Abstract
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.
Highlights
Bertrand duopoly model is frequently used when the competitive behaviors are discussed in proper research
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
The dynamic behavior of the system is researched by simulation and the stability domain and the bifurcation phenomenon are shown clearly
Summary
Bertrand duopoly model is frequently used when the competitive behaviors are discussed in proper research. Xiao and Yang [1] established a price-service competition model with the circumstance whereby the demand is uncertainty in two competing supply chains considering the risk sensitivity. Naimzada and Tramontana [8] studied the liner demand and cost functions with product differentiation, and a dynamic model was established to probe into the stability properties in the mixed Cournot-Bertrand duopoly model. Esmaeilzadeh and Taleizadeh [18] conducted the optimal pricing decisions for two complementary products in a twoechelon supply chain under different market powers with game theory approaches.
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