scholarly journals The Complex Dynamics of Bertrand-Stackelberg Pricing Models in a Risk-Averse Supply Chain

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Junhai Ma ◽  
Qiuxiang Li
Keyword(s):  
Supply Chain ◽  
Complex Dynamics ◽  
Stackelberg Game ◽  
Price Adjustment ◽  
Stable Region ◽  
Uncertain Demand ◽  
Risk Averse ◽  
Pricing Models ◽  
Increase With Increase ◽  
Adjustment Speed

We construct dynamic Bertrand-Stackelberg pricing models including two manufacturers and a common retailer in a risk-averse supply chain with the uncertain demand. The risk-averse supply chain follows these strategies: Bertrand game between the two manufacturers and Stackelberg game between the manufacturer and the retailer. We study the effect of the price adjustment speed, the risk preference, and the uncertain demand on the stability of the risk-averse supply chain using bifurcation, power spectrum, attractor, and so forth. It is observed that there exists slip bifurcation when the price adjustment speed across some critical value, the stable region, and total profit of the risk-averse supply chain will increase with increase ofRM1and decrease with increase ofσ. The profit of the supply chain and the two manufacturers will decrease and the weaker (retailer) is a beneficiary when the supply chain is in chaos. The fluctuation in the supply chain can be gradually controlled by the control of the price adjustment speed.

Study and Simulation on Dynamics of a Risk-Averse Supply Chain Pricing Model with Dual-Channel and Incomplete Information

2016 ◽  
Vol 26 (09) ◽  
pp. 1650146 ◽  
Author(s):  
Lijian Sun ◽  
Junhai Ma
Keyword(s):  
Supply Chain ◽  
Incomplete Information ◽  
Dynamic Pricing ◽  
Wholesale Price ◽  
Price Adjustment ◽  
Phase Portraits ◽  
Largest Lyapunov Exponent ◽  
Risk Averse ◽  
Dual Channel ◽  
Adjustment Speed

Under the industrial background of dual-channel, volatility in demand of consumers, we use the theory of bifurcations and numerical simulation tools to investigate the dynamic pricing game in a dual-channel supply chain with risk-averse behavior and incomplete information. Due to volatility of demand of consumers, we consider all the players in the supply chain are risk-averse. We assume there exist Bertrand game and Manufacturers’ Stackelberg in the chain which are closer to reality. The main objective of the paper is to investigate the complex influence of the decision parameters such as wholesale price adjustment speed, risk preference and service value on stability of the risk-averse supply chain and average utilities of all the players. We lay emphasis on the influence of chaos on average utilities of all the players which did not appear in previous studies. The dynamic phenomena, such as the bifurcation, chaos and sensitivity to initial values are analyzed by 2D bifurcation phase portraits, Double Largest Lyapunov exponent, basins of attraction and so on. The study shows that the manufacturers should slow down their wholesale price adjustment speed to get more utilities, if the manufacturers are willing to take on more risk, they will get more profits, but they must keep their wholesale prices in a certain range in order to maintain the market stability.

scholarly journals Complex Characteristics of Multichannel Household Appliance Supply Chain with the Price Competition

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Junhai Ma ◽  
Wandong Lou
Keyword(s):  
Supply Chain ◽  
Supply Chains ◽  
Price Competition ◽  
Domain Of Attraction ◽  
Bullwhip Effect ◽  
Price Adjustment ◽  
Stable Region ◽  
Supply Chain System ◽  
Household Appliance ◽  
Internet Channel

This paper studies the complex characteristics caused by the price competition in multichannel household appliance supply chains. We consider a two-level household appliance supply chain system consisting of a manufacturer with an Internet channel and a retailer with a traditional channel and an Internet channel. Each channel’s price-setting follows the bounded rational decision process in order to obtain the optimal profit or more market share. Considering that the price competition often leads to the demand and order fluctuation, we also investigate the bullwhip effect of the multichannel supply chains on the basis of the order-up-to-inventory policy. From the numerical simulation, we find a system in a chaotic state will suffer larger bullwhip effect than a stable system, and the manufacturer’s Internet channel is helpful to mitigate the bullwhip effect. Our results provide some useful managerial inspirations for the household manufacturer and retailers. Firstly, each channel should make their retail price with a suitable price adjustment speed in the stable region, and each time pricing cannot exceed the domain of attraction. Secondly, the manufacturer can adopt a more radical pricing strategy in their Internet channel to mitigate the bullwhip effect. Thirdly, the price adjustment should be reviewed and be appropriately reduced if the price adjustment is too large.

scholarly journals Dynamic Game and Coordination Strategy of Multichannel Supply Chain Based on Brand Competition

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-26 ◽  
Author(s):  
Junhai Ma ◽  
Fang Zhang ◽  
Binshuo Bao
Keyword(s):  
Supply Chain ◽  
Dynamic Pricing ◽  
Tracking System ◽  
Wholesale Price ◽  
Stable Region ◽  
Selling Price ◽  
Direct Channel ◽  
Channel Competition ◽  
Brand Competition ◽  
Adjustment Speed

In is very important for the corresponding author to have a linked ORCID (Open Researcher and Contributor ID) account on MTS. To register a linked ORCID account, please go to the Account Update page (http://mts.hindawi.com/update/) in our Manuscript Tracking System and after you have logged in click on the ORCID link at the top of the page. This link will take you to the ORCID website where you will be able to create an account for yourself. Once you have done so, your new ORCID will be saved in our Manuscript Tracking System automatically.”"?>this paper, two noncooperative dynamic pricing strategies are used in a supply chain. Two dynamic Stackelberg game models have been built involving both a manufacturer and a retailer assumed to be the leader in order. In the two models, the manufacturer sells national-brand (NB) product to an independent retailer or directly to consumers through a direct channel. The retailers sell a store-brand (SB) product when they sell the NB product coming from the manufacturer. Thus, there is competition both in different channels and in products with different brands. To analyze the complexity of the model, parameter bifurcation diagrams and strange attractor diagrams have been therefore plotted. The results show that the game leader has advantages when the market is stable, but it turns disadvantageous if the state falls into unstable as the game follower can quickly adjust the strategy to seize the market. The wholesale price and the direct selling price are high that they incur larger profits if the manufacturer is dominant, but it gets worse when the adjustment speed increases. While in the model where the retailer plays a dominant role, the increase in the adjustment speed is unfavorable to retailer. By controlling the total cost of the direct channel and increasing channel competition strength and brand competition strength, the manufacturers can increase their profits in the game dominated by the retailer. In addition, the stable region within the system will be narrow since the market is sensitive to the channel competition, brand competition, and advertising indifference.

scholarly journals Pricing Decisions of a Dual-Channel Closed-Loop Supply Chain under Uncertain Demand of Indirect Channel

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
Jie Gao ◽  
Xiong Wang ◽  
Qiuling Yang ◽  
Qin Zhong
Keyword(s):  
Supply Chain ◽  
Closed Loop ◽  
Stackelberg Game ◽  
Uncertain Demand ◽  
Direct Channel ◽  
Closed Loop Supply Chain ◽  
Pricing Decisions ◽  
Dual Channel ◽  
Decentralized Decision Making ◽  
The Impact

The dual-channel closed-loop supply chain (CLSC) which is composed of one manufacturer and one retailer under uncertain demand of an indirect channel is constructed. In this paper, we establish three pricing models under decentralized decision making, namely, the Nash game between the manufacturer and the retailer, the manufacturer-Stackelberg game, and the retailer-Stackelberg game, to investigate pricing decisions of the CLSC in which the manufacturer uses the direct channel and indirect channel to sell products and entrusts the retailer to collect the used products. We numerically analyze the impact of customer acceptance of the direct channel (θ) on pricing decisions and excepted profits of the CLSC. The results show that when the variableθchanges in a certain range, the wholesale price, retail price, and expected profits of the retailer all decrease whenθincreases, while the direct online sales price and manufacturer’s expected profits in the retailer-Stackelberg game all increase whenθincreases. However, the optimal recycling transfer price and optimal acquisition price of used product are unaffected byθ.

scholarly journals The Impact of Service and Channel Integration on the Stability and Complexity of the Supply Chain

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-27 ◽  
Author(s):  
Jianheng Zhou ◽  
Xingli Chen
Keyword(s):  
Supply Chain ◽  
Dynamic Models ◽  
Stackelberg Game ◽  
Profit Sharing ◽  
System Stability ◽  
Stable Region ◽  
Channel Integration ◽  
Profit Allocation ◽  
The Stability ◽  
The Impact

This paper constructs a supply chain consisting of a manufacturer and a retailer. Considering channel integration and service cooperation, two dynamic Stackelberg game models are established: one without unit profit allocation M and the other one with unit profit allocation Mε. In two dynamic models, we analyze the influence of relevant parameters on the stability and complexity of the dynamic system and system profit by nonlinear system theory and numerical simulation. We find that the higher adjustment parameters can cause the system to lose stability, showing double period bifurcation or wave-shape chaos. The stable region becomes larger with increase in service value and value of unit profit sharing. Besides, when the system is in chaotic state, we find that the profit of the system will fluctuate or even decline sharply; however, keeping the parameters in a certain range is helpful in maintaining the system stability and is conducive to decision-makers to obtain steady profits. In order to control the chaos phenomenon, the state feedback method is employed to control the chaotic system well. This study provides some valuable significance to supply chain managers in channel integration and service cooperation.

scholarly journals Analysis of Price Stackelberg Duopoly Game with Bounded Rationality

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Lian Shi ◽  
Yun Le ◽  
Zhaohan Sheng
Keyword(s):  
Bounded Rationality ◽  
Stackelberg Game ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Price Adjustment ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Existence And Stability ◽  
Theoretical And Numerical Analysis ◽  
Stackelberg Duopoly

The classical Stackelberg game is extended to boundedly rational price Stackelberg game, and the dynamic duopoly game model is described in detail. By using the theory of bifurcation of dynamical systems, the existence and stability of the equilibrium points of this model are studied. And some comparisons with Bertrand game with bounded rationality are also performed. Stable region, bifurcation diagram, The Largest Lyapunov exponent, strange attractor, and sensitive dependence on initial conditions are used to show complex dynamic behavior. The results of theoretical and numerical analysis show that the stability of the price Stackelberg duopoly game with boundedly rational players is only relevant to the speed of price adjustment of the leader and not relevant to the follower’s. This is different from the classical Cournot and Bertrand duopoly game with bounded rationality. And the speed of price adjustment of the boundedly rational leader has a destabilizing effect on this model.

scholarly journals Stackelberg Game of Buyback Policy in Supply Chain with a Risk-Averse Retailer and a Risk-Averse Supplier Based on CVaR

PLoS ONE ◽  
2014 ◽  
Vol 9 (9) ◽  
pp. e104576 ◽  
Author(s):  
Yanju Zhou ◽  
Qian Chen ◽  
Xiaohong Chen ◽  
Zongrun Wang
Keyword(s):  
Supply Chain ◽  
Stackelberg Game ◽  
Risk Averse

scholarly journals Risk-Averse Facility Location for Green Closed-Loop Supply Chain Networks Design under Uncertainty

2018 ◽  
Vol 10 (11) ◽  
pp. 4072 ◽  
Author(s):  
Xiao Zhao ◽  
Xuhui Xia ◽  
Lei Wang ◽  
Guodong Yu
Keyword(s):  
Supply Chain ◽  
Facility Location ◽  
Co2 Emissions ◽  
Closed Loop ◽  
Emission Rate ◽  
Uncertain Demand ◽  
Risk Averse ◽  
Closed Loop Supply Chain ◽  
Linearization Technique ◽  
Reformulation Linearization

With the increasing attention given to environmentalism, designing a green closed-loop supply chain network has been recognized as an important issue. In this paper, we consider the facility location problem, in order to reduce the total costs and CO2 emissions under an uncertain demand and emission rate. Particularly, we are more interested in the risk-averse method for providing more reliable solutions. To do this, we employ a coherent risk measure, conditional value-at-risk, to represent the underlying risk of uncertain demand and CO2 emission rate. The resulting optimization problem is a 0-1 mixed integer bi-objective programming, which is challenging to solve. We develop an improved reformulation-linearization technique, based on decomposed piecewise McCormick envelopes, to generate lower bounds efficiently. We show that the proposed risk-averse model can generate a more reliable solution than the risk-neutral model, both in reducing penalty costs and CO2 emissions. Moreover, the proposed algorithm outperforms and classic reformulation-linearization technique in convergence rate and gaps. Numerical experiments based on random data and a ‘real’ case are performed to demonstrate the performance of the proposed model and algorithm.

Impact of price adjustment speed on the stability of Bertrand–Nash equilibrium and profit of the retailers

Kybernetes ◽  
2018 ◽  
Vol 47 (8) ◽  
pp. 1494-1523
Author(s):  
Rofin T.M. ◽  
Biswajit Mahanty
Keyword(s):  
Supply Chain ◽  
Nash Equilibrium ◽  
Chaotic Dynamics ◽  
Price Adjustment ◽  
Online Retailer ◽  
Content Type ◽  
Dual Channel ◽  
Adjustment Speed ◽  
The Stability ◽  
Dual Channel Supply Chain

Purpose The purpose of this paper is to investigate the impact of price adjustment speed on the stability of Bertrand–Nash equilibrium in the context of a dual-channel supply chain competition. Design/methodology/approach The paper considers a dual-channel supply chain comprising a manufacturer, a traditional retailer and an online retailer. A two-dimensional discrete dynamical system is used to examine the Bertrand competition between the retailers. The retailers are assumed to follow bounded rational expectations. Local stability of Bertrand–Nash equilibrium is investigated with respect to the price adjustment speed. Findings As the price adjustment speed increases, the stability of Bertrand–Nash equilibrium is lost, leading to complex chaotic dynamics. The results showed that chaotic dynamics deteriorates the profit of the retailers. The authors also found that the chaos can be controlled using an adaptive adjustment mechanism and the retailers enjoy higher profit when the chaos is controlled. Practical implications This study helps retail managers to choose an appropriate price adjustment speed to maximize profit. Originality/value The heterogeneity of the retailers is not considered in the studies involving dynamics of retailer competition. This paper contributes to the literature by considering the operational difference between a traditional retailer and an online retailer, i.e. price adjustment speed. In addition, the study establishes a link between price adjustment speed and profit.

scholarly journals A Dynamic Price Game Model in a Low-Carbon, Closed-Loop Supply Chain Considering Return Rates and Fairness Concern Behaviors

2019 ◽  
Vol 16 (11) ◽  
pp. 1978 ◽  
Author(s):  
Qiuxiang Li ◽  
Mengnan Shi ◽  
Yimin Huang
Keyword(s):  
Supply Chain ◽  
Price Adjustment ◽  
Stable Region ◽  
Game Model ◽  
Low Carbon ◽  
Return Rates ◽  
Dynamic Price ◽  
Price Game ◽  
Fairness Concern ◽  
Parameter Values

In this paper, we developed a dynamic price game model for a low-carbon, closed-loop supply chain system in which (1) the manufacturer had fairness concern and carbon emission reduction (CER) behaviors, and market share and profit maximization were their objectives, and (2) the retailer showed fairness concern behaviors in market competition and provided service input to reduce return rates. The retailer recycled old products from customers, and the manufacturer remanufactured the recycled old products. The effects of different parameter values on the stability and utility of the dynamic price game model were determined through analysis and numerical simulation. Results found that an increasing customer loyalty to the direct marketing channel decreased the stable region of the manufacturer’s price adjustment and increase that of the retailer. The stable region of the system shrank with an increase of CER and the retailer’s service level, which expanded with return rates. The dynamic system entered into chaos through flip bifurcation with the increase of price adjustment speed. In the chaotic state, the average utilities of the manufacturer and retailer all declined, while that of the retailer declined even more. Changes to parameter values had a great impact on the utilities of the manufacturer and retailer. By selecting appropriate control parameters, the dynamic system can return to a stable state from chaos again. The research of this paper is of great significance to participants’ price decision-making and supply chain operation management.

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