American Institute of Mathematical Sciences

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October  2019, 15(4): 1831-1856. doi: 10.3934/jimo.2018125

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

Nina Yan 1,, , Tingting Tong 2, and  Hongyan Dai 1,

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  October 2019 Early access  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.

Keywords: Supply chain finance, multi-attribute utility, decision optimization, coordination, capital constraints, newsvendor.
Mathematics Subject Classification: Primary: 90B05; Secondary: 91A12.
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, 2019, 15 (4) : 1831-1856. 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.  Google Scholar

[2]

D. Bowersox, C. M. David and B. Cooper, Supply Chain Logistics Management, McGraw-Hill, 2012. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

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M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.  Google Scholar

[6]

Demica Report Series, The growing role of Supply Chain Finance in a changing world, 2007. Google Scholar

[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.  Google Scholar

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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.  Google Scholar

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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.  Google Scholar

[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.  Google Scholar

[11]

R. L. Keeney and H. Raiffa, Decision with Multiple Objectives: Preferences and Value Trade-offs, John Wiley & Sons, New York, 1976.  Google Scholar

[12]

R. L. Keeney, Decision analysis: An overview, Operations Research, 30 (1982), 803-838.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

show all references

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.  Google Scholar

[2]

D. Bowersox, C. M. David and B. Cooper, Supply Chain Logistics Management, McGraw-Hill, 2012. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[5]

M. Dada and Q. Hu, Financing newsvendor inventory, Operations Research Letters, 36 (2008), 569-573.  doi: 10.1016/j.orl.2008.06.004.  Google Scholar

[6]

Demica Report Series, The growing role of Supply Chain Finance in a changing world, 2007. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[11]

R. L. Keeney and H. Raiffa, Decision with Multiple Objectives: Preferences and Value Trade-offs, John Wiley & Sons, New York, 1976.  Google Scholar

[12]

R. L. Keeney, Decision analysis: An overview, Operations Research, 30 (1982), 803-838.   Google Scholar

[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.   Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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. Google Scholar

[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. Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

Figure 1.  SCF's MAU with different ${K_r}$
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Figure 2.  Coordination effect under different ${K_r}$ and decision
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Figure 3.  optimal MAUs under different ${K_r}$ and decision
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Figure 4.  Optimal orders under different $B$
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Figure 5.  Optimal orders under different $\alpha$
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Figure 6.  Retailer's best response to the wholesale price under different ${K_r}$
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Figure 7.  Optimal wholesale price under different ${K_r}$
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Figure 8.  Manufacturer's profit under different ${K_r}$
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Table 1.  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 (-) $wq$ $p \cdot \min \left\{ {\hat x\left( q \right),x} \right\}$
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Download as excel

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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