This paper explores a coordination model for a three-echelon supply chain including two different manufacturers, one distributer and one retailer via the combined option and back contracts. And one manufacturer provides the high wholesale price with low supply disruption risk and the other is completely the opposite. This differs from the previous supply chain coordination model. Firstly, supply disruption is added to the three-echelon supply chain. Secondly, considering the coordination of the supply chain, we deploy the combined option and back contracts which are seldom used in the previous study. Furthermore, it is interesting that supply disruption risk and buyback factor do not affect the distributor’s order quantity from the manufacturer who has low product price and unreliable operating ability, while the order quantity increases with the rise of option premium and option strike price. The distributor’s order quantity from the manufacturer, which has high product price and reliable operating ability, increases with the rise of supply disruption risk but decreases when the buyback factor, option premium, and option strike price decrease.
With the growing popularity of the online shopping, logistics industry in China has shown significant development recently. Nevertheless, many unexpected changes may hinder the normal operation of the supply chain, for instance, the insufficient supply of spare parts in Toyota in 1997, the shortage of chips in Apple in 1999, the fire at a supplier of Ericsson in 2000, and the sea earthquake in Miyagi in Japan resulting in disruption of supply of car spare parts on 11 March, 2011. All of the accidents discussed above have led to a sense of danger among the people or a great loss to both the local economy and people’s lives. Supply chain can be disrupted by many events, such as natural disasters, bankruptcy, strikes by workers, terrorist attacks, and policy failures. Supply chain enterprises have to face diverse external risks and the internal risks of supply chains are ubiquitous. Supply chain enterprises are independent economic entities in market, pursuing the maximum individual profits, and potential conflicts of interest exist as stance, rationality, knowledge background, and mindsets of enterprises vary and engender variations in understanding. All the players of a supply chain are greatly affected by such demand disruptions, which can also affect the performance of a supply chain significantly and cause irreversible losses to the supply chain. This poses a challenge to managers regarding what can be done to maintain coordination of the supply chain and reduce the damage. The issue of how to tackle the uncertain disruptions efficiently and effectively has become increasingly significant to the managers nowadays. To the best of our knowledge, little attention has been paid to such problems in current research and how to coordinate the supply chain with interruption risk is another problem we intend to tackle.
With regard to the problem of coordinating the supply chain, option contract has been widely used. And the option contract means that the player orders some product before the selling season with certain wholesale price per unit and purchases the product with another strike price per unit. Its advantage is that the option contract is beneficial to solve the supply chain in an unstable environment, which had been investigated in the previous study. Ritchken and Tapiero [
In addition to the option contract, growing importance has also attached to the buyback contract because of its advantage. For example, it is easy to calculate the parameter of buyback or it is equal to the revenue sharing contract [
Most of the research discussed above is concerned with one single option contract or buyback contract based on two-echelon supply chains, whose external environment is relatively stable. It is seldom to see the use of combined contracts to tackle the supply chain with disruption risk under unstable environment, which is not inevitable in practice. The buyback contract has been extensively studied in the previous research, which has received considerable attention in practice. Certainly, the option contract has its own advantage, and thus we choose the combined contract. Therefore, this paper attempts to address these problems. Firstly, integrating the advantages of the option contract and the buyback contract, this paper applies the two contracts together to coordinating the supply chain. Secondly, to be closer to the real-life environment, we consider the three-echelon supply chain model with two different suppliers (called dual sourcing purchase), one distributor and one retailer. In addition, considering the recent situation, we cannot neglect the disruption risk factors in the supply chain. Consequently, supply disruption risk factors are considered in this paper. And the buyback contract is deployed to stimulate and lead the retailers to increase ordering quantity; the distributor shares the partial risk engendered by demand uncertainty; a balance can be struck between marginal revenue and marginal cost of distributors and retailers. The disruption risk can be hedged by distributors who select options.
Here, the single three-echelon supply chain includes two manufacturers, one distributor and one retailer, among which Manufacturer 1 can reduce supplies of low-price products and supply disruption is likely to occur; Manufacturer 2’s products have a relatively higher price, but they are stable and reliable. The upstream enterprises provide single products for downstream enterprises that are mutually independent, without cross-echelon relations. Before sales, the manufacturer and the distributor offer contracts to the downstream enterprises; retailers determine the ordering quantity in terms of the market demand and the contract provided by the distributor. At the same time, the distributor determines their ordering quantity according to the ordering quantity of retailers and the contract of the manufacturers (see Figure
Research network chart.
At the same time, the symbols used in the modes are shown in Notations. The superscript
The following are the hypotheses used for building and testing the models.
Participants in supply chains are completely rational, and they are risk-neutral.
All distribution functions are two-echelon and differential, and there are strict single inverse functions.
With
With
With
Manufacturers play leading roles and the distributer acts as the follower.
In centralized supply chains, the manufacturers, the distributor, and the retailer are considered as a whole, and the objective is to maximize the overall profits of the supply chain, regardless of the internal transference of payments between member enterprises. There is no “dual-marginalized effect” in supply chains, and it is a typical newsvendor model.
Below is the overall profit of supply chains when disruptions occur to Manufacturer 1:
Below is the overall profit of supply chain when disruptions do not happen to Manufacturer 1:
Now, below is the overall profit expected of supply chain:
With
The optimum ordering quantity can be derived based on the above equations.
The optimum ordering quantity is
Equation (
Manufacturers play a leading role in supply chains. The optimal wholesale price and option contracts can be determined by the possible responses of the distributors, and distributors follow manufacturers. The distributor’s optimal ordering quantity is determined by the manufacturer’s information. Then, the distributor plays a leading role and the Stackelberg game comes into play between the distributor and the retailer. The decision is made through Stackelberg reverse induction. The sequence of steps in the option order is as follows. At the beginning, the distributor reserves the future The distributor is informed about the disruption from Manufacturer 1. The distributor obtains the ordering information from the retailer. The distributor invokes some option contracts from Manufacturer 2. Manufacturer 2 satisfies the distributor’s demands.
Calculating the first-order value of the distributor’s profit, we can get the optimal order quantity from the manufacturer. Below is the distributors’ profit when disruptions occur, in which the notations
Below is the distributor’s profit without disruptions:
Now, below is the expected profit of the distributor:
With
The proof of
With
The optimal conditions of KKT (the Karush-Kuhn-Tucker) are based on the ideas proposed by Karush [
The four possibilities to be analyzed are (a)
Calculating the first derivation value of the retailer’s profit, we can get the optimal order quantity from the distributor and the optimal wholesale price given by the distributor to the retailer. Below is the retailer’s profit with disruptions:
Below is the retailer’s profit without disruptions:
Now, below is the expected retailer’s profit:
When the above equation is calculated for
Here, the option contract is combined with buyback contract, and the three-echelon supply chain is coordinated and optimized through designing the corresponding parameters. In the allied contracts, the following conditions must be satisfied to achieve complete coordination of the supply chain.
In the allied contract consisting of the option contract and the buyback contract, if complete coordination is to be achieved in the supply chain, then the contract parameters must satisfy the following cases. Case 1. Consider the following: Case 2. Consider the following:
Equations (
When the three-stage supply chain is coordinated, the buyback factor
When
The increase of the ordering quantity from Manufacturer 1 does not follow the rise of the disruption risks, and the ordering quantity from Manufacture 2 does not decline with the rise of the disruption risks.
The larger the buyback factor
The ordering quantity by distributors from Manufacturer 1 does not decline with the rise of option purchasing prices and option strike prices, and the ordering quantity by the distributor does not increase with the rise of option premium and the option strike prices.
When
With
As the first derivation of
With
With
The first derivation
Likewise, with
The first derivation of
We deploy MATLAB to do the simulation. Similar to Li et al. [
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150 | 25 | 5 | 45 | 40 | 80 | 5 | 10 | 0.1 | 0.1 | 1350 | 380 |
The optimal ordering quantity under decentralization and each contract is shown in Table
The optimal ordering quantity under decentralization and each contract.
Decentralized | Buyback contract | Option contract | |
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Economic ordering quantity | 1365.367393 | 1375.084489 | 1849.519365 |
The optimal profit under decentralization and contract coordination is shown in Table
The optimal profits with decentralized model and contract coordination.
Supply chain type | Retailer’s profits | Distributor’s profits | Overall profits of manufacturers | Total profits of supply chain |
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Decentralized model | 77745.8466 | 40961.0218 | 34134.18483 | 152841.0533 |
Contract coordination | 78259.9824 | 45268.9764 | 37137.92283 | 160666.8817 |
Tables
If other parameters are definite, the possibility of occurrence of different disruption risks, buyback factors, option strike prices, and changes of option premium will have an impact on ordering quantity (Figures
The impact of different disruption risks on ordering quantity.
Figure
It can be seen from Figure
The impact of different buyback factors
Figures
The impact of different option strike prices
The impact of different option premium
The main findings of this paper are as follows. Firstly, integrating the advantages of the option contract and the buyback contract, this paper applies these two contracts together to coordinating the supply chain. Secondly, to be closer to the practical environment, we consider the three-echelon supply chain model with two different suppliers (called dual sourcing purchase): one distributor and one retailer. In addition, considering the practical situation in recent years, we cannot ignore the disruption risk factors in the supply chain. Consequently, supply disruption risk factors are considered in this paper. And the buyback contract is used to stimulate and lead the retailer to increase ordering quantity; the distributor shares the partial risk engendered by demand uncertainty; a balance can be struck between marginal revenue and marginal cost of the distributor and the retailer. The disruption risk can be hedged by the distributor who selects options.
This study has investigated the three-echelon supply chain mode with random demand, where distributors are able to choose one of two manufacturers; one has lower-price products but disruptions are more likely to occur, and the other has stable supply but its price of products is relatively higher. The proposed model incorporates an option contract and a buyback contract, whose coordination can help achieve the optimal ordering strategies. It is revealed that increased ordering from a stable source can mitigate the disruption risks in supply chains, suggesting greater adaptability and robustness in optimization of the operation of supply chains. In dual sourcing purchasing, disruption risks do not affect the ordering quantity from enterprises with lower-price products and unstable operations, whereas the ordering quantity of option contracts from enterprises with high-price products and stable supply will increase accordingly. In specific circumstances, it is likely to choose suppliers with relatively stable operations but relatively higher prices. The buyback factor, option premium, and option strike prices influence the ordering decisions by the distributor. When the buyback factor, option purchasing prices, and option strike prices are greater, the distributor reduces the ordering quantity of products which are stable but costly and tends to buy unstable and cheaper products which tend to increase with the rise of option premium and option strike prices but will not be affected by the buyback efficiency. The buyback factor can stimulate the order from the retailer. These conclusions might provide important references for supply chain members when they make decisions.
Here, it is assumed that the risks of supply chain enterprises are neutral, and it is worth investigating the circumstances with different risk preferences. In addition, there are many measures to mitigate the supply chain disruptions, but we only consider the dual sourcing purchasing strategy, whereas other different strategies can also be addressed in future research to develop the many-to-many models. The disruption risks and demand uncertainties can be estimated, and further research can consider the impact engendered by estimation errors of measurement or different strategies in misjudgment on profits of supply chain enterprises.
The ordering quantity of distributors from Manufacturer 1
The option purchasing quantity of distributors from Manufacturer 2
Option premium
Option strike prices
The probability of disruptions for Manufacturer 1 (
Production cost of the two manufacturers
Wholesale prices provided by Manufacturer 1 for distributors
Wholesale prices provided by distributors 1 for the retailer
Sale prices of the retailer
Buyback price factor of distributors
Shortage cost of the retailer and commodity salvage, respectively
The random demand of the retailer’s market; the random variable is continuous
The random demand probability density function of the retailer’s market; random demand cumulative distribution function of the retailer’s market
The random demand probability distribution function of the retailer’s market;
The overall profit of centralized supply chain without contract
The expected overall profit of centralized supply chains without contracts
Ordering quantity of the retailer
The optimum ordering quantity of the centralized supply chain system without contract
The optimum ordering quantity of the decentralized supply chain system without contracts
Profits of the retailer
Profits of the distributor
Expected profits of the retailer
Expected profits of the distributor.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This paper is financially supported by the Natural Science Foundation of China (Grant no. 71172194, Grant no. 71390330, Grant no. 71390331, and Grant no. 71221001).