When the demand is sensitive to retail price, revenue sharing contract and two-part tariff contract have been shown to be able to coordinate supply chains with risk neutral agents. We extend the previous studies to consider a risk-averse retailer in a two-echelon fashion supply chain. Based on the classic mean-variance approach in finance, the issue of channel coordination in a fashion supply chain with risk-averse retailer and price-dependent demand is investigated. We propose both single contracts and joint contracts to achieve supply chain coordination. We find that the coordinating revenue sharing contract and two-part tariff contract in the supply chain with risk neutral agents are still useful to coordinate the supply chain taking into account the degree of risk aversion of fashion retailer, whereas a more complex sales rebate and penalty (SRP) contract fails to do so. When using combined contracts to coordinate the supply chain, we demonstrate that only revenue sharing with two-part tariff contract can coordinate the fashion supply chain. The optimal conditions for contract parameters to achieve channel coordination are determined. Numerical analysis is presented to supplement the results and more insights are gained.
Fashion supply chain is characterized by short product life cycle, high volatile customer demand, and clients’ varying tastes [
Coordination among supply chain agents via setting incentive alignment contracts is a hot topic in supply chain management. Under the coordinating contracts, the incentives of supply chain agents are aligned with the objective of the whole supply chain so that the decentralized supply chain behaves as well as the vertically integrated supply chain. Without supply chain coordination, problems involving double marginalization will prevail [
Revenue-sharing contract indicates that the newsvendor retailer pays the upstream manufacturer a unit wholesale price for each unit ordered plus a proportion of his revenue from selling the product. Both theoretical and empirical studies have been carried out on the effect of revenue-sharing contract in the video cassette rental industry [
Under a two-part tariff contract, the retailer gives the manufacturer a fixed transfer payment apart from the unit wholesale price for each unit purchased. And it has also been shown that a two-part tariff contract coordinates the supply chain, when the optimal value of unit wholesale price equals the manufacturer’s unit production cost [
Sales rebate and penalty (SRP) is based on the retailer’s sales performance. With a SRP contract, the manufacturer will specify a certain sales target prior to the selling season. Different from sales rebate which executes rebate only, for each unit sold above the target level, the retailer will be granted a unit rebate, or else the retailer must pay the manufacturer a penalty. In supply chain management, both SRP contract and sales rebate contract have been demonstrated unable to coordinate the channel when the demand is sensitive to retail price or the retailer’s sales effort [
Early studies considered retail price exogenous, leaving the retailer with the decision of order quantity alone in order to maximize expected profit. As retail price plays an important role in marketing channel, a new steam of research on supply chain coordination and contracting integrates pricing into the order quantity decision of the retailer under different demand models. Reviews of this work [
However, the common results derived from the previous studies may not be precise in operations management since, in the real world, different decision makers may have different degrees of risk aversion. in light of this, we extend the results of proceeding studies to explore the issue of supply chain coordination with risk-averse fashion retailer and price-dependent demand. Specifically, we investigate a single period, one-manufacturer one-retailer fashion supply chain with a variety of contracts. The manufacturer, acting as the leader in the Stackelberg game, offers the retailer a contract with a set of contract parameters. The fashion retailer, acting as the follower, sets self-interest order quantity and retail price as a response. We propose both single contracts and combined contracts with the optimal values of contract parameters to achieve channel coordination within fashion supply chain.
The main objectives of our study cover the following: firstly, to explore whether the coordinating revenue-sharing contract and two-part tariff contract in supply chains with risk neural retailer can still coordinate the fashion supply chain with risk-averse retailer who has to choose retail price in addition to stocking quantity; secondly, to compare the performance of a more complicated sales rebate and penalty contract in supply chain coordination with the performances of revenue-sharing contract and two-part tariff contract; finally, when joint contracts are got by taking advantages of the three single contracts, to probe whether the resulting combined contracts are useful to coordinate the supply chain.
In recent years, an increasing number of researchers have noticed the importance and the impact of risk aversion in supply chain contracting and coordination and sought in succession for the criteria to depict supply chain agents’ risk aversion attitude or preference. In the literature, the measures for describing risk aversion involve mean-variance (MV) [
This paper is closely linked to the literature on supply chain coordinating and contracting with price-dependent demand [
The paper is organized as follows. Model formulation and notation definition are presented in Section
Consider a two-echelon fashion supply chain with a risk-neutral manufacturer and a risk-averse retailer. The retailer sells a fashion product whose demand is sensitive to retail price. The upstream manufacturer produces the product and sells it through a vertically separated retailer. The sequence of events in the supply chain is as follows. The manufacturer, as the leader of a Stackelberg game, offers the retailer a contract. After knowing the details of the contract, the fashion retailer commits his order quantity and retail price. Then the manufacturer organizes the production and delivers the finished products to the retailer prior to the selling season. Afterwards, the selling season starts, and the demand is realized. At the end of the selling season, based on the agreed contract, both the manufacturer and the retailer perform the respective contract terms and achieve transfer payments between each other.
Let
In the literature, there are two fashions in which the demand
In order to ensure the existence and uniqueness of model results, we give the following definitions of
By definition,
Price elasticity
For the ease of position, in this paper, we suppose a linear demand of
Define
It is noted that, in the literature, various random distributions exhibit IFR property, involving uniform and normal distributions.
To capture the decision making of risk-averse fashion retailer, we adopt the same risk aversion decision model as in [
First, we offer a benchmark by analyzing the case when the fashion supply chain is vertically integrated so that the manufacturer owns its own retailer. Note that the type of contract does not affect the performance of the integrated fashion supply chain. The optimal solutions to this model are production level
Let
Under the additive price-dependent demand, the integrated supply chain’s optimal joint decision
For any given
From (
By taking
Substituting (
Define
From Definition
Hence, there exists a unique retail price
Since
Proposition
Now we consider the case when the fashion supply chain is decentralized. In the decentralized supply chain, the manufacturer and the fashion retailer are independent and enter a Stackelberg game as described before. Specifically, the retailer is assumed to be risk-averse with an expected profit threshold
With a SRP contract
In this setting, the fashion retailer’s profit, expected profit and the variance of profit are
For a given SRP contract
For any given
From (
Thus, we know that
Substituting
From (
By taking (
Similar to Proposition
By Comparing (
A revenue-sharing contract
For a given revenue-sharing contract
Similar to Proposition
Comparing (
With a two-part tariff contract
For a given two-part tariff contract
Similar to Proposition
By comparing (
Now, by considering the risk aversion decision model, as given in
Under single contracts, for any given
From (
Given the retailer’s expected threshold
From the proceeding analysis, we know that under single contracts, such as SRP contract, revenue-sharing contract and two-part tariff contract,
From Proposition
A contract provided by the upstream manufacturer is said to coordinate the supply chain if it is able to align the incentives of the manufacturer and the retailer so that the independent retailer makes the same decisions as the integrated supply chain, namely,
For any given
If a contract achieves supply chain coordination, then
If
From Proposition
Next, we investigate in more detail whether the single contracts above could achieve supply chain coordination.
For any given
From Proposition
From
For any given for revenue-sharing contract, for two-part tariff contract,
According to Proposition
Similarly, for two-part tariff contract, from
From Propositions
From Proposition
In the above section, we investigate the role of three single contracts in coordinating fashion supply chains and find that a more complicated SRP contract fails to coordinate the supply chain while two other simpler contracts perfectly achieve channel coordination. In this section, we further explore contracts that combine the advantages of the above contracts. Specifically, we try to explore whether the resulting contracts are effective to coordinate the supply chain when the coordinating contracts and the failed contract combine with each other. Define similarly
Under this contract, the fashion retailer’s profit, expected profit, and the variance of profit are
For a given SRP with revenue-sharing contract offered by the manufacturer, the risk-neutral fashion retailer’s optimal joint decision
Similar to Proposition
By comparing (
In this setting, the fashion retailer’s expected profit and the variance of profit are given by
For a given SRP with two-part tariff contract offered by the manufacturer, the risk-neutral fashion retailer’s optimal joint decision
Comparing (
Under a revenue sharing with two-part tariff contract, the fashion retailer’s expected profit and the variance of profit are as follows:
Similar to SRP with two-part tariff contract, the optimal joint ordering-pricing decision for the risk-neutral fashion retailer under revenue sharing with two-part tariff contract is equal to that under a single revenue-sharing contract. Hence, revenue sharing with two-part tariff contract is able to achieve channel coordination in the fashion supply chain with risk-averse retailer and price-dependent demand.
As a result, it only remains uncertain whether SRP with revenue-sharing contract could achieve supply chain coordination with risk-averse retailer. Following the similar approach as presented in Section
From (
For any given
From Proposition
It is interesting to discover that, although a single revenue-sharing contract itself could coordinate the quantity and pricing decisions in the fashion supply chain with risk sensitive retailer, the combined SRP with revenue-sharing contract cannot optimize the whole supply chain’s profit. To some extent, this means that, when faced with more intricate supply chain circumstance, perhaps a simpler contract is more effective and efficient to achieve channel coordination in comparison with a more complicated one.
Furthermore, when a single revenue-sharing contract and a single two-part tariff contract can coordinate the supply chain with risk-averse retailer and price-dependent demand, a composite contract of these two contracts would still be effective to coordinate the supply chain. Instead, a single SRP contract cannot achieve channel coordination; thus when it combines with revenue-sharing contract or two-part tariff contract, the resulting combined contract is still unable to coordinate the fashion supply chain.
In this section, we present numerical analysis to gain more insights on supply chain coordination with contracts. We focus on the coordinating revenue-sharing contract, two-part tariff contract, and the combined revenue sharing with two-part tariff contract here. Numerical analysis can be decomposed into two parts: one is to investigate how to determine the optimal values of contract parameters, and the other is sensitivity analysis to explore the impacts of some important parameters on supply chain coordination and objectives of supply chain members.
First, we give the values of parameters used in this section. Suppose the base demand
We consider six values of
Optimal values of contract parameters for different values of
|
Revenue-sharing contract | Two-part tariff contract | Revenue sharing with two-part tariff contract | ||||
---|---|---|---|---|---|---|---|
|
|
|
|
|
|
| |
1000 | 2.37 | 0.16 | 15 | 5326.70 | 0.2 | 3 | 265.34 |
2000 | 4.74 | 0.32 | 15 | 4326.70 | 0.4 | 6 | 530.68 |
3000 | 7.11 | 0.47 | 15 | 3326.70 | 0.5 | 7.5 | 163.35 |
4000 | 9.48 | 0.63 | 15 | 2326.70 | 0.7 | 10.5 | 428.69 |
5000 | 11.85 | 0.79 | 15 | 1326.70 | 0.8 | 12 | 61.36 |
6000 | 14.23 | 0.95 | 15 | 326.70 | 0.96 | 14.4 | 73.63 |
From Table
Now, we study the effects of some important parameters on supply chain coordination and objectives of supply chain members. Firstly, we focus on revenue-sharing contract with parameters such as base demand
Sensitivity analysis for revenue-sharing contract.
Parameter |
|
|
|
|
|
|
|
|
| |
---|---|---|---|---|---|---|---|---|---|---|
|
400 | 87.47 | 180.69 | 30.68 | 2000 | 13.97 | 0.93 | 2147.18 | 676524.01 | 586954.45 |
500 | 98.67 | 239.54 | 35.91 | 3000 | 11.31 | 0.75 | 3977.72 | 1236932.08 | 703589.94 | |
600 | 106.74 | 296.18 | 41.06 | 5000 | 11.85 | 0.79 | 6362.70 | 1931261.13 | 1206220.67 | |
700 | 112.89 | 351.36 | 46.15 | 8000 | 13.06 | 0.87 | 9187.50 | 2751202.56 | 2085967.18 | |
800 | 117.74 | 405.53 | 51.22 | 10000 | 11.95 | 0.80 | 12556.40 | 3691564.92 | 2341424.45 | |
900 | 121.67 | 458.97 | 56.27 | 14000 | 12.78 | 0.85 | 16431.10 | 4748912.61 | 3447602.58 | |
1000 | 124.93 | 511.85 | 61.31 | 20000 | 14.42 | 0.96 | 20810.09 | 5920873.15 | 5468870.88 | |
| ||||||||||
|
10 | 106.74 | 296.18 | 41.06 | 200 | 0.47 | 0.03 | 6362.70 | 1931261.13 | 1929.95 |
15 | 84.57 | 240.96 | 29.57 | 200 | 1.04 | 0.07 | 2895.46 | 578223.79 | 2758.79 | |
20 | 64.53 | 188.77 | 23.79 | 200 | 2.18 | 0.15 | 1375.39 | 185400.79 | 3920.33 | |
25 | 46.29 | 138.99 | 20.29 | 200 | 4.89 | 0.33 | 613.05 | 54132.63 | 5761.4 | |
30 | 29.57 | 91.15 | 17.95 | 200 | 13.33 | 0.89 | 225.07 | 11800.57 | 9317.77 | |
| ||||||||||
CV | 15% | 118.25 | 290.64 | 42.76 | 4000 | 8.15 | 0.53 | 7537.51 | 269951.09 | 76023.73 |
35% | 255.40 | 383.92 | 47.15 | 4000 | 6.30 | 0.42 | 9522.90 | 6935423.41 | 1223642.39 | |
55% | 296.77 | 424.47 | 47.23 | 4000 | 6.62 | 0.44 | 9059.38 | 18604230.72 | 3626893.02 | |
75% | 94.84 | 291.40 | 40.34 | 4000 | 10.12 | 0.67 | 5930.02 | 2154476.37 | 980278.33 | |
95% | 45.88 | 258.58 | 38.73 | 4000 | 11.21 | 0.75 | 5354.43 | 649949.19 | 362321.17 |
From Table
However, it can be found from Table
In addition, we also try to illustrate the effect of different degrees of demand uncertainty. We define demand uncertainty as
Similarly, following the same method, we could also get the results of sensitivity analysis for the other two coordinating contracts—two-part tariff contract and revenue sharing with two-part tariff contract. They are summarized in Tables
Sensitivity analysis for two-part tariff contract.
Parameter |
|
|
|
| |
---|---|---|---|---|---|
|
400 | 2000 | 15 | 147.18 | 676524.01 |
500 | 3000 | 15 | 977.72 | 1236932.08 | |
600 | 5000 | 15 | 1326.70 | 1931261.13 | |
700 | 8000 | 15 | 1187.50 | 2751202.56 | |
800 | 10000 | 15 | 2556.40 | 3691564.92 | |
900 | 14000 | 15 | 2431.11 | 4748912.61 | |
1000 | 20000 | 15 | 810.09 | 5920873.15 | |
| |||||
|
10 | 200 | 15 | 6126.70 | 1931261.13 |
15 | 200 | 15 | 2659.46 | 578223.79 | |
20 | 200 | 15 | 1175.39 | 185400.79 | |
25 | 200 | 15 | 413.05 | 54132.63 | |
30 | 200 | 15 | 25.07 | 11800.57 | |
| |||||
CV | 15% | 4000 | 15 | 3537.51 | 269951.09 |
35% | 4000 | 15 | 5522.90 | 6935423.41 | |
55% | 4000 | 15 | 5059.38 | 18604230.72 | |
75% | 4000 | 15 | 1930.02 | 2154476.37 | |
95% | 4000 | 15 | 1354.43 | 649949.19 |
Sensitivity analysis for revenue-sharing with two-part tariff contract.
Parameter |
|
|
|
|
| |
---|---|---|---|---|---|---|
|
400 | 2000 | 0.95 | 14.25 | 39.83 | 610562.93 |
500 | 3000 | 0.8 | 12 | 182.18 | 791636.53 | |
600 | 5000 | 0.8 | 12 | 61.36 | 1236007.12 | |
700 | 8000 | 0.9 | 13.5 | 268.75 | 2228474.07 | |
800 | 10000 | 0.85 | 12.75 | 672.94 | 2667155.65 | |
900 | 14000 | 0.9 | 13.5 | 787.99 | 3846619.22 | |
1000 | 20000 | 0.98 | 14.7 | 393.89 | 5686406.57 | |
| ||||||
|
10 | 200 | 0.1 | 1.5 | 432.67 | 19312.61 |
15 | 200 | 0.2 | 3 | 379.09 | 23128.95 | |
20 | 200 | 0.4 | 6 | 350.15 | 29664.13 | |
25 | 200 | 0.7 | 10.5 | 229.13 | 26524.99 | |
30 | 200 | 0.9 | 13.5 | 2.56 | 9558.46 | |
| ||||||
CV | 15% | 4000 | 0.7 | 10.5 | 1276.26 | 132276.03 |
35% | 4000 | 0.6 | 9 | 1713.74 | 2496752.43 | |
55% | 4000 | 0.5 | 7.5 | 529.69 | 4651057.68 | |
75% | 4000 | 0.8 | 12 | 744.02 | 1378864.88 | |
95% | 4000 | 0.9 | 13.5 | 818.99 | 526458.84 |
From Table
Similar analysis could be realized for the joint revenue sharing with two-part tariff contract. What is worth noting here is that, in Table
In this paper, the issue of supply chain coordination with risk-averse retailer and price-dependent demand is studied. We extend in this paper the previous works to consider a risk-averse retailer in a two-stage fashion supply chain. Adopting the additive price-sensitive demand model, we construct the benchmark solution to the integrated fashion supply chain. Using the classic MV formulation in portfolio management in finance to characterize the risk sensitive fashion retailer’s decision models, we propose both single contracts and combined contracts to achieve channel coordination. We find that, under single contracts, the coordinating revenue-sharing contract and two-part tariff contract in supply chains with risk-neutral agents could still coordinate the supply chain with risk sensitive retailer. However, a more complicated sales rebate and penalty contract fails to do so. Then we try to combine traditional single contracts to explore whether the resulting joint contracts are useful to coordinate the supply chain. It is found that only the joint revenue sharing with two-part tariff contract is able to achieve supply chain coordination. By presenting numerical analysis to illustrate analytical results, we discuss the determination of optimal values of contract parameters in coordinating contracts as well as sensitivity analysis to explore the effects of base demand, price elasticity, and the degree of demand uncertainty on supply chain coordination and objectives of supply chain members.
We highlight the managerial insights of our results in the following. Mean-variance formulation for risk analysis in supply chains is intuitive to decisions makers, making it easy and applicable for managers and practitioners in fashion supply chains to use proposed models to determine the type of contract and the optimal values of contract parameters to achieve channel coordination. This paper captures the fundamental feature of retailing fashion channel that the fashion retailer could influence the end demand by setting appropriate retail price. Our findings indicate that, in such complicated retailing situation, it may be more effective for real managers to adopt relatively simple contracts, so as to achieve coordination. Moreover, the theoretical results offer references to decision makers on the conditions a contract must satisfy to coordinate fashion supply chains, which is significant for improving efficiency in such supply chains with effective retailing channels and fashion retailer’s risk aversion preference or attitude.
In this paper, we just focus on channel coordination in single period, single manufacture, and single retailer fashion supply chain. Future research on supply chain coordination over multiple periods or with multiple competing risk-averse retailers would be a meaningful direction and could produce more insights.
The authors sincerely thank the Editor-in-Chief and the three anonymous reviewers for their valuable comments and suggestions on the revision of the paper. This paper was supported in part by (1) the Fund for Humanity and Social Science of the Ministry of Education, China, under Grant 09YJC630230; (2) the Natural Science Foundation of Hunan Province, China, under Grant 10JJ3023.