Dynamic competitive game study of a green supply chain with R&D level

https://doi.org/10.1016/j.cie.2021.107785Get rights and content

Highlights

  • A dynamic green competition model based on bounded rationality is established.

  • The stability analysis of equilibrium points and the complex dynamical behaviors are discussed in detail.

  • The synchronization behaviors of two enterprises in the supply chain are studied.

  • The global stability of the system is analyzed by numerical simulation.

  • The phenomenon of path dependence is researched in this paper.

Abstract

Green and low carbon is an important way to coordinate economic and social development, which is also true for enterprises. Hence, the essay mainly builds up a green supply chain consisting of one supplier and two manufacturers. Gradient adjustment mechanism is used to establish a dynamic green competition model based on bounded rationality in this paper. Subsequently, the stability of four equilibrium points is researched through different methods. Dynamic behaviors are analyzed by 1-D bifurcation diagrams, the largest Lyapunov exponent, as well as 2-D bifurcation diagrams. We have found that the system goes from a steady state to chaos mainly via flip bifurcation. The chaotic state of system can be alleviated as the increase of adjustment speed in a certain range. Furthermore, invariant sets and natural transverse Lyapunov exponent are used to study synchronization behavior. Basins of attraction under the coexistence of attractors are simulated numerically. The results indicate that the system will have two and four groups of coexisting attractors, where the structure and size of the attractor and its basin will change as the speed of adjustment increases. When the attractor contacts with the boundary of its basin of attraction, the global bifurcation occurs.

Introduction

With the development of economy and the increasing impact of human beings on the environment, the problems of ecology and environmental protection have increasingly become the common concern of governments and people from poles to poles. Green R&D refers to the development and production of products using green technology and materials to minimize environmental pollution, such as the creation of nanoscale solar cells and hybrid train. Green supply chain comes into being with green R&D. The green supply chain refers to adding environmental protection factors on the basis of the traditional supply chain and considering environmental issues. Its purpose is to make the produced products more low-carbon friendly, thus more competitive in the market. It is not only a kind of behavior with great social benefits, but also an effective means to obtain great economic benefits. It can improve the social consciousness of enterprises, so that their sense of social responsibility has been enhanced. Furthermore, it also plays an important role in saving resources and preventing waste of resources.

Take the following companies for example. First of all, P&G announced in April 2012 that its Environmental Sustainability Scorecard tool will be freely available to any company to help it measure and interpret key environmental sustainability indicators in its supply chain, as well as identify sustainability progress and opportunities for improvement. By making this tool available for free, P&G hopes to inspire other companies to be more committed and focused on improving their environmental footprint.

AUCMA, a world renowned supplier of refrigeration equipment, is one of the leading manufacturers of refrigerating appliances, environmentally friendly electric vehicles and home appliances all over the world. Under the guidance of “To create the first competitiveness of the refrigeration industry, to become the creator of green, environmental protection and high quality life” for the development strategy of the company, AUCMA attaches great importance to environmental responsibility from a strategic height, and builds a green industrial chain comprehensively.

Founded in 1988, Quanta Computer Co. LTD is the largest company in the research and development, design and manufacturing of notebook computers all over the world. The company has been devoted to building a “green supply chain” from raw materials to end products. Through a series of green actions, Quanta has improved the energy consumption of the production of computers and reduced the pressure on the environment.

In addition, Germany Siemens group is committed to green design for automotive, electronics, machinery, chemical, pharmaceutical and other industries manufacturing enterprises to develop green products to provide green design overall solutions. And Lafarge Group, the French building materials company, strictly implements green management requirements. For example, in the service link, it cooperates extensively with the government, consumers and downstream enterprises to continuously improve the green and environmental performance of products and strive to reduce the impact of buildings on human health and the environment.

Hence, it can be seen that green environmental protection is the trend pursued by global enterprises today and in the future.

The organizational structure in this essay is described below: In section 2, relevant literatures are stated in this paper. In section 3, the assumptions and notations of this paper are summarized and explained. In section 4, on the basis of two manufacturers purchase homogeneous parts and components of the product from the supplier and sell finished products to retailers, a dynamic competition game model of a green supply chain with nonlinear variable green input cost based on bounded rationality is established. In section 5, under the condition that all the parameters are equal except for the adjustment speed of two manufacturers, the stability of equilibrium points in the system is considered. What’s more, eigenvalues of Jacobian matrices for equilibrium points and Jury criterion are used to talk about types and local stability of the equilibrium point. In section 6, the impact of adjustment speeds on the stability of system is studied by numerical simulation, and the existence of stray points in 2-D bifurcation diagrams is verified to represent the occurrence of coexistence attractors. In section 7, synchronization and global stability are discussed and analyzed, where the synchronization behavior is studied by using invariant sets and natural transverse Lyapunov exponent, then the phenomena of path dependence and global bifurcation are considered via numerical simulation. Finally, in section 8, the research results are summarized.

Section snippets

Literature review

The ultimate goal of a supply chain is to maximize profits of participants while satisfying needs for customers. At present, many scholars have studied the competition in the supply chain from different perspectives. Relevant references to this article can be divided into the following parts.

Assumptions

Assumption 1.

It is assumed that the two manufacturers buy the homogeneous products at the same wholesale price from the supplier.

Assumption 2.

Because the products bought by the two manufacturers are homogeneous, and according to the model of Bao and Ma (2017) and the research results of Dixit, 1979, Singh and Vives, 1984, the inverse demand function of the manufacturer i is assumed to be

pi=a-bqi+qj+eisi-fisji,j=1,2,ij

Here, the maximum market price for per unit product is a, and a>0; the amount of price reduction for

The model

Consider a green supply chain consisting of one supplier and two manufacturers, where two manufacturers purchase homogeneous parts and components of the product from the supplier at the same wholesale price and sell finished products to retailers through traditional sales channels at different prices by adjusting their respective levels of green R&D.

According to Assumption 2 and Assumption 3, the profit function of manufacturers 1, 2 can be expressed as follows,π1=p1-wq1-c1=a-bq1+q2+e1s1-f1s2-wq

Stability analysis of equilibrium points

Through solving s1t+1=s1ts2t+1=s2t, we can get four equilibrium points in system (8), they are,E0=0,0,E1=0,2A2D9bη2-2A22,E2=2A1D9bη1-2A12,0,E*=2A1D2A2B1+2A22-9bη24A1A2B1B2-2A12-9bη12A22-9bη2,2A2D2A1B2+2A12-9bη14A1A2B1B2-2A12-9bη12A22-9bη2

It is evident that there are three boundary equilibrium points E0, E1, E2 and an unique Nash equilibrium point E* in it. Furthermore, the four equilibrium points represent different strategies taken by the two manufacturers. For the sake of ensuring economic

Numerical simulation

In this section, 1-D bifurcation diagram, the largest Lyapunov exponent diagram, 2-D bifurcation diagram and so on are primarily used to research dynamic characteristics in system (9).

Fig. 1 exhibits the 1-D bifurcation diagram for the green R&D level of manufacturers 1, 2 in connection with the manufacturer 1′s adjustment speed α1 and the largest Lyapunov exponent diagram corresponding to them respectively under different manufacturer 2′s adjustment speeds α2. Other remaining parameters are

Synchronization

This section mainly studies the synchronization phenomenon generated by the system. Synchronization refers to selecting initial values near the diagonal and observing whether they get back to the diagonal after a finite number of iterations. In this instance, we refer to the phenomenon of returning to the diagonal after iterations as synchronization. By focusing on the dynamic behaviors of the diagonal, we make the values of adjustment speeds of two manufacturers equal and denote them as α1=α2=α

Conclusion

This paper establishes a dynamic green competition model based on bounded rationality under the condition that two manufacturers purchase homogeneous parts and components of the product and sell finished products to retailers at different prices. First of all, we get the scope of system parameters, and the stability analysis of four equilibrium points of the system is studied where other parameters are equal except for the adjustment speeds of two manufacturers. The types and stabilities of the

CRediT authorship contribution statement

Xuewei Liu: Model building, Formal analysis, Numerical simulation, Writing the first draft. Wei Zhou: Verify, Supervision, Writing – review & editing. Lei Xie: Methodology, Formal analysis.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

The paper is supported by the of A Hundred Youth Talents Training Program of Lanzhou Jiaotong University, the Innovation Fund Project of Colleges and Universities in Gansu Province (No. 2021A-040).

References (41)

  • K. Matsui

    Asymmetric product distribution between symmetric manufacturers using dual-channel supply chains

    European Journal of Operational Research

    (2016)
  • Y.i. Tian et al.

    Coordination and control of multi-channel supply chain driven by consumers’ channel preference and sales effort

    Chaos, Solitons and Fractals

    (2020)
  • Y.u. Wang et al.

    A duopoly game with heterogeneous green supply chains in optimal price and market stability with consumer green preference

    Journal of Cleaner Production

    (2020)
  • J. Wang et al.

    Pricing decisions in a dual-channel green supply chain with product customization

    Journal of Cleaner Production

    (2020)
  • D.i. Wu et al.

    Contract coordination of dual channel reverse supply chain considering service level

    Journal of Cleaner Production

    (2020)
  • L. Xie et al.

    Study the complexity and control of the recycling-supply chain of China’s color TVs market based on the government subsidy

    Communications in Nonlinear Science and Numerical Simulation

    (2016)
  • Z. Zhang et al.

    Quality differentiation in a dual-channel supply chain

    European Journal of Operational Research

    (2021)
  • X. Zhang et al.

    Return decision model of the manufacturer-leading dual-channel supply chain

    Mathematical Problems in Engineering

    (2020)
  • B. Bao et al.

    Dynamic Game Behavior of Retailers Considering the Quality of Substitute Products Based on Delay Decision

    International Journal of Bifurcation and Chaos

    (2017)
  • G.I. Bischi et al.

    Bubbling, riddling, blowout and critical curves

    Journal of Difference Equations and Applications

    (2017)
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      Although stabilization (i.e., a state where variables converge to their equilibrium values) is a favorable result, some complicated dynamical behaviors still could be observed in supply chains. Besides the widely observed amplification of variation (bullwhip effect) in supply chains with random signals (Disney and Towill, 2003; Ma and Ma, 2017; Ponte et al., 2020), complicated behaviors also occur in deterministic systems (Guo, 2019; Liu et al., 2022; Ma and Wang, 2022). Hwarng and Xie (2008) investigated the supply chain dynamics under the influence of demand patterns.

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