$, where $B \le c({D_r} + {D_d})$ $\le w{D_r}{ + }B$. ${\pi _i}$ The supply chain member's annual profit, $i = m, r, sc$ refer to the manufacturer, the retailer and the supply chain separately. $*$ Represents the optimal value of a decision variable. Decision variables ${p_d}$ Direct price decided by the manufacturer, ＄/unit, with ${p_d} > w > c$. ${p_r}$ Retail price decided by the retailer, ＄/unit, with ${p_r} > w > c$. Superscript $S$ The Stackelberg game with the retailer as the leader $C$ The centralized decision $RS$ The revenue-sharing contract $DP$ The retail channel price discount contract $PR$ The case with green products in the dual-channel supply chain Subscript $m$ Manufacturer $r$ Retailer $sc$ Supply chain
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