资金约束的供应商融资:买方贷款vs银行贷款
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摘要
当供应商因资金约束而不能提供足够的零部件时,不仅影响其自身的销售收入,也会造成其下游制造商(买方)的损失。因此,制造商有意愿向其供应商提供贷款用于提高产量。在由单一供应商和单一制造商组成的供应链中,制造商面临随机的市场需求,而供应商的资金是有限的。在市场需求确定之前,先由供应商决定其备货量,必要时供应商可向其下游制造商借款(买方贷款)。在需求确定之后,制造商向供应商采购产品,供应商用销售收入尽量还款。制造商可通过调节批发价格和贷款利率影响供应商的备货量和借款额。研究表明,相比于银行贷款,制造商可通过提供买方贷款获得更高的利润,所以制造商始终愿意向供应商提供贷款。制造商提供最优的买方贷款合同时,买方贷款的利率要低于银行贷款的利率。数值例子表明:当供应商的自有资金较小时,供应商在银行贷款中可获得更高的利润;当供应商的自有资金较大时,供应商在买方贷款中可获得更高的利润。
The manufacturer needs to purchase components from its supplier. The supplier faces the capital constraint when making the production decision.The common solution for the supplier is to apply for a loan from a bank(bank lending). However, the supplier may be unqualified for the loan due to her lack of collateral and credit history. If the supplier can't provide enough components due to capital constraint, the supplier will lose sales profit, and the manufacturer(buyer) will also bear the loss resulted by the constrained production. Therefore, to avoid the inefficiency resulted by the capital constraint, the manufacturer has the motivation to finance the supplier(buyer lending) to increase her production quantity. Some powerful manufacturers are an important source of financing for their suppliers.In this paper, we use a game-theoretical model to capture the interactions between the supplier and the manufacturer so that we can examine the relative efficiency of these two schemes(buyer lending and bank lending). The manufacturer faces uncertain demand, and the supplier has limited initial capital. Before the demand is realized, the supplier needs to decide how many components to produce. In the buyer lending scheme, the supplier can borrow a loan from the manufacturer if needed. After the demand is realized, the manufacturer will purchase components from the supplier and the supplier will use its sales revenue to repay the loan to the extent possible. The manufacturer and the supplier play a Stackelberg game. As a leader, the manufacturer can affect the supplier's decision by adjusting the wholesale price and the interest rate of the loan. In the bank lending scheme, most assumptions remain the same except that the supplier borrows from a bank and the bank loan is priced at the risk-free interest rate, i.e., the expected repayment of the loan equals to the loan principal plus risk-free interest. In both schemes, the supplier's and manufacturer's opportunity cost of capital are both equal to the risk-free rate because they are in a competitive capital market.In the buyer lending scheme, the wholesale price and the interest rate are both decision variables for the manufacturer. The interest rate should be larger than the supplier's opportunity cost of capital to rule out the overlending situation. The manufacturer's expected profit can be viewed as a function of the interest rate when the wholesale price is optimized for a given interest rate. The manufacturer's expected profit is demonstrated to be decreasing in the interest rate. Therefore, the optimal interest rate is equal to the supplier's opportunity cost of capital, i.e., the risk-free rate. The manufacturer's expected profit is decreasing in the production cost, the supplier's capital and the risk-free rate. The supplier's production quantity at equilibrium is decreasing in the risk-free rate.In the bank lending scheme, by adjusting the nominal interest rate as the number of loan changes, the bank always obtains expected return rate equal to the risk-free rate. The nominal interest rate for a bank loan is higher than the risk-free rate. Therefore, buyer loan is cheaper than a bank loan for the supplier.Besides, the manufacturer can always obtain higher expected profit in the buyer lending scheme than in the bank lending scheme. A numerical example shows that the buyer lending scheme is more beneficial to the supplier than the bank loan if the supplier's capital is high. However, a poor supplier prefers the bank loan.
The manufacturer needs to purchase components from its supplier. The supplier faces the capital constraint when making the production decision.The common solution for the supplier is to apply for a loan from a bank(bank lending). However, the supplier may be unqualified for the loan due to her lack of collateral and credit history. If the supplier can't provide enough components due to capital constraint, the supplier will lose sales profit, and the manufacturer(buyer) will also bear the loss resulted by the constrained production. Therefore, to avoid the inefficiency resulted by the capital constraint, the manufacturer has the motivation to finance the supplier(buyer lending) to increase her production quantity. Some powerful manufacturers are an important source of financing for their suppliers.In this paper, we use a game-theoretical model to capture the interactions between the supplier and the manufacturer so that we can examine the relative efficiency of these two schemes(buyer lending and bank lending). The manufacturer faces uncertain demand, and the supplier has limited initial capital. Before the demand is realized, the supplier needs to decide how many components to produce. In the buyer lending scheme, the supplier can borrow a loan from the manufacturer if needed. After the demand is realized, the manufacturer will purchase components from the supplier and the supplier will use its sales revenue to repay the loan to the extent possible. The manufacturer and the supplier play a Stackelberg game. As a leader, the manufacturer can affect the supplier's decision by adjusting the wholesale price and the interest rate of the loan. In the bank lending scheme, most assumptions remain the same except that the supplier borrows from a bank and the bank loan is priced at the risk-free interest rate, i.e., the expected repayment of the loan equals to the loan principal plus risk-free interest. In both schemes, the supplier's and manufacturer's opportunity cost of capital are both equal to the risk-free rate because they are in a competitive capital market.In the buyer lending scheme, the wholesale price and the interest rate are both decision variables for the manufacturer. The interest rate should be larger than the supplier's opportunity cost of capital to rule out the overlending situation. The manufacturer's expected profit can be viewed as a function of the interest rate when the wholesale price is optimized for a given interest rate. The manufacturer's expected profit is demonstrated to be decreasing in the interest rate. Therefore, the optimal interest rate is equal to the supplier's opportunity cost of capital, i.e., the risk-free rate. The manufacturer's expected profit is decreasing in the production cost, the supplier's capital and the risk-free rate. The supplier's production quantity at equilibrium is decreasing in the risk-free rate.In the bank lending scheme, by adjusting the nominal interest rate as the number of loan changes, the bank always obtains expected return rate equal to the risk-free rate. The nominal interest rate for a bank loan is higher than the risk-free rate. Therefore, buyer loan is cheaper than a bank loan for the supplier.Besides, the manufacturer can always obtain higher expected profit in the buyer lending scheme than in the bank lending scheme. A numerical example shows that the buyer lending scheme is more beneficial to the supplier than the bank loan if the supplier's capital is high. However, a poor supplier prefers the bank loan.
引文
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[15]Kouvelis P,Zhao W.The Newsvendor Problem and Price-Only Contract When Bankruptcy Costs Exist[J].Production and Operations Management,2011,20(6):921-936.
[16]Kouvelis P,Zhao W.Financing the newsvendor:supplier vs.bank,and the structure of optimal trade credit contracts[J].Operations Research,2012,60(3):566-580.
[17]占济舟,卢锐.零售商采购资金约束下供应链融资方式的选择策略研究[J].管理工程学报,2016(3):106-113.
[18]Jing B,Chen X,Cai GG.Equilibrium financing in a distribution channel with capital constraint[J].Production and Operations Management,2012,21(6):1090-1101.
[19]王文利,骆建文.零售商提前支付与贷款担保下的供应商融资策略[J].管理工程学报,2013(1):178-184.
[20]王文利,骆建文,李彬.需求依赖价格下的供应链预付款融资策略[J].系统管理学报,2014,23(5):642-649.
[21]肖肖,骆建文.面向资金约束制造商的双渠道供应链融资策略[J].系统管理学报,2016,25(1):121-128.
[22]Lariviere MA,Porteus EL.Selling to the newsvendor:An analysis of price-only contracts[J].Manufacturing&Service Operations Management,2001,3(4):293-305.
[23]Porteus EL.Foundations of stochastic inventory theory[M].California:Stanford University Press,2002.
[2]Gerchak Y,Wang Y.Revenue-Sharing vs.Wholesale-Price Contracts in Assembly Systems with Random Demand[J].Production and operations Management,2004,13(1):23-33.
[3]Beranek W.Financial implications of lot-size inventory models[J].Management Science,1967,13(8):B-401-B-408.
[4]Hu QJ,Sobel MJ.Echelon base-stock policies are financially sub-optimal[J].Operations Research Letters,2007,35(5):561-566.
[5]Xu X,Birge JR.Joint production and financing decisions:Modeling and analysis[R].Available at SSRN 652562,2004.
[6]Dada M,Hu Q.Financing newsvendor inventory[J].Operations Research Letters,2008,36(5):569-573.
[7]Buzacott JA,Zhang RQ.Inventory management with asset-based financing[J].Management Science,2004,50(9):1274-1292.
[8]Archibald T,Thomas L,Betts J,Johnston R.Should start-up companies be cautious?Inventory policies which maximize survival probabilities[J].Management Science,2002,48(9):1161-1174.
[9]Chao X,Chen J,Wang S.Dynamic inventory management with cash flow constraints[J].Naval Research Logistics,2008,55(8):758-768.
[10]Gong X,Chao X,Simchi-Levi D.Dynamic inventory control with limited capital and short-term financing[J].Naval Research Logistics,2014,61(3):184-201.
[11]Katehakis MN,Melamed B,Shi JJ.Cash-Flow Based Dynamic Inventory Management[J].Production and Operations Management,2016,25(9):1558-1575.
[12]Li L,Shubik M,Sobel MJ.Control of dividends,capital subscriptions,and physical inventories[J].Management Science,2013,59(5):1107-1124.
[13]Gupta D,Wang L.A stochastic inventory model with trade credit[J].Manufacturing&Service Operations Management,2009,11(1):4-18.
[14]Luo W,Shang K.Joint inventory and cash management for multidivisional supply chains[J].Operations Research,2015,63(5):1098-1116.
[15]Kouvelis P,Zhao W.The Newsvendor Problem and Price-Only Contract When Bankruptcy Costs Exist[J].Production and Operations Management,2011,20(6):921-936.
[16]Kouvelis P,Zhao W.Financing the newsvendor:supplier vs.bank,and the structure of optimal trade credit contracts[J].Operations Research,2012,60(3):566-580.
[17]占济舟,卢锐.零售商采购资金约束下供应链融资方式的选择策略研究[J].管理工程学报,2016(3):106-113.
[18]Jing B,Chen X,Cai GG.Equilibrium financing in a distribution channel with capital constraint[J].Production and Operations Management,2012,21(6):1090-1101.
[19]王文利,骆建文.零售商提前支付与贷款担保下的供应商融资策略[J].管理工程学报,2013(1):178-184.
[20]王文利,骆建文,李彬.需求依赖价格下的供应链预付款融资策略[J].系统管理学报,2014,23(5):642-649.
[21]肖肖,骆建文.面向资金约束制造商的双渠道供应链融资策略[J].系统管理学报,2016,25(1):121-128.
[22]Lariviere MA,Porteus EL.Selling to the newsvendor:An analysis of price-only contracts[J].Manufacturing&Service Operations Management,2001,3(4):293-305.
[23]Porteus EL.Foundations of stochastic inventory theory[M].California:Stanford University Press,2002.