资金约束供应链合作广告协调模型

doi:10.16381/j.cnki.issn1003-207x.2021.0133

摘要/Abstract

摘要：

在供应商面临资金约束且分担零售商的广告费开展合作广告的情形下，探讨了收益共享契约和回购契约的协调问题，分三种情形进行讨论：正常支付（不融资模式）、零售商垫付广告费用和提前支付货款（两种融资模式）。刻画了契约实现渠道协调及完成渠道收益任意分配的资金临界条件，比较分析了两个契约的协调性：在正常支付下，两个契约等价；在资金短缺且融资下，回购契约优于收益共享契约。特别地，在提前支付下，回购契约不仅能协调供应链，还可实现渠道收益的任意分配。基于契约协调的柔性比较了三种支付模式，结果表明：提前支付模式优于垫付广告费用模式，而后者又优于正常支付模式。最后，分析了初始资金和分配份额对契约协调的影响：供应商初始资金越多，或索要的分配份额越小，供应链的协调越有可能实现。

关键词: 供应链管理, 资金约束, 合作广告, 契约协调

Abstract:

The capital shortage hinders transaction activities， and thereby results in low efficiency of the supply chain. If an upstream firm does not have enough cash flow， it will be incapable to meet order requirements of its downstream firm， and subsequently affects performance and efficiency of the entire supply chain. A natural question arises： Is it possible to achieve supply chain coordination if the supplier is shortage of funds and has to shoulder advertising costs？ With the help of trade credit， can it realize channel coordination？ What contract mechanism can coordinate the supply chain？ Besides， the supplier’s working capital affects its production capacity， and the working capital is affected by the supplier’s initial capital， the timing of payment for goods， and the timing of advertising expenses split. This arises another related question. What is impact of the initial capital， the timing of payment for goods， and the timing of advertising expenses split on coordination of the supply chain？To answer the above-mentioned questions， a supply chain composed of a cash-constrained supplier and a well-funded retailer is considered. The two firms cooperatively carry out advertising， in which the retailer can finance for the supplier by paying the advertising expenses or the ordered products in advance. Three scenarios is discussed as below： normal payment （non-financing mode）， the retailer paying advertising expenses for the supplier， and payment of the products ordered in advance （two financing modes）. This study focus on revenue sharing contract and buyback contract， for the two contracts are widely used in business practice， and obtain the most extensive attention in theory. Furthermore， the two contracts are equivalent， and hence provides a benchmark for us to investigate their equivalence in a new setting.Firstly， all contracts are classified， according to coordination of contracts， into three categories： complete coordination contract， partial coordination contract and non-coordination contract. The superiority of two contracts is defined under channel coordination， i.e.， both the two contracts can achieve the expected profit maximization. Contract A is superior to contract B， if Contract A can replicate any split scheme that Contract B can achieve， but the contrary is not true. Put another words， Contract A is more flexible than Contract B.In the subsequent， the threshold conditions are characterized， from perspective of the initial capital， for realization of supply chain coordination and arbitrary profit split via the two contracts. The coordination of the two contracts is analyzed， and it is shown that the two are equivalent if the supplier faces no cash shortage or the retailer doesn’t provide financing support towards the supplier， albeit suffered from cash shortage. In the presence of capital shortage and financing， buyback contract is superior to revenue sharing contract. Moreover， their advantages and disadvantages are disaussed under the three scenarios， and the conclusions are obtained as follows. Under either contract， the advance payment mode is superior to that of paying advertisement fee for the supplier， whereas the latter is superior to the normal payment mode. In particular， the buyback contract can always coordinate the supply chain under the advance payment mode， even though the supplier’s initial capital is extremely short.Lastly， the impact of the initial capital and profit split on coordination of the two contracts is investigated. The likelihood that the supply chain coordination can be achieved via the two contracts increases in the initial capital and decreases in the split share claimed by the supplier.From discussion we obtain the following managerial guidance. First， in the case of funds shortage， the retailer should provide financing to the supplier by paying advertising expenses or the products ordered in advance， and payment for the products ordered in advance is better than that of paying advertising expenses in advance. Second， if the supplier is facing shortage of funds， it should adopt payment for the products ordered in advance and make use of the buyback contract to coordinate the supply chain.

Key words: supply chain coordination, financial constraints, cooperative advertising, coordination via contracts

中图分类号:

C931

代建生,李革. 资金约束供应链合作广告协调模型[J]. 中国管理科学, 2023, 31(9): 83-93.

Jian-sheng DAI,Ge LI. Coordination of Supply Chain Cooperative Advertising with Financial Constraints[J]. Chinese Journal of Management Science, 2023, 31(9): 83-93.

图/表 11

表1

符号及其含义"

符号	含义
$p$	销售价格
$w$	批发价格， $w ∈ (0, p)$
$c$	单位生产成本， $c ∈ (0, p)$
$ξ$	市场需求，随机变量
$F (?)$ ， $f (?)$	市场需求的累积分布函数和概率密度函数
$Q$	订货量
$D (M)$	广告投放对市场需求的改善程度，其中 $M$ 表示广告资金， $D (?)$ 凹、增、二次可微^[13]
$φ$	供应商的成本分担比例， $φ ∈ (0,1)$
$?$	供应商的收益分享比例， $? ∈ (0,1)$
$b$	回购价格， $b < w$
$B$	供应商拥有的初始运营资金， $B > 0$
$π H i$	在契约 $i$ 下 $H$ 的利润， $H ∈ {S, ? R, ? S C}$ 分别指代供应商、零售商和供应链， $i ∈ {0,1, 2}$ 分别指代成本分担、收益共享和回购契约
$(a, 1 - a)$	利益分配方案，供应商和零售商分配比例分别为 $a$ 和 $1 - a$ ， $a ∈ (0,1)$
$E [X]$	随机变量 $X$ 的数学期望

表1

图1

表2

表3

协调契约释义"

符号	含义
$(w, φ)$	商品采购价格为 $w$ ，广告成本由双方共同承担，其中供应商承担的比例为 $φ$ 。
$(w, ?, φ)$	期初，供应商按价格 $w$ 提供商品，销售收入实现后，双方共同分享，并共担广告成本
$(w, b, φ)$	供应商按价格 $w$ 提供商品，在销售期末，经双方核实剩余商品数量，供应商以 $b$ 的价格回购未售出的商品，双方分摊广告成本

表3

表4

收益共享契约和回购契约的协调性"

支付模式	自有资金	$B < c Q *$	$c Q * < B < B *$	$B ≥ B *$
正常支付	收益共享	不可协调	部分协调	完全协调
正常支付	回购契约	不可协调	部分协调	完全协调
垫付费用	收益共享	不可协调	部分协调	完全协调
垫付费用	回购契约	不可协调	完全协调	完全协调
提前支付	收益共享	部分协调	部分协调	完全协调
提前支付	回购契约	完全协调	完全协调	完全协调

表4

表5

渠道协调下供应商分配份额的取值区间"

支付模式	自有资金	$B < c Q *$	$c Q * ≤ B < B *$	$B ≥ B *$
正常支付	收益共享	$a ∈ Φ$	$a ∈ (0, φ (B)]$	$a ∈ (0,1)$
正常支付	回购契约	$a ∈ Φ$	$a ∈ (0, φ (B)]$	$a ∈ (0,1)$
垫付费用	收益共享	$a ∈ Φ$	$a ∈ (0, B / B *]$	$a ∈ (0,1)$
垫付费用	回购契约	$a ∈ Φ$	$a ∈ (0,1)$	$a ∈ (0,1)$
提前支付	收益共享	$a ∈ (0, B / B *]$	$a ∈ (0, B / B *]$	$a ∈ (0,1)$
提前支付	回购契约	$a ∈ (0,1)$	$a ∈ (0,1)$	$a ∈ (0,1)$

表5

表6

收益共享和回购契约优劣性比较"

初始资金	$B < c Q *$	$c Q * < B < B *$	$B ≥ B *$
正常支付	—	两个契约等价	两个契约等价
垫付费用	—	回购契约更优	两个契约等价
提前支付	回购契约更优	回购契约更优	两个契约等价

表6

图2

图3

图4

图5

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