Risk-neutral Supplier Research Articles

Loss-Averse Supply Chain Coordination with a Revenue-Sharing Contract

As economic fluctuations and market uncertainty intensify, supply chain members face enormous challenges. To explore the role of revenue-sharing contracts in supply chain members with different risk preferences, we study the risk-averse two-stage supply chain coordination in a revenue-sharing contract under three different scenarios: the supplier is risk-averse and the retailer is risk-neutral, or the retailer is risk-averse and the supplier is risk-neutral, or both are risk-averse. We find that the revenue-sharing contract mechanism allows the supplier to offer a lower wholesale price, effectively bearing part of the retailer’s cost risk. In return, the retailer compensates the supplier with a larger portion of their revenue, and the lower wholesale price also stimulates the retailer’s desire to order more products. In addition, risk aversion always reduces the optimal order quantity in the supply chain. Interestingly, when the retailer’s risk aversion level is low, the supplier charges a higher wholesale price under the risk-averse supply chain than that under the risk-neutral supply chain. However, if the retailer’s risk aversion level is high enough, the supplier should charge a lower price to stimulate the retailer under the risk-averse supply chain to retain the order size to maintain the channel profit.

Weather rebate contracts for different risk attitudes of supply chain members

Firms that deal with weather-sensitive products are often exposed to weather risk. How a weather rebate contract can be implemented to improve the performance of a supplier-retailer supply chain is investigated. The supplier offers a weather rebate to the retailer to compensate for the loss of sales due to weather risk. Depending on certain weather conditions, the retailer receives the rebate if it orders beyond a predefined ordering quantity. Depending on its risk attitude, the supplier uses weather derivatives to minimize the downside risk. The performance of weather rebate contracts is analyzed for three cases: risk-neutral supplier and risk-averse retailer, risk-averse supplier and risk-neutral retailer, and risk-averse supplier and risk-averse retailer. Conditional Value at Risk (CVaR) is used as the risk measure. The supply chain coordination under weather risk is investigated, and the specific conditions of a weather rebate contract leading to a Pareto-improving solution for both parties are obtained. To the best of the authors’ knowledge, this is the first study that investigates the weather rebate contract incorporating the risk attitude of the firms using a cooling degree days (CDD)/heating degree days (HDD)-based rebate structure. A comparative analysis between the weather rebate and wholesale price contracts is carried out based on the actual temperature and demand data. The results show that the weather rebate contract outperforms the regular wholesale price contract in all three cases. The study also demonstrates how to use weather derivatives to improve the performance of a supply chain dealing with weather-sensitive products.

Remanufacturing vs. greening: Competitiveness and harmony of sustainable strategies of supply chain under uncertain yield

This paper explores the interaction between a risk-neutral supplier and a risk-averse manufacturer in a supply chain considering the remanufacturing of green defective products under scarce yield information. The minimax-regret criterion is adopted by the manufacturer in response to the risk of scarce the information. In order to overcome the conservatism of minimax-regret criterion, we improve the model by integrating ideal profit and minimax regret. Based on the Stackelberg game framework, it is revealed that there is competitiveness between the sustainable strategies. Furthermore, this paper analyzes the evolutionary equilibrium between the competitive strategies based on the evolutionary game theory. Different from the conclusions in existing research that some sustainable strategies can cause free-riding behavior, this paper finds that the supplier’s greening raw materials may lead to a negative effect on the manufacturer by increasing her minimax regret, while the manufacturer’s remanufacturing defective products may reduce the supplier’s profit. The evolutionary stable strategy of the improved model indicates that the supplier will always prefer to the greening strategy. However, it is interesting to find that higher remanufacturing production cost, lower actual yield, and production cost can motivate the manufacturer to implement the remanufacturing strategy. The numerical results illustrate the impact of some factors, such as greening difficulty, consumer preference, as well as the upper and lower bounds of yield on the evolution speed and direction. Moreover, the improved model has a higher possibility of achieving better performance. The results can promote the harmonious transformation of supply chain to sustainable development.

Coordinating a three-level contract farming supply chain with option contracts considering risk-averse farmer and retailer.

We considered a three-level contract farming supply chain comprising a risk-averse farmer, a risk-neutral supplier, and a risk-averse retailer. The farmer plants and grows fresh agricultural products with yield uncertainty, the supplier is the leader of the supply chain and the designer of the contracts, and the retailer sells processed products with random demand. Under CVaR criterion, this paper discusses three option contracts between the supplier and the retailer, as well as wholesale price contracts or replenishment cost-sharing contracts between the supplier and the farmer. Results show that when the farmer is risk-neutral, option contracts with or without replenishment cost-sharing contracts can maximize the total profit and increase the profits of all members simultaneously. When the farmer and the retailer are risk-averse, only option contracts with replenishment cost-sharing contracts can ensure supply chain full coordination and Pareto improvement by adjusting the option parameters and making the farmer's sharing ratio equal to his risk aversion coefficient. Moreover, through numerical analysis, we discovered that the interval of the Pareto improvement decreases with the retailer's risk aversion coefficient and the quantity loss rate, and increases with the farmer's risk aversion coefficient. The supplier will not be able to increase his own profits when the loss rate is excessively large. Therefore, the leader should consider the risk aversion degree of all parties and the quantity loss rate of fresh agricultural products before choosing contracts.

Optimization and coordination in a service-constrained supply chain with the bidirectional option contract under conditional value-at-risk

<p style='text-indent:20px;'>This paper investigates the optimal operational decisions for the risk-neutral supplier and the risk-averse retailer in the supply chain with a service requirement under the conditional value-at-risk. Specifically, the optimal order and production policies with and without the bidirectional option contract are derived. Further, this paper shows that the optimal conditional value-at-risk of the retailer is non-increasing in the service requirement, while the optimal expected profit of the supplier is non-decreasing in the service requirement. When the service requirement is binding, the optimal conditional value-at-risk of the retailer is increasing in the risk aversion, while the optimal expected profit of the supplier is decreasing in the risk aversion. In addition, it is shown that with the bidirectional option contract, the service level provided by the retailer is equivalent to (higher than) that without them when the service requirement is (not) binding. Finally, this paper demonstrates that the bidirectional option contract can mitigate the effect of risk aversion on the retailer's order quantity, benefit both the retailer and supplier, and improve the performance of the supply chain. Numerical experiments are conducted to further confirm our results.</p>

Supply Chain Performance with Target-Oriented Firms

Problem definition: We study a supply chain in which a supplier sets the wholesale price and a retailer responds with an order quantity. Both of the two firms can be either risk-neutral—maximizing the expected profit—or target-oriented, which is to maximize her or his ability to reach a target profit. Academic/practical relevance: Our work not only sheds light on the benefit/loss of trading with target-oriented decision makers but also, adds new knowledge to the supply chain coordination literature. Methodology: We provide strong support for firms’ target-based preference and the linear target formation model through a survey as well as analyzing company data. With the firms’ target-oriented behavior evaluated by a CVaR-satisficing measure, we apply a game theoretical framework to investigate how the target-based preference affects supply chain performance. Results: A firm, be it a supplier or a retailer, is always hurt by its target-based preference but can benefit from its trading partner’s target-based preference. A risk-neutral supplier, for example, can sometimes reap the whole supply chain’s profit if the retailer is target-oriented, and a target-oriented supplier always performs better with a target-oriented retailer than a risk-neutral one. Furthermore, a target-oriented retailer and/or supplier can help alleviate the double-marginalization effect and with a specific target, can help the supply chain achieve the same efficiency level as in a risk-neutral centralized system, with just a wholesale price contract. Another important finding is that if both firms are target-oriented, then the supply chain can have a higher expected profit under a decentralized system than a centralized one. This contrasts with the case when both firms are risk-neutral. We also investigate the role of outside option and retailer-type misidentification and find that both can alleviate the retailer’s disadvantage of being target-oriented. Managerial implications: (i) The target-based preference can be exploited by the trading partner, and hence, a firm should adopt the target-oriented decision criterion with caution. (ii) A target-oriented retailer can explore strategies such as revealing his outside option or hiding his target-based preference in order to be less manipulated. (iii) Whether a firm (and the supply chain) can benefit from its trading partner’s target-based preference often depends on how ambitious the trading partner (and the firm itself if it is target-oriented) sets the target. (iv) Target-based preference of one or both firms can help the supply chain reach the first-best efficiency. (v) When both firms are target-oriented, decentralization can be preferred to centralization.

Wholesale price versus buyback: A comparison of contracts in a supply chain with a behavioral retailer

Traditional modeling in supply chain contract analysis shows that a wholesale price contract cannot coordinate a supply chain, whereas a buyback contract can coordinate. In this study, we consider a supply chain involving a risk-neutral supplier and a behavioral retailer under wholesale price and buyback contracts. We characterize the structural properties of the wholesale price contract in a supply chain with a behavioral retailer. Our study reveals that a wholesale price contract can coordinate a supply chain with a behavioral retailer under certain conditions. Under the same conditions, our analysis shows that a buyback contract coordinates the supply chain. Furthermore, we derive the conditions under which a buyback contract will not coordinate a supply chain involving a behavioral retailer. We validate our model with the existing experimental results on supply chain contracts. Finally, we show that a wholesale price contract can outperform a buyback contract in a supply chain having a behavioral retailer.

Research on Coordination of Fresh Agricultural Product Supply Chain considering Fresh-Keeping Effort Level under Retailer Risk Avoidance

Considering that the demand for fresh agricultural products is affected by product freshness and price, a two-level fresh agricultural product supply chain decision model consisting of a risk-neutral supplier and a risk-averse retailer is constructed. In order to increase consumer demand for fresh agricultural products, the supplier will make appropriate efforts to preserve the freshness of agricultural products. The optimal fresh-keeping effort level of the supplier and the optimal pricing decision of the retailer under the centralized decision-making and decentralized decision-making modes were studied, respectively; through the design of traditional cost-sharing contracts, traditional cost and revenue-sharing contracts, and cost-sharing and compensation strategies, the supplier was encouraged to improve their fresh-keeping effort. The research shows that the traditional cost-sharing contract and the traditional cost-benefit sharing contract cannot coordinate the supply chain. Under the strategy of cost sharing and compensation, when the amount of compensation meets certain conditions, the coordination of supply chain can be realized. Finally, the important parameters of the model are analyzed by numerical simulation.

Supply Chain Coordination with a Risk-Averse Retailer and the Call Option Contract in the Presence of a Service Requirement

This paper investigates a supply chain consisting of a single risk-neutral supplier and a single risk-averse retailer with the call option contract and a service requirement, where the retailer’s objective is to maximize the Conditional Value-at-Risk about profit. The optimal ordering quantity of the retailer and the optimal production quantity of the supplier are derived with the call option contract in the presence of a service requirement. Furthermore, by investigating the effect of the service level and the risk aversion on the supply chain, it is found that the retailer’s optimal Conditional Value-at-Risk is non-increasing in the service requirement and increasing in the risk aversion, while the supplier’s optimal expected profit is non-decreasing in the service and decreasing in the risk aversion. In addition, this paper demonstrates the impact of contract parameters on the service-constrained supply chain, and finds that the retailer’s optimal Conditional Value-at-Risk may be increasing, constant or decreasing in unit exercise price. Finally, with the call option contract, a distribution-free coordination condition is derived to achieve the Pareto improvement under Conditional Value-at-Risk criterion in the presence of a service requirement.

Coordinating Vulnerable Supply Chains with Option Contracts

We investigate vulnerable supply chain coordination with an option contract in the presence of supply chain disruption risk caused by external and internal disturbances. The supply chain consists of a single risk-neutral supplier and a risk-averse retailer. We characterize the retailer’s order quantity decision under the Conditional Value-at-Risk (CVaR) criterion and the supplier’s production decision. The results show that facing disruption risk and risk-aversion, both the retailer and the supplier would be more prudent to order and produce less than the risk-neutral scenario, inducing damage to the supply chain performance. The number of options purchased is decreasing in disruption risk and the risk-aversion of the retailer. The supplier will increase production as the disruption risk decreases or the shortage penalty increases. When the supplier does not know the risk-aversion of the retailer, the former will produce more and bear a higher overstock risk. We also investigate conditions that facilitate vulnerable supply chain coordination and find that the existence of risk-aversion and disruption risk restrict the option price and exercise price to lower price levels. Finally, we compare the option contract with wholesale price contract from the supplier’s and retailer’s perspectives through a numerical study.

A trade-credit-based incentive mechanism for a risk-averse retailer with private information

In a two-tier supply chain composed of a risk-neutral supplier and a risk-averse retailer, we consider the retailer’s sales cost to be private information and study the incentive effect of trade credit under information asymmetry. The model is formulated based on the principal–agent framework. We obtain the optimal trade credit contract configuration and further derive the optimal decision of the retailer, which are then compared with the results obtained from the benchmark case with symmetric information. We also analyze the influence of the retailer’s private information and risk-aversion behavior on the contract parameters and the retail price. The study shows that when the retailer’s risk aversion coefficient is within a certain range, the reasonable trade credit contract designed by the supplier can effectively encourage the retailer to report her real sales cost, and increase the supply chain profitability. Finally, numerical examples validate the theoretical model, and illustrate the impacts of private information and risk aversion on the profits of supply chain members and the system.

Coordination of a supply chain with a loss-averse retailer under supply uncertainty and marketing effort

<p style='text-indent:20px;'>This paper deals with a one-period two-stage supply chain, in which a loss-averse retailer facing stochastic demand orders products from a risk-neutral supplier subject to yield uncertainty. Marketing effort exerted by the retailer is employed to enhance the final market demand. We first establish a performance benchmark, and show that the wholesale price contract fails to coordinate the supply chain due to the effects of double marginalization and loss aversion. Then we propose a revenue-cost-sharing contract in order to achieve supply chain coordination. It is verified that a properly designed revenue-cost-sharing contract can achieve perfect coordination and a win-win outcome synchronously. Our results reveal that it is simple to implement and arbitrarily allocate the total channel profit between the retailer and the supplier. In addition, we examine the effect of the retailer's loss aversion degree on contract parameters and profit allocation, and we show that both the retailer and the supplier can benefit from marketing effort.</p>

Optimal decisions in supply chains with a call option contract under the carbon emissions tax regulation

Carbon emissions tax has been recognized as an effective market-based mechanism to curb carbon emissions, which makes every participant in the supply chain rethink their optimal operational decisions. Motivated by an iron and steel supply chain under the carbon emissions tax regulation, this paper investigates the optimal operational decisions for both supplier and retailer in the supply chain with a call option contract. Specifically, this paper considers a supply chain consisting of one risk-neutral supplier and one risk-averse retailer. To effectively match supply with the uncertain demand while reducing the carbon emissions, the retailer can choose to purchase call options from the supplier, and thus is allowed to adjust the final order quantities after the demand realization. The optimal order and production policies with and without the call option contract are derived. Further, it is demonstrated that the call option contract can benefit both the retailer and supplier, improve the performance of the whole supply chain and decrease invalid carbon emissions. In addition, the introduction of call option contracts can mitigate the effect of carbon emissions tax and risk aversion on the order quantity of the retailer. Finally, numerical experiments based on a real-world iron and steel supply chain are conducted to validate the theoretical findings and provide useful managerial insights.

Asymmetric information in subcontracting decisions: the effects of the first mover advantage

Purpose of the paper: The article analyses, in an adverse selection set-up, the effects of the first mover advantage in subcontracting decision between a manufacturer and a supplier in the situation of asymmetric information. Methodology: The study proposes a game theory model to analyze a supply chain consisting of a single risk-neutral supplier and a single risk-neutral manufacturer facing a contract definition problem. Results: The model suggests the strategies to obtain a more convenient arrangement for the manufacturer both in screening and signaling framework. Research limitations: The empirical examination with real-life data needs to be expanded and performed in a cross-sector context. Practical implications: The model helps the manufacturer in designing the appropriate arrangement for subcontracting relations and extracting hidden information from the suppliers. Originality of the paper: Our approach provides a comprehensive quantitative analysis of the effects of the first mover advantage in manufacturer-supplier relationships.

Supply Chain Performance with A Target-Oriented Retailer

Problem definition: We study a supply chain in which a supplier sets the wholesale price and a retailer responds with an order quantity. Both the two firms can be either risk-neutral—maximizing the expected profit—or target-oriented, which is to maximize her/his ability to reach a target profit. Academic/Practical relevance: Our work not only sheds light on the benefit/loss of trading with target-oriented decision makers, but also adds new knowledge to the supply chain coordination literature. Methodology: We provide a strong support for firms' target-based preference and the linear target formation model through a survey as well as analyzing company data. With the firms' target-oriented behavior evaluated by a CVaR-satisficing measure, we apply a game theoretical framework to investigate how the target-based preference affects supply chain performance. Results: A firm, be it a supplier or a retailer, is always hurt by its target-based preference, but can benefit from its trading partner's target-based preference. A risk-neutral supplier, for example, can sometimes reap the whole supply chain's profit if the retailer is target-oriented; and a target-oriented supplier always performs better with a target-oriented retailer than a risk-neutral one. Furthermore, a target-oriented retailer or/and supplier can help alleviate the double marginalization effect, and with a specific target can help the supply chain achieve the same efficiency level as in a risk-neutral centralized system, with just a wholesale price contract. Another important finding is that if both firms are target-oriented, then the supply chain can have a higher expected profit under a decentralized system than a centralized one. This contrasts to the case when both firms are risk-neutral. We also investigate the role of outside option and retailer type misidentification, and find that both can alleviate the retailer's disadvantage of being target-oriented. Managerial insights: i) the target-based preference can be exploited by the trading partner and hence a firm should adopt the target-oriented decision criterion with caution; ii) a target-oriented retailer can explore strategies such as revealing his outside option or hiding his target-based preference in order to be less manipulated; iii) whether a firm (and the supply chain) can benefit from its trading partner's target-based preference often depends on how ambitious the trading partner (and the firm itself if it is target-oriented) sets the target; iv) target-based preference of one or both firms can help the supply chain reach the first-best efficiency; and v) when both firms are target-oriented, decentralization can be preferred to centralization.

Supply chain coordination with risk-averse retailer and option contract: Supplier-led vs. Retailer-led

We investigate the coordination of both the supplier-led and the retailer-led supply chains under option contract. Specifically, we consider the option pricing, ordering, and producing problems in a supply chain consisting of a risk-neutral supplier and a risk-averse retailer behaving under the conditional value-at-risk (CVaR) criteria. The results show that, in a supplier-led supply chain, the supplier's production quantity equals the retailer's order quantity only if the penalty cost is high enough. In a retailer-led supply chain, the retailer will set the option price as low as possible in order to shift more risks to the supplier. By comparing results under both supply chain structures, we find that the retailer purchases more options at a lower price in the retailer-led supply chain, but the supplier's production quantities remain the same under both supply chain structures. Finally, we prove that both the supplier-led and the retailer-led supply chains can be coordinated under the same conditions, which is different from the conclusions obtained by previous studies.

Supply Chain Coordination with a Risk-Averse Retailer and a Combined Buy-Back and Revenue Sharing Contract

This paper investigates the ability of a combined buy-back (BB) and revenue sharing (RS) contract to improve the efficiency of a supply chain involving a risk-neutral supplier and a risk-averse retailer facing stochastic demand. We show that the combined contract can coordinate the supply chain under mild conditions. Further, the effects of risk aversion and contract parameters on the agents’ decision-making are analyzed when the retailer’s risk aversion is modeled by the conditional value-at-risk (CVaR) criterion. In contrast to individual BB and RS contracts, the combined contract is able to mitigate the effect of risk-aversion and allow the supplier to obtain higher expected profit. Moreover, situations exist where the combined contract can coordinate the supply chain when neither the BB nor the RS contract can coordinate it. Numerical experiments conducted further confirm the analytical results derived.

Optimal strategies for a three-level contract-farming supply chain with subsidy

We consider a three-level contract-farming supply chain with a risk-averse farmer, a risk-neutral supplier and a risk-neutral distributor, in which the farmer faces a yield uncertainty and the government offers agricultural subsidy to the farmer. The CVaR criterion is used to describe the risk-averse behavior of the farmer. We derive the optimal strategies of the supply chain and perform some sensitivity analysis to investigate the effects of the government subsidy and other factors. The results indicate that, as the subsidy increases, the farmer's total target production increases. Further analysis shows that the total production increase is mainly from the increased farm size, and the farmer's endeavor actually decreases. In addition, the results indicate that the profits of the supplier and the distributor both increase with respect to the subsidy. However, the impact of the subsidy on the farmer's profit depends on the farmer's degree of risk-averse. In particular, the impact of the subsidy to the farmer's profit tends to be positive for farmers with high degree of risk-averse, and the impact tends to be negative for those with low degree of risk-averse. The sensitivity analysis is also performed for the level of yield uncertainty in term of the standard deviation.

Effective and necessary: Individual supplier behavior in revenue sharing and wholesale contracts

We consider under what conditions a revenue sharing contract is most effective at improving system efficiency relative to a simple wholesale price contract. We find that a complex coordinating contract is not always necessary because the wholesale price contract may perform sufficiently well; and coordinating contracts are not always effective if decision makers are strongly risk averse. Using a behavioral laboratory approach, we investigate how a supplier's risk aversion and fairness concerns influence how they set the pricing parameter(s) of a contract. We find that risk-neutral self-interested suppliers were able to improve the system and their own profits significantly under revenue sharing compared to wholesale pricing. However, individual behavioral factors of risk aversion or fairness preferences often made the more complicated revenue sharing contract either ineffective or unnecessary. Specifically, given a fairness-seeking supplier, the simple wholesale price contract is comparably efficient to the revenue sharing contract set by a risk-neutral supplier and we find the coordinating contract is unnecessary. Conversely, given a strongly risk-averse supplier with no concerns for fairness a revenue sharing contract is ineffective in overcoming double marginalization.

Optimal Decisions of a Supply Chain With a Risk-Averse Retailer and Portfolio Contracts

In this paper, we investigate a supply chain involving one risk-neutral supplier and one risk-averse retailer, where the retailer adopts the conditional value-at-risk (CVaR) criterion as his performance measure. To hedge against high risk, the retailer purchases call options from the supplier to adjust his firm orders. We derive the optimal order and production policies, with and without a call option contract and demonstrate that the call option contract can benefit both the retailer and the supplier. In addition, we also generate insights regarding how the contract parameters, level of risk aversion and shortage cost impact the retailer’s optimal policy, highlighting the importance of considering the risk aversion and shortage cost simultaneously. Finally, we derive the condition for the supply chain to be coordinated and show that compared to non-coordinating contracts, the wholesale price and call option portfolio contracts proposed in this paper can achieve Pareto optimality. Numerical experiments are conducted to demonstrate theoretical results and observations.