Abstract: Delayed payment belongs to supply chain finance and is a financing tool widely-used in retailing, wherein suppliers grant credits for a specified time, and retailers should fulfill the repayment within the limited period. Delayed payments can increase sales for suppliers, resulted from the increased orderings amount by capital-constrained retailers, but they bring non-payment risk, due to the transferred demand uncertainty. For the sake of risk aversion, suppliers usually set interest rates for delayed payments.
In this paper, we consider that a retailer purchases products from a supplier, but faces capital-constrained problem. The supplier would announce the interest rate for delayed payments, and then the retailer decides her ordering amount. After the demand is realized, the retailer repays the debt if her revenue is sufficient, otherwise she declares bankruptcy after repaying her entire realized revenue. In the process, there are three questions: 1)How will the supplier determine the interest rate contingent on the retailer's financial constraints? 2)When will the retailer prefer delayed payments for purchase, and how about her ordering decision based on the interest rate? 3)Does delayed payment achieve the supply chain coordination, if not, how to coordinate the supply chain with contracts?
Our study considers a two-echelon supply chain consisting of a supplier and a financial-constrained retailer under demand uncertainty and constructs a Stackelberg game model to analyze the supplier's optimal interest rate for delayed payment and the retailer's optimal strategy on ordering and payment. In addition, we investigate the supply chain coordination under delayed payment, and two contracts, including buy-back contract and revenue-sharing contract, are employed to coordinate the supply chain. Specifically, we adopt backward inductionto solve the problem and consider two scenarios wherein the retailer purchases with her own capital or the delayed payment. First, we derive the retailer's optimal order quantity, conditional on a given interest rate, and figure out her payment decision by comparing her profits in the two scenarios. Then, contingent on the ordering and payment decisions, we analyze the interest rate and find out the optimal interest rate with the retailer's initial capital level.
The results can be described as: 1) The retailer purchases with delayed payment only when the interest rate is lower than a specific threshold, otherwise the retailer orders with all herinitial capital; 2) Under the delayed payment option, the retailer's optimal ordering decreases with the interest rate, meanwhile the supplier's optimal interest rate will not increase with the retailer's initial capital level; 3) Delayed payments can only partially coordinate the supply chain, and the buy-back contract cannot help to achieve the supply chain coordination under the delayed payment; 4) There exists a Pareto zone wherein the revenue-sharing contract can fully coordinate the supply chain under the delayed payment.
To verify the results, we conduct numerical experiments and show that the order quantity always decreases with the interest rate, and exceeds the optimum ordering amount without capital constraints as the rate is lower than a certain threshold. On the one hand, the profit in a decentralized supply chain always decreases with the interest rate, but the supplier could gain more profits as the interest rate increases until the rate reaches a certain level, and the profit decreases since then. On the other hand, the profit in a decentralized supply chain is always lower than that in a centralized supply chain under the buy-back contract, regardless of the buy-back price, indicating that the buy-back contract cannot achieve the supply chain coordination. Under the revenue-sharing contract, the retailer gains more profits but the supplier earns less as the retailer takes up a larger revenue share, but both of them benefit from the contract when the share stays medium, referred to as the Pareto zone.
Finally, we can provide some insights: 1)Delayed payment can improve the whole supply chain efficiency and benefit all supply chain members, but it goes along with the demand uncertainty transfer, thus suppliers should limit the non-payment risks and set the interest rates based on the retailer's financial status, demand uncertainty and product price. 2)In spite of the efficiency improvement, delayed payment can only partially coordinate the supply chain but cannot reach the optimum, and suppliers can fully coordinate the supply chain under the revenue-sharing contract, instead of the buy-back contract.

Key words: capital constraint, delayed payments, supply chain coordination, demand uncertainty, Stackelberg game

摘要： 本文研究了随机需求下两级供应链的延期支付问题,其中供应商作为主导者将首先设置延期支付利率,而受资金约束的零售商作为追随者将根据利率来确定订货量。通过构建Newsvendor模型对供应链各成员的利润进行了分析,并基于Stackelberg博弈研究了两级供应链下的延迟支付策略,得到了零售商的最优订货量及供应商的最优利率。此外,我们还研究了延期支付条件下的供应链协调问题,分别探讨了产品回购契约和收益共享契约下的供应链协调。研究结果表明:只有当供应商设置的利率低于特定阈值时,受资金约束的零售商才会采用延期支付,否则零售商会将全部初始资金用于采购而不采用延期支付;在延期支付条件下,提高利率将导致零售商订货量减少,并且供应商设置的利率不会随零售商的初始资金增大;延期支付只能部分协调供应链,同时在延期支付条件下,通过产品回购契约无法实现供应链的完全协调;在延期支付条件下,存在关于收益占比的帕累托改进区间,使得收益共享契约在该区间内能够实现供应链协调。最后,我们通过数值实验对研究结论进行了验证。

关键词: 资金约束, 延期支付, 供应链协调, 随机需求, Stackelberg博弈