Coordinating Vulnerable Supply Chains with Option Contracts

2021 ◽  
pp. 2050053
Author(s):  
Zhongyi Liu ◽  
Shengya Hua ◽  
Guanying Wang
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Numerical Study ◽  
Supply Chain Coordination ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Option Contract ◽  
Risk Neutral ◽  
Disruption Risk

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.

scholarly journals Supply Chain Coordination with a Loss-Averse Retailer and Combined Contract

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 586
Author(s):  
Wei Liu ◽  
Shiji Song ◽  
Ying Qiao ◽  
Han Zhao
Keyword(s):  
Supply Chain ◽  
Loss Aversion ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Optimal Order ◽  
Confidence Levels ◽  
Quantity Flexibility ◽  
Quantity Flexibility Contract

This paper studies the supply chain coordination where the retailer is loss-averse, and a combined buyback and quantity flexibility contract is introduced. The loss-averse retailer’s objective is to maximize the Conditional Value-at-Risk of utility. It is shown the combined contract can coordinate the chain and a unique coordinating wholesale price exists if the confidence level is below a threshold. Moreover, the retailer’s optimal order quantity, expected utility and coordinating wholesale price are decreasing in loss aversion and confidence levels, respectively. We also find that when the contract parameters are restricted, the combined contract may coordinate the supply chain even though neither of its component contracts coordinate the chain.

Wholesale Price for Supply Chain Coordination via Conditional Value-at-Risk Minimization

2010 ◽  
Vol 20-23 ◽  
pp. 88-93 ◽  
Author(s):  
Chuan Xu Wang
Keyword(s):  
At Risk ◽  
Supply Chain ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Optimal Order ◽  
Individual Member ◽  
Risk Minimization ◽  
Proposed Model

The theory of the conditional value-at-risk (CVaR) in financial risk management is considered in this paper to develop a model of supply chain coordination with a wholesale pricing policy. The proposed model solves the drawbacks of objective function in current supply chain coordination model. A numerical example is given to demonstrate the effectiveness of the proposed model. The following helpful conclusions are drawn from the paper: with the increase of the degree of risk averting for supply chain individual member, the optimal order quantity of supply chain is decreasing, while the optimal profit is decreasing; If supplier’s risk averting degree increases, supplier has to increase wholesale price to achieve supply chain coordination; If retailer’s risk averting degree increases, supplier has to decrease wholesale price to achieve supply chain coordination.

scholarly journals Emergency Quantity Discount Contract with Suppliers Risk Aversion under Stochastic Price

Mathematics ◽  
2021 ◽  
Vol 9 (15) ◽  
pp. 1791
Author(s):  
Shuangsheng Wu ◽  
Qi Li
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Risk Measure ◽  
Supply Chain Coordination ◽  
Conditional Value At Risk ◽  
Market Demand ◽  
Step Size ◽  
Quantity Discount ◽  
Related Factors

This paper constructs an emergency quantity discount contract to explore the inherent law of the contract coordinating the supply chain with stochastic market demand and price and the risk-averse supplier. Meanwhile, the conditional value-at-risk (CVaR) risk measure criterion is revised to study the influence of supplier’s risk aversion attitude on supply chain coordination. The results show that supplier risk aversion will cause the bifurcation of the relevant factors in the supply chain under the stochastic price. Within the bifurcation region, the supply chain cannot be coordinated; out of the bifurcation region, the supply chain can achieve coordination. The supply chain related factors’ variation range in the bifurcation region is related to the step size of the risk aversion factor and the normal distribution function’s variance of the market demand, and it increases with the latter.

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

2019 ◽  
Vol 36 (05) ◽  
pp. 1950028 ◽  
Author(s):  
Han Zhao ◽  
Shiji Song ◽  
Yuli Zhang ◽  
Jatinder N. D. Gupta ◽  
Anna G. Devlin ◽  
...  
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Numerical Experiments ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Mild Conditions ◽  
Buy Back

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.

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

Mathematics ◽  
2021 ◽  
Vol 9 (7) ◽  
pp. 787
Author(s):  
Han Zhao ◽  
Hui Wang ◽  
Wei Liu ◽  
Shiji Song ◽  
Yu Liao
Keyword(s):  
At Risk ◽  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Call Option ◽  
Service Requirement ◽  
Option Contract ◽  
The Impact

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 Supply Chain with Buy-Back Contracts in the Presence of Risk Aversion

2018 ◽  
Vol 35 (02) ◽  
pp. 1840008 ◽  
Author(s):  
Chunlin Luo ◽  
Xin Tian ◽  
Xiaobing Mao ◽  
Qiang Cai
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Value At Risk ◽  
Performance Measure ◽  
Expected Profit ◽  
Conditional Value At Risk ◽  
Allocation Rule ◽  
Risk Averse ◽  
Buy Back ◽  
The Impact

This paper addresses the operational decisions and coordination of the supply chain in the presence of risk aversion, where the risk averse retailer’s performance is measured by a combination of the expected profit and conditional value-at-risk (CVaR). Such performance measure reflects the desire of the retailer to maximize the expected profit on one hand and to control the downside risk of the profit on the other hand. The impact of risk aversion on the supply chain’s decision and performance is also explored. To overcome the inefficiency due to the double marginalization and the aggravation resulting from risk aversion, we investigate the buy-back contract to coordinate the supply chain. Such contract can largely increase the supply chain’s profit, especially when the retailer is more risk averse. Lastly, we extend such risk measure to the widely-used business model nowadays — platform selling model, and explore the impact of the allocation rule on the manufacturer’s decision.

scholarly journals Optimal Decision of Deferred Payment Supply Chain considering Bilateral Risk-Aversion Degree

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Liu Liang ◽  
Li Futou
Keyword(s):  
Supply Chain ◽  
Risk Aversion ◽  
Wholesale Price ◽  
Conditional Value At Risk ◽  
Optimal Order ◽  
Risk Averse ◽  
Order Quantity ◽  
Initial Capital ◽  
Optimal Order Quantity ◽  
Degree Of Risk

This paper aims to fill up the gap that the previous research has never explored, the deferred payment supply chain with a risk-averse supplier. To this end, the conditional value-at-risk (CVaR) was adopted as a criterion to measure the influence of retailer’s deferred payment on supply chain performance. According to this criterion, the retailer’s optimal order quantity and the supplier’s optimal wholesale price per unit product were investigated under decentralized decision-making. Then, the existence of a unique optimal strategy was discussed for risk-averse supplier and retailer, and the values of risk-averse, initial capital, and wholesale price were calculated in detail. Finally, the theoretical results were testified through a numerical example. It is concluded that retailer’s optimal order quantity is negatively correlated with the wholesale price, initial capital, and degree of risk aversion, so that the retailer can benefit through proper risk aversion; the supplier’s expected profit decreases with the increase in the degree of risk aversion, yet the optimal wholesale price is determined by the degree of risk aversion of supplier and retailer. The research findings shed valuable new light on how to manage a supply chain involving risk-averse supplier and retailer.

scholarly journals Optimal Decisions for Adoption of Item-Level RFID in a Retail Supply Chain with Inventory Shrinkage under CVaR Criterion

2016 ◽  
Vol 2016 ◽  
pp. 1-17
Author(s):  
Chunming Xu ◽  
Daozhi Zhao
Keyword(s):  
Supply Chain ◽  
Recovery Rate ◽  
Value At Risk ◽  
Wholesale Price ◽  
Revenue Sharing ◽  
Conditional Value At Risk ◽  
Decentralized System ◽  
Revenue Sharing Contract ◽  
Item Level ◽  
Inventory Shrinkage

This paper investigates the effect of item-level RFID on inventory shrinkage in the retail supply chain, which consists of a risk-neutral manufacturer and a risk-averse retailer. Under conditional value-at-risk (CVaR) criterion, two different supply chain settings are discussed as follows. In the centralized setting, we develop the models in both RFID case and no RFID case, respectively. Comparisons between the two cases are made. In particular, a sufficient condition is given to judge whether to adopt item-level RFID. In the decentralized setting, we focus on discussing two different contract types including wholesale price contact and revenue sharing contract. Finally, number examples and sensitivity analysis are given to illustrate the proposed models. The results show that, for the centralized system, the sales-available rate, the recovery rate, and the tag cost are mainly the driving factors in evaluating the benefit of an item-level RFID. In particular, when the sales-available rate and the tag cost are quite small and the recovery rate is higher, the supply chain partners’ profits obtained by investment for RFID are improved significantly. For the decentralized system, under revenue sharing contract, Pareto improving outcome and coaffording risk can be achieved if the retailer sets an appropriate parameter for the manufacturer.

SUPPLY CHAIN COORDINATION WITH CVaR CRITERION

2009 ◽  
Vol 26 (01) ◽  
pp. 135-160 ◽  
Author(s):  
LEI YANG ◽  
MINGHUI XU ◽  
GANG YU ◽  
HANQIN ZHANG
Keyword(s):  
Supply Chain ◽  
Value At Risk ◽  
Supply Chain Coordination ◽  
Revenue Sharing ◽  
Retail Price ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Mild Conditions ◽  
Quantity Flexibility ◽  
Buy Back

We study the coordination of supply chains with a risk-neutral supplier and a risk-averse retailer. Different from the downside risk setting, in a conditional value-at-risk (CVaR) framework, we show that the supply chain can be coordinated with the revenue-sharing, buy-back, two-part tariff and quantity flexibility contracts. Furthermore the revenue-sharing contracts are still equivalent to the buy-back contracts when the retail price is fixed. At the same time, it is shown that the risk-averse retailer of the coordinated supply chain can increase its profit by raising its risk-averse degree under mild conditions.

scholarly journals Single-stage gradient-based stellarator coil design: stochastic optimization

2021 ◽  
Author(s):  
Florian Wechsung ◽  
Andrew Giuliani ◽  
M. Landreman ◽  
Antoine J Cerfon ◽  
Georg Stadler
Keyword(s):  
Stochastic Optimization ◽  
Value At Risk ◽  
Optimization Problems ◽  
Numerical Study ◽  
Single Stage ◽  
Conditional Value At Risk ◽  
Risk Averse ◽  
Coil Design ◽  
Risk Neutral ◽  
Gradient Based

Abstract We extend the single-stage stellarator coil design approach for quasi-symmetry on axis from [Giuliani et al, 2020] to additionally take into account coil manufacturing errors. By modeling coil errors independently from the coil discretization, we have the flexibility to consider realistic forms of coil errors. The corresponding stochastic optimization problems are formulated using a risk-neutral approach and risk-averse approaches. We present an efficient, gradient-based descent algorithm which relies on analytical derivatives to solve these problems. In a comprehensive numerical study, we compare the coil designs resulting from deterministic and risk-neutral stochastic optimization and find that the risk-neutral formulation results in more robust configurations and reduces the number of local minima of the optimization problem. We also compare deterministic and risk-neutral approaches in terms of quasi-symmetry on and away from the magnetic axis, and in terms of the confinement of particles released close to the axis. Finally, we show that for the optimization problems we consider, a risk-averse objective using the Conditional Value-at-Risk leads to results which are similar to the risk-neutral objective.

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