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

Nina Yan; Tingting Tong; Hongyan Dai

doi:10.3934/jimo.2018125

Article Contents

2019, Volume 15, Issue 4: 1831-1856. Doi: 10.3934/jimo.2018125

This issue Previous Article Uncertain portfolio selection with mental accounts and background risk Next Article An economic order quantity for deteriorating items with allowable rework of deteriorated products

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
* Corresponding author: Nina Yan

Received: September 2017

Revised: March 2018

Early access: August 2018

Published: July 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 90B05; Secondary: 91A12.

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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	$p \cdot \min \left\{ {q,x} \right\}$
$ $0$ \leqslant q < {\hat q_{NR}}$	Outflows (-)	$wq$	0
$q \geqslant {\hat q_{NR}}$	Inflows (+)	$wq - {K_r}$	$p \cdot \min \left\{ {q,x} \right\}$
$q \geqslant {\hat q_{NR}}$	Outflows (-)	$wq$	$p \cdot \min \left\{ {\hat x\left( q \right),x} \right\}$

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