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doi: 10.3934/jimo.2018125

## Capital-constrained supply chain with multiple decision attributes: Decision optimization and coordination analysis

 1 Business School, Central University of Finance and Economics, 39 South College Road, Haidian District, Beijing 100081, China 2 International Business College, Dongbei University of Finance and Economics, Dalian, Liaoning 116025, China

* Corresponding author: Nina Yan

Received  September 2017 Revised  March 2018 Published  August 2018

A Supply Chain Finance (SCF) system involving and a commercial bank and a capital-constrained retailer is designed in the imperfect capital market with non-zero bankruptcy costs. A decentralized borrower-lender game is analyzed, and the optimal centralized strategy is developed for SCF from the perspective of multi-attribute utility (MAU) maximization, including maximizing the expected profit and the service level, as well as minimizing the bankruptcy cost. Furthermore, we analytically and numerically explore the coordination condition for SCF and conclude that the bank financing scheme with a suitable combination of decision preferences can realize coordination, even super coordination. Through sensitivity analyses and numerical experiments, we discuss the impacts of the borrower's initial capitals on the upstream firm's pricing decision and dig out why he has incentives to support the retailer's choice of adopting SCF. The findings of this study reveal that the capital-constrained retailer would require more initial capital when maximizing MAU than maximizing the expected profit, and thus the equilibrium order quantity and the bankruptcy risk would also be higher. Moreover, based on a suitable combination of decision preferences, our proposed bank financing scheme can realize coordination, even super coordination.

Citation: Nina Yan, Tingting Tong, Hongyan Dai. Capital-constrained supply chain with multiple decision attributes: Decision optimization and coordination analysis. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2018125
##### References:
 [1] Y. Alan and V. Gaur, Operational investment and capital structure under asset-based lending, Manufacturing and Service Operations Management, Published online in Articles in Advance, 2018. doi: 10.2139/ssrn.1716925. [2] D. Bowersox, C. M. David and B. Cooper, Supply Chain Logistics Management, McGraw-Hill, 2012. [3] A. J. Brito and A. T. de Almeida, Modeling a multi-attribute utility newsvendor with partial backlogging, European Journal of Operational Research, 220 (2012), 820-830. doi: 10.1016/j.ejor.2012.02.027. [4] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. doi: 10.1287/mnsc.1040.0278. [5] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573. doi: 10.1016/j.orl.2008.06.004. [6] Demica Report Series, The growing role of Supply Chain Finance in a changing world, 2007. [7] R. J. P. Ferreira, A. T. de Almeida and C. A. V. Cavalcante, A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis, Reliability Engineering & System Safety, 94 (2009), 905-912. doi: 10.1016/j.ress.2008.10.001. [8] W. J. Hahn, Making decisions with multiple criteria: A case in energy sustainability planning, EURO Journal on Decision Processes, 3 (2015), 161-185. doi: 10.1007/s40070-014-0025-x. [9] B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. doi: 10.1016/j.dss.2013.01.013. [10] B. Jing, X. Chen and G. Cai, Equilibrium financing in a distribution channel with capital constraint, Production and Operations Management, 21 (2012), 1090-1101. doi: 10.1111/j.1937-5956.2012.01328.x. [11] R. L. Keeney and H. Raiffa, Decision with Multiple Objectives: Preferences and Value Trade-offs, John Wiley & Sons, New York, 1976. [12] R. L. Keeney, Decision analysis: An overview, Operations Research, 30 (1982), 803-838. [13] P. Kouvelis and W. Zhao, The newsvendor problem and price-only contract when bankruptcy costs exist, Production and Operations Management, 20 (2011), 921-936. [14] 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. [15] M. A. Lariviere, A note on probability distributions with increasing generalized failure rates, Operations Research, 54 (2016), 602-604. doi: 10.1287/opre.1060.0282. [16] R. V. Rao, Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision making methods, in Springer Series in Advanced Manufacturing, Springer-Verlag London, 2013. [17] N. R. Srinivasa Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. doi: 10.1016/j.ijpe.2009.11.014. [18] J. H. P. Warren, L. S. Samuel and B. Rob, How managers can use decision analysis techniques to include both quantitative and qualitative factors in their decision-making, Graziadio Business Review, 15 2012. [19] X. D. Xu and J. R. Birge, Joint Production and Financing Decisions: Modeling and Analysis, Working Paper, Graduate School of Business, University of Chicago, 2004, Available at SSRN: http://ssrn.com/abstract=652562. [20] N. Yan, H. Dai and B. Sun, Optimal bi-level Stackelberg strategies for supply chain financing with both capital-constrained buyers and sellers, Applied Stochastic Models in Business and Industry, 30 (2013), 783-796. doi: 10.1002/asmb.2021. [21] N. Yan, B. Sun, H. Zhang and C. Liu, A partial credit guarantee contract in a capital-constrained supply chain: Financing equilibrium and coordinating strategy, International Journal of Production Economics, 173 (2016), 122-133. doi: 10.1016/j.ijpe.2015.12.005. [22] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, Published online in Articles in Advance, 2017. doi: 10.1287/mnsc.2017.2799. [23] L. Zhao and A. Huchzermeier, Operations-finance interface models: A literature review and framework, European Journal of Operational Research, 244 (2015), 905-917. doi: 10.1016/j.ejor.2015.02.015.

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##### References:
 [1] Y. Alan and V. Gaur, Operational investment and capital structure under asset-based lending, Manufacturing and Service Operations Management, Published online in Articles in Advance, 2018. doi: 10.2139/ssrn.1716925. [2] D. Bowersox, C. M. David and B. Cooper, Supply Chain Logistics Management, McGraw-Hill, 2012. [3] A. J. Brito and A. T. de Almeida, Modeling a multi-attribute utility newsvendor with partial backlogging, European Journal of Operational Research, 220 (2012), 820-830. doi: 10.1016/j.ejor.2012.02.027. [4] J. A. Buzacott and R. Q. Zhang, Inventory management with asset-based financing, Management Science, 50 (2004), 1274-1292. doi: 10.1287/mnsc.1040.0278. [5] M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573. doi: 10.1016/j.orl.2008.06.004. [6] Demica Report Series, The growing role of Supply Chain Finance in a changing world, 2007. [7] R. J. P. Ferreira, A. T. de Almeida and C. A. V. Cavalcante, A multi-criteria decision model to determine inspection intervals of condition monitoring based on delay time analysis, Reliability Engineering & System Safety, 94 (2009), 905-912. doi: 10.1016/j.ress.2008.10.001. [8] W. J. Hahn, Making decisions with multiple criteria: A case in energy sustainability planning, EURO Journal on Decision Processes, 3 (2015), 161-185. doi: 10.1007/s40070-014-0025-x. [9] B. Jing and A. Seidmann, Finance sourcing in a supply chain, Decision Support Systems, 58 (2014), 15-20. doi: 10.1016/j.dss.2013.01.013. [10] B. Jing, X. Chen and G. Cai, Equilibrium financing in a distribution channel with capital constraint, Production and Operations Management, 21 (2012), 1090-1101. doi: 10.1111/j.1937-5956.2012.01328.x. [11] R. L. Keeney and H. Raiffa, Decision with Multiple Objectives: Preferences and Value Trade-offs, John Wiley & Sons, New York, 1976. [12] R. L. Keeney, Decision analysis: An overview, Operations Research, 30 (1982), 803-838. [13] P. Kouvelis and W. Zhao, The newsvendor problem and price-only contract when bankruptcy costs exist, Production and Operations Management, 20 (2011), 921-936. [14] 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. [15] M. A. Lariviere, A note on probability distributions with increasing generalized failure rates, Operations Research, 54 (2016), 602-604. doi: 10.1287/opre.1060.0282. [16] R. V. Rao, Decision making in the manufacturing environment using graph theory and fuzzy multiple attribute decision making methods, in Springer Series in Advanced Manufacturing, Springer-Verlag London, 2013. [17] N. R. Srinivasa Raghavan and V. K. Mishra, Short-term financing in a cash-constrained supply chain, International Journal of Production Economics, 134 (2011), 407-412. doi: 10.1016/j.ijpe.2009.11.014. [18] J. H. P. Warren, L. S. Samuel and B. Rob, How managers can use decision analysis techniques to include both quantitative and qualitative factors in their decision-making, Graziadio Business Review, 15 2012. [19] X. D. Xu and J. R. Birge, Joint Production and Financing Decisions: Modeling and Analysis, Working Paper, Graduate School of Business, University of Chicago, 2004, Available at SSRN: http://ssrn.com/abstract=652562. [20] N. Yan, H. Dai and B. Sun, Optimal bi-level Stackelberg strategies for supply chain financing with both capital-constrained buyers and sellers, Applied Stochastic Models in Business and Industry, 30 (2013), 783-796. doi: 10.1002/asmb.2021. [21] N. Yan, B. Sun, H. Zhang and C. Liu, A partial credit guarantee contract in a capital-constrained supply chain: Financing equilibrium and coordinating strategy, International Journal of Production Economics, 173 (2016), 122-133. doi: 10.1016/j.ijpe.2015.12.005. [22] S. A. Yang and J. R. Birge, Trade credit, risk sharing, and inventory financing portfolios, Management Science, Published online in Articles in Advance, 2017. doi: 10.1287/mnsc.2017.2799. [23] L. Zhao and A. Huchzermeier, Operations-finance interface models: A literature review and framework, European Journal of Operational Research, 244 (2015), 905-917. doi: 10.1016/j.ejor.2015.02.015.
SCF's MAU with different ${K_r}$
Coordination effect under different ${K_r}$ and decision
optimal MAUs under different ${K_r}$ and decision
Optimal orders under different $B$
Optimal orders under different $\alpha$
Retailer's best response to the wholesale price under different ${K_r}$
Optimal wholesale price under different ${K_r}$
Manufacturer's profit under different ${K_r}$
Retailer's cash flow
 Cash flow $t=0$ $t = T$ 0$\leqslant q < {\hat q_{NR}}$ Inflows (+) 0 $p \cdot \min \left\{ {q,x} \right\}$ Outflows (-) $wq$ 0 $q \geqslant {\hat q_{NR}}$ Inflows (+) $wq - {K_r}$ $p \cdot \min \left\{ {q,x} \right\}$ Outflows (-) $wq$ $p \cdot \min \left\{ {\hat x\left( q \right),x} \right\}$
 Cash flow $t=0$ $t = T$ 0$\leqslant q < {\hat q_{NR}}$ Inflows (+) 0 $p \cdot \min \left\{ {q,x} \right\}$ Outflows (-) $wq$ 0 $q \geqslant {\hat q_{NR}}$ Inflows (+) $wq - {K_r}$ $p \cdot \min \left\{ {q,x} \right\}$ Outflows (-) $wq$ $p \cdot \min \left\{ {\hat x\left( q \right),x} \right\}$
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