scholarly journals Complexity Dynamic Character Analysis of Retailers Based on the Share of Stochastic Demand and Service

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12
Author(s):  
Junhai Ma ◽  
Weiya Di ◽  
Hao Ren
Keyword(s):  
Stochastic Demand ◽  
Stable State ◽  
Service Level ◽  
Price Adjustment ◽  
Stable Region ◽  
Largest Lyapunov Exponent ◽  
Market Demand ◽  
Price Fluctuation ◽  
Adjustment Speed ◽  
The Stability

Apart from the price fluctuation, the retailers’ service level becomes another key factor that affects the market demand. This paper depicts a modified price and demand game model based on the stochastic demand and the retailer’s service level which influences the market demand decided by customers’ preference, while the market demand is stochastic in this model. We explore how the price adjustment speed affects the stability of the supply chain system with respect to service level and stochastic demand. The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly. The largest Lyapunov exponent and the chaotic attractor are also given to confirm the chaotic characteristic of the system. The simulation results indicate that relatively small price adjustment speed may maintain the system at stable state. With the price adjustment speed gradually increasing, the price system gets unstable and finally becomes chaotic. This chaotic phenomenon will perturb the product market and this phenomenon should be controlled to keep the system stay in the stable region. So the chaos control is done and the chaos can be controlled completely. The conclusion makes significant contribution to the system referring to the price fluctuation based on the service level and stochastic demand.

Analysis of Pricing and Service Effort in Dual-Channel Supply Chains with Showrooming Effect

2020 ◽  
Vol 30 (16) ◽  
pp. 2050241
Author(s):  
Junhai Ma ◽  
Yaping Li ◽  
Zongxian Wang
Keyword(s):  
Supply Chain ◽  
Wholesale Price ◽  
Stable State ◽  
Dynamic Game ◽  
Price Adjustment ◽  
Flip Bifurcation ◽  
Stability Range ◽  
Dual Channel ◽  
Adjustment Speed ◽  
The Stability

Showrooming has become common practice of consumers in the context of dual-channel retailing. Under different intensities of showrooming, the manufacturer can decide whether to directly retail online (the M-R case) or resell through an e-retailer (the E-R case). Dual-channel supply chain models and dynamic game models are developed and both online selling formats are investigated. The dynamic game process of the supply chain is numerically simulated. The stability of the Nash equilibrium point is investigated by parameter basins for periodical cycles and bifurcation diagrams. The results show that the price adjustment speeds have a larger stability range in the M-R case while the service effort adjustment speed has a larger stability range in the E-R case. The stability of the systems is more sensitive to price adjustment speed than service effort adjustment speed in both supply chain structures. It is found that the systems will enter chaos through a flip bifurcation or a Neimark–Sacker bifurcation. The changes in attractors and basins of attraction indicate that both channels can reach the equilibria more easily when they choose a lower speed of retail price adjustment. The effects of showrooming on decision variables are greater in the M-R case than in the E-R case. When the showrooming effect is moderate, the manufacturer should choose the M-R case; when the showrooming effect is sufficiently large or sufficiently small, the manufacturer should choose the E-R case. We propose a wholesale price markdown strategy which can: (i) eliminate the double marginalization and coordinate the supply chain; (ii) effectively control the chaos caused by the overhigh adjustment speed of wholesale price, and restore the system to a stable state; (iii) improve the retailer’s service effort.

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 The Complex Dynamics of Sharing Platform Competition Game

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Jianli Xiao
Keyword(s):  
Feedback Control ◽  
Rapid Development ◽  
Stable State ◽  
Sharing Economy ◽  
System Stability ◽  
Largest Lyapunov Exponent ◽  
Platform Competition ◽  
Chaotic State ◽  
Price Increases ◽  
Adjustment Speed

With the rapid development of Internet technologies and online sharing platforms, sharing economy has become a major trend in economy. The entry of sharing economy leads to profound impacts on incumbent industry. We build a dynamic sharing platform competition model with which agents are bounded rational, and consumer side is heterogeneous. Then, we present the fixed points and the stability conditions of the bifurcation of the dynamic model. We simulate the adjustment speed of sharing platform, sharing platform price, and costs of traditional firm effects on system stability, and we present stable area, bifurcation diagram, the largest Lyapunov exponent, and strange attractor of different parameters, and we give a feedback control method at last. Our main results are as follows: (1) when adjustment speed of sharing platform increases, the system becomes bifurcation, and finally, the system goes into a chaotic state; when the system is stable, price of traditional firm and fee decision of sharing platform are constant. (2) When price of sharing platform increases, sharing platform is more stable while traditional firm is more vulnerable. Suppose the system is in the stable state; when sharing platform price increases, traditional firm price increases, while sharing platform fees decreases. (3) When traditional firm cost is small, the system would be more stable. When the system is stable, with traditional firm cost increasing, traditional firm price increases quicker than sharing platform consumer fee, while sharing platform seller fee decreases. (4) Feedback control can alleviate the chaotic state of system. With feedback control parameter increases, the system becomes more stable.

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 Chaotic Characteristics and Application of Cooperative Game and Evolutionary Game

2014 ◽  
Vol 2014 ◽  
pp. 1-13 ◽  
Author(s):  
Yujing Yang ◽  
Junhai Ma ◽  
Hongliang Tu
Keyword(s):  
Chaos Control ◽  
Evolutionary Game ◽  
Time History ◽  
Renewable Resource ◽  
Stable Region ◽  
Cournot Duopoly ◽  
Nash Equilibrium Point ◽  
Cournot Game ◽  
Adjustment Speed ◽  
The Stability

According to a dynamical multiteam Cournot game in exploitation of a renewable resource, a new dynamic Cournot duopoly game model with team players in exploitation of a renewable resource is built up in this paper. Based on the theory of bifurcations of dynamical systems, the stability of the system is studied and the local stable region of Nash equilibrium point is obtained. The effect of the output adjustment speed parameters and the weight parameter of the system on the dynamic characteristics of the system are researched. The complexity of the system is described via the bifurcation diagrams, the Lyapunov exponents, the phase portrait, the time history diagram, and the fractal dimension. Furthermore, the chaos control of the system is realized by the parameter adjustment method. At last, an evolutionary game as a special dynamic system is constructed and analyzed which is more useful and helpful in application. The derived results have very important theoretical and practical values for the renewable resource market and companies.

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 Complexity and Entropy Analysis of a Multi-Channel Supply Chain Considering Channel Cooperation and Service

Entropy ◽  
2018 ◽  
Vol 20 (12) ◽  
pp. 970 ◽  
Author(s):  
Qiuxiang Li ◽  
Xingli Chen ◽  
Yimin Huang
Keyword(s):  
Supply Chain ◽  
Stackelberg Game ◽  
Equilibrium Points ◽  
Service Level ◽  
Stability Domain ◽  
Largest Lyapunov Exponent ◽  
Game Model ◽  
Nash Game ◽  
Profit Distribution ◽  
The Stability

In this paper, based on the background of channel cooperation and service of the supply chain, this paper constructs a Nash game model and a Stackeberg game model in the multi-channel supply chain considering an online-to-store channel (OSC). Based on maximizing the profits and the bounded rationality expectation rule (BRE), this paper builds a dynamic game model, respectively, and analyzes the stability of the equilibrium points by mathematical analysis and explores the influences of parameters on stability domain and entropy of the system by using bifurcation diagram, the entropy diagram, the largest Lyapunov exponent and the chaotic attractor etc. Besides, the influences of service level and profit distribution rate on system’s profit are discussed. The theoretical results show that the greater the service level and profit distribution rate are, the smaller the stability domain of the system is; the system will go into chaotic state and the system’s entropy will increase when operators adjust her/his price decision quickly; when the manufacturer or the retailer keeps service level in the appropriate value which is conducive to maximizing her/his profit; the manufacturer should carefully set the service level of OSC to ensure the system’s profit; in Nash game model, the stability of the system weakens than that in Stackelberg game model. Furthermore, this paper puts forward some suggestions to help the manufacturer and retailer in multi-channel supply chain to do the better decision.

Dynamics of bilateral control system with state feedback for price adjustment strategy

2021 ◽  
pp. 2150031
Author(s):  
Meng Zhang ◽  
Yi Zhao ◽  
Xinyu Song
Keyword(s):  
Dynamic Properties ◽  
Price Adjustment ◽  
Bilateral Control ◽  
Positive Role ◽  
Price Fluctuation ◽  
Adjustment Strategy ◽  
Adjustment Strategies ◽  
The Stability ◽  
Theoretical Results

The price fluctuation of commodities affects their demand, and it strongly influences the development of industry and the stability of the international economy. A price-output model with two price-dependent impulses is presented in this paper to describe their mutual restrictions and the price adjustment strategies. The equilibria and dynamic properties of the impulsive-free price-output model are qualitatively analyzed, and the results show the hazard of free price fluctuation. For the price-output model with two price-dependent impulses, conditions for the existence of the order-2 periodic solution are obtained, and the orbital asymptotic stability is proved. Those results reveal the positive role of price adjustment strategies. Finally, some numerical simulations are carried out to verify the theoretical results.

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.

Surge Vibration-Induced Nonlinear Behavior Regulation of Power Amplifier for Magnetic Bearing in a 315 kW Centrifugal Compressor

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Yin Zhang ◽  
Shiqiang Zheng ◽  
Chen Ma ◽  
Cheng Chen ◽  
Can Wang
Keyword(s):  
Power Amplifier ◽  
Centrifugal Compressor ◽  
Load Capacity ◽  
Stable State ◽  
Magnetic Bearing ◽  
Rotating Stall ◽  
Active Magnetic Bearing ◽  
Stable Region ◽  
Experimental Investigations ◽  
The Stability

The severe vibration induced by surge and rotating stall is an obstacle to the stability of a magnetically suspended centrifugal compressor (MSCC). In order to suppress the severe vibration caused by surge instability, this paper focuses on compressor surge performance improvements enabled by power amplifier control improvements which result in increased dynamic load capacity (DLC) of the systems axial thrust magnetic bearing. A complete discrete-time model of the active magnetic bearing (AMB) power amplifier, composed of three piecewise linear intervals, is developed. A comprehensive view of the dynamic evolution process from stable state to bifurcation for the power amplifier is also analyzed. In order to stabilize the unstable periodic orbits in the power amplifier, a time-delay feedback control (TDFC) method is introduced to enhance the stability of the power amplifier, while the MSCC is subjected to the surge instability. Simulation results show that the stable region of the power amplifier is extended significantly using the TDFC method. Finally, the experimental investigations performed by an MSCC test rig demonstrate the effectiveness of the proposed solution under the conditions of modified surge and mild surge.

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