Original articles
Dynamical complexity of pricing and green level for a dyadic supply chain with capital constraint

https://doi.org/10.1016/j.matcom.2021.12.015Get rights and content

Abstract

In this paper, based on bounded rationality, the dynamic game models are established to study the performance of a dyadic supply chain with one supplier and two competing retailers. According to supply chain practices, capital constraints and greenness issues are taken into consideration. Two financing models are involved respectively, corresponding to two models and scenarios: full trade credit (FTC) and hybrid trade credit (HTC). The equilibrium points of the two models were obtained, and the influence of key parameters such as different decision-making adjustment speeds and trade credit ratios on the local stability of the system was analyzed. Besides, the expected profits of the supplier and two capital-constrained retailers are discussed. It is found that, compared with the adjustable speeds of the two retailers, the supplier’s adjustable speed has a more obvious impact on system stability and expected profits. For the two downstream competitive retailers, the high trade credit ratio leads to the increase in dynamic green levels, wholesale prices, supplier profits, and dynamic pricing of other retailers provided by full trade credit. However, when the market potential is the same, hybrid trade credit may hurt the profits of both retailers.

Introduction

As we all know, shortage of funds is usually a huge challenge that plagues many companies, especially small and medium-sized enterprises (SMEs) generally have insufficient funds in their operations. Supply chain financing came into being, and trade credit financing is one of the most flexible sources of financing in the supply chain. Goyal [13] and Taleizadeh, Pentico, and Jabalameli [33] pointed out that the provision of trade credit to retailers by well-funded suppliers could significantly improve the performance of the entire supply chain. Similarly, Du, Banerjee, Kim [11] and Kouvelis, Zhao [19] found that trade credit financing might ease the retailer’s financial constraints to a certain extent and increased the efficiency of the supply chain.

Recently, environmental issues have received more and more attention from people. From a global perspective, consumers’ positive attitudes towards green products have basically taken shape, and more and more consumers have moved from recognizing and accepting green products to actively purchase [24], [36]. Green supply chains are increasingly being valued by researchers and supply chain managers. Mardani, Kannan and Hooker et al. presented a comprehensive review by utilizing the structural equation modeling in the assessment of sustainable and green supply chain management [23]. They pointed out that most companies nowadays were required to green their overall business supply chain due to higher environmental regulations and higher supply chain complexity. In other words, under the pressure of the public, laws and environmental standards, companies must pay attention to environmental issues while seeking economic benefits. Inevitably, more R&D costs are paid by the supply chain members to improve product greening and reduce the adverse impact on the environment to achieve sustainable operations [25], [32]. Thus the funding shortage situation has been further aggravated. It is noteworthy that product green innovation is a typical inter-period performance, with long cycles and high uncertainty, and multi-stage dynamic decision which may be closer to the practices in reality. For example, Gree Air Conditioning has developed a photovoltaic air-conditioning system through technological innovation to increase the green level of its products, which will reduce 1.312 billion tons of carbon dioxide emissions each year. In fact, the photovoltaic air-conditioning system was only realized after 4 years of research, 386 troubleshooting, 500 motor burns, and investment of tens of millions of yuan. Besides, taking electrical appliances as an example, Gree, Midea, and Haier usually used two or more competing retailers to sale their products. Therefore, in this paper we also consider the supply chain consisting of a supplier and two competitive retailers. Based on the above, it is necessary to build the dynamic game model for upstream supplier and downstream retailers with long-term characteristics, and to explore the dynamic evolution of equilibrium strategy for supply chain members. To the best of our knowledge, few studies have explored the topic presently. Several questions arise in the following:

    (i)

    When taking capital constraints and green level into account, how should dynamic decision making of the supplier and the retailers be made in a dyadic supply chain in the multi-period dynamic framework?

    (ii)

    What is the complexity and dynamics of the dyadic supply chain system? What role can the trade credit play when there is full trade credit or hybrid trade credit?

    (iii)

    How do the critical parameters affect the dynamic strategies and the performance of the supply chain system? What managerial insights can be obtained to improve the sustainable development of supply chain?

In order to introduce the exact research gap, literature is reviewed as follows. The research related to our work mainly focuses on the following two aspects: operation research and dynamic evolution of complex systems. The first stream of the research is the operational decision making related to trade credit financing in green supply chain. From this perspective, most of the existing contributions mainly shed light on the operational decision in single-period static framework. For example, An, Li, Song and Chen [2] found that green crediting could effectively restrain the carbon emissions of the enterprises and the strength of the inhibition depended on the bank’s interest rate in green supply chain. Cao and Yu [7] developed the newsvendor model and compared the optimal strategies in two scenarios, i.e., decentralization and centralization. The authors showed that the difference from decentralized decision-making was that the retailer’s order quantity in centralized decision-making had nothing to do with carbon emissions. Similarly, Wu, Yang and Olson [36] examined a green supply chain in the newsvendor framework, where the bank credit financing and trade credit financing were considered. The authors found that the supply chain achieved a win–win outcome for production quantity and emissions reduction when the manufacturer invested in emissions reduction. Note that these studies have emphasized the interaction of financial and operational decision based on an emission-dependent demand with trade credit financing, rather than on the product greenness. Besides, the demand function is stochastic. Recently, taking the consumer sensitivity to the level of green products in deterministic demand, Yang, Miao and Zhao [37] attempted to explore the impact of the trade credit strategies on the green supply chain performance in three scenarios. The authors concluded that improving green level of the products and utilizing trade credit financing among members in supply chain could not only protect environment but also the requirement to promote economic. Besides, in recent years, dynamic complexity often enter the process of the economic systems to explain some important phenomena, such as business cycles, speculative bubbles and financial crashes, etc [3]. The bounded rationality rule was introduced by Bischi [4], [6] and subsequently considered in supply chain to explore the complex and dynamics of closed-loop, capital-constrained and risk-averse supply chain, respectively [1], [8], [9], [14], [16], [21], [22], [39].

Operation management is the most active branch of modern business management science, and it is also a branch where new ideas and new theories have emerged in large numbers. Thus the literature on the green sustainable development is broad and multidisciplinary. We select the representative literature related to this work and briefly review them as follows. Based on the combined approach of the analytical hierarchical process (AHP) and the fuzzy inference system (FIS), Omair, Noor and Tayyab et al. dealed with the development of a decision support framework for the prioritization of suppliers on sustainability factors [26]. Bhuniya, Pareek and Sarkar introduced different business strategies based on constant and fuzzy demands. There were two types of constraints considered in this model to avoid the backorder cost [5]. Dey, Bhuniya and Sarkar built a smart supply chain model taking the factors of lead time reduction with variable variance and variable demand into consideration. The authors proved that considering a flexible production rate and investing a small amount for the advertisement, demand must increase, and the joint total cost must decrease [10]. Tirkolaee, Mahdavi and Esfahani et al. designed an efficient municipal solid waste management system and a robust green location–allocation–inventory problem was also investigated by formulating the problem as a mixed-integer linear programming (MILP) model under uncertain demand of waste [34]. Pervin, Magfura and Sankar et al. developed a multi-item inventory model for deteriorating items and presented an easy analytical solution procedure with stock-dependent demand function based on manufacturer’s and retailer’s perspective when the retailer adopted the trade-credit policy. Nash equilibrium solution of the joint profit was also obtained [28]. Dubey, Rameshwar and Surajit et al. reported on an empirical study to examine the impact of green supply chain practices on organizational performance in Indian rubber industry by statistical methods [12]. Khalilpourazari, Teimoori and Mirzazadeh proposed a new mathematical model for multi-item Economic Order Quantity model with random disruption considering defective supply batches and partial backordering under uncertainty [17]. On the technical aspects of the sustainable supply chain, Ozceylan, Eren and Surendra et al. presented the efficient quantitative techniques when faced the production and distribution operations in terms of smart manufacturing and sustainability issue [27]. Recently, in the field of stochastic model research in the financial field, Savku, Emel and Weber studied a stochastic optimal control problem for a delayed Markov regime-switching jump–diffusion model in finance and illustrated the results by a optimal consumption problem from a cash flow with delay [29]. Savku and Weber applied dynamic programming principle the stochastic differential games to research two optimal investment problems in finance [30]. Weber, Kropat and Akteke et al. surveyed the advances and mathematical foundations of gene-environment networks in operational research and environmental protection. The authors pointed out that nonlinear differential equations are extracted to describe and analyze the interactions and regulating effects between the data items of interest and the environmental items [35]. Gupta, Haq and Ali et al. examined bilevel programming with the intuitionistic fuzzy parameters for modeling a supply chain network problem under multi-objective and effectively solved it using a fuzzy goal programming approach to reach a satisfying solution for the decision-making environment [15]. The authors adopted the technique of fuzzy bi-level multi-objective in methodology, which is different from the assumption of single objective and stochastic demand in our study. Khurshid, Maqsood and Omair et al. proposed an improved evolution strategy to reduce the makespan of Permutation Flow Shop Scheduling Problems. The authors tested the performances of both evolution strategy variants on two test domains and applied to the real-life problem for the manufacturing of batteries to demonstrate its effectiveness [18].

Table 1 lists gaps in the literature that were fulfilled by this work, which indicates that most of dynamic models were developed with uncertain but few of them including complexity analysis. Moreover, the few literatures that studied dynamic complexity did not take into account the green theme and shortage of capital. It is well known that dynamics characteristic of bifurcation and chaos often enter the process of some economic system to explain some important phenomena. Based on this, in order to fill this research gap, in this paper we explore the dynamic decision making of a dyadic supply chain with one supplier and two competing retailers, where the greenness of products and supply chain financing are considered.

This paper aims to bridge the gap between theory and practice in supply chain management, and extend the dyadic supply chain to a dynamic supply chain in which the capital-constrained retailers are financed by full trade credit or hybrid trade credit. The greenness of the product is determined by the upstream supplier. In our setting, two scenarios are analyzed respectively depending on the supplier provides trade credit to one or two retailers: (a) the supplier provides both retailers with full trade credit (FTC); (b) the supplier only provides full trade credit to one retailer (R1) and another retailer (R2) partial trade credit (HTC). R2 can seek external financing from the bank [20], [38]. Based on the bounded rationality criterion, the two retailers utilize the local information of the slope in the expected profit function to dynamically adjust their pricing strategies. Then, in above scenarios we establish the dynamic game models for the two competitive retailers and upstream suppliers respectively. Then, applying complex system theory to analyze the stability of the equilibrium point, the bifurcation to chaos, the Largest Lyapunov Index (LLE), and the basin of attraction. In addition, the dynamic evolution process of the system and the performance of the supply chain are also investigated with the critical parameters.

The contributions of our work are as follows. We probe the dynamical strategies of supply chain members in a dyadic supply chain and the impact of FCF and HTC on supply chain system coupling with the appearance of the green awareness. We also explore the complex characteristics of the decision making in supply chain. Furthermore, the impact of critical parameters such as different adjustment speeds and trade credit ratios on the local stability of the system are analyzed. Lastly, to the best of our knowledge, our study will make an attempt to analyze the dynamical property of the green supply chain in a competitive setting in a dyadic supply chain. More importantly, introducing greenness and supply chain financing into the dynamical decision-making system, we add to the literature and expanded the application of the bounded rationality criterion in supply chain.

The rest of this paper is organized as follows. In Section 2, we show some notations, assumptions and model descriptions. Section 3 gives the main results, in which two-echelon dynamic game models are proposed in two scenarios. Combining the theoretical analysis and numerical simulations, the complex dynamic properties of the models are also analyzed. Finally, the paper is concluded in Section 4 and summary, managerial insights, limitations and directions for future research are also made.

Section snippets

Model descriptions and notations

We consider a dyadic supply chain, which consists of two budget-constrained retailers (denoted by R1 and R2 respectively) facing non-negative random demand and a supplier (denoted by S) that produces green products and sells to downstream retailers at the same wholesale price w. Retailers sell products to customers at retail prices of p1 and p2 respectively. Further, we assume that the customers are not only sensitive to retail prices, but also sensitive to green levels. The market demand has a

Scenario 1

For any given wholesale price, the retailer Ri places an order of qi(1)(i=1,2). If the realized demand is Di given by Eq. (2.1), the sales income of Ri is pi(1)min{Di,qi(1)}. Please note that the retailer has limited funds and cannot afford the order, so the supplier provides trade credit to Ri, i=1,2. The retailer should pay the supplier w1qi(1)(1+rt) when the sale ends. Therefore, πR11=p1(1)min{D1,q1(1)}w(1)q1(1)(1+rt)πR21=p2(1)min{D2,q2(1)}w(1)q2(1)(1+rt)πS1=w(1)q1(1)+q2(1)(1+rt)cq1(1)+q2(

Conclusion

Acknowledgments

The presented work was supported by the Chinese National Funding of Social Science (19BGL094, Operational Strategy and Guidance Mechanism of Financing Joint Low Carbon in Agricultural Supply Chain), the National Natural Science Foundation of China (71902041, 72001048, 72072041), the Natural Science Foundation of Guangdong Province, China (G172071082) and Humanities and Social Sciences Research and Planning Fund of the Ministry of Education of China (20YJA630053).

References (39)

Cited by (6)

  • How carbon allowance allocation rule affects manufacturing/remanufacturing decisions under the carbon credits buy-back policy

    2022, Energy Reports
    Citation Excerpt :

    Cao and Yu (2019) studied supply chain operations and emissions reduction decisions considering the capital-constrained manufacturer can obtain loans from banks by pledging carbon credits. Taking capital constraint and product green level decision into account, Chen et al. (2022) studied the dynamic game problem of a two-stage supply chain under pure commercial credit and mixed commercial credit. However, the above studies focus on traditional operational issues.

  • Dynamic production and carbon emission reduction adjustment strategies of the brand-new and the remanufactured product under hybrid carbon regulations

    2022, Computers and Industrial Engineering
    Citation Excerpt :

    Elsadany (2017) proposed a Cournot model with two heterogeneous products and found that the independence between products can increase the stability of the system. Chen et al. (2022) analyzed the impacts of trade credit and adjustment speed on the stability of a two-echelon supply chain system with capital constraints. Lin et al. (2021) investigated the dynamic pricing and CER strategies in a low-carbon supply chain when the retailer shows a preference for social welfare.

View full text