Research on the Bullwhip Effect Based on Retailers’ Overconfidence in the Sustainable Supply Chain
Round 1
Reviewer 1 Report
Comments and Suggestions for Authors This paper investigates the impact of retailers' overconfidence on the bullwhip effect in sustainable supply chains. However, there are several areas for improvement. First, the introduction should provide a stronger motivation for the study by clearly articulating the practical implications and the gap in the existing literature that this research aims to fill. Second, the paper lacks a dedicated literature review section. Third, the conclusion should compare the findings of this study with related literature. Moreover, the authors assume that demand follows an AR(1) model. They need to clarify the application scenarios for this assumption and specify which types of products are suitable for this assumption. And the study focuses on a single-stage supply chain, which may not fully reflect the characteristics of multi-stage supply chains. Lastly, some figures, such as Figure 4, are of poor quality.Author Response
Dear Reviewer 1：
Thank you very much for taking the time to review this manuscript. We strongly agree with your comments. Next, we reply to your comments and suggestions one by one. Meanwhile, we mark all the modifications made to the original paper in red. Your advice provides us with great inspiration and good guidance.
Reviewer #1: This paper investigates the impact of retailers' overconfidence on the bullwhip effect in sustainable supply chains. However, there are several areas for improvement.
Point-by-point response to Comments and Suggestions for Authors
Comments 1:
First, the introduction should provide a stronger motivation for the study by clearly articulating the practical implications and the gap in the existing literature that this research aims to fill.
Response 1:
Thank you for pointing this out. We agree with this comment. Your professional advice has prompted us to seriously consider how to provide a stronger motivation for the study in the introduction by clearly articulating the practical implications and the gap in the existing literature. We have referred to the research direction of sustainable supply chains and reviewed the relevant literature on sustainable supply chains published in the journal 《Sustainability》. Finally, we have arrived at the following thoughts. Following your advice, we have revised the introduction of the paper to more clearly articulate the practical implications of the study and the gap in the existing literature. Therefore, we have made the following revisions:
- Reorganize the introduction to highlight the significance of the research:
To more clearly articulate the practical significance and the gap in the existing literature that this study aims to fill, thereby providing a stronger motivation for this research, I have restructured the order of the sections in the original manuscript and extracted the literature review into the second section of the article. In the introduction, the significance of the research in the field of sustainable supply chains has been emphasized. On page 2 of 27, in the third paragraph, we emphasized the practical significance of the research.
“Analyzing the impact of retailers' overconfidence on the bullwhip effect is of great significance in promoting the practice of sustainable supply chain concepts. In terms of environmental sustainability, reducing demand distortion caused by overconfidence can mitigate the bullwhip effect in sustainable supply chains. This, in turn, reduces inventory overstocking and overproduction, decreases transportation frequency and volume, and so on. As a result, it can lower energy consumption and waste emissions, improve the environmental performance of the supply chain, and help companies achieve their sustainable development goals. From the perspective of economic sustainability, overconfidence may trigger a crisis of trust among supply chain members and increase coordination costs, thereby inhibiting long - term cooperation. By mitigating the bullwhip effect, the overall efficiency and economic resilience of the supply chain can be enhanced. From the perspective of social sustainability, stable supply chain operations help safeguard labor rights (such as reducing the misuse of temporary workers due to order fluctuations) and ensure fair allocation of community resources. It also helps to increase the transparency and traceability of the supply chain, strengthen supervision and management of companies at various stages of the supply chain, and encourage businesses to better fulfill their social responsibilities.”
- Supplementary explanation of the research gaps filled by this paper
In the existing research on sustainable supply chains, some researchers have considered the impact of overconfidence of supply chain participants on decision-making and their own profits, but the analysis of the bullwhip effect has not been addressed. There is also no study that has considered the impact of retailers' overconfidence on the bullwhip effect. Therefore, this study fills this research gap. On page 3 of 27, in the second paragraph, we have supplemented the shortcomings of existing research：
“In the existing research on sustainable supply chains, some scholars have considered the impact of overconfidence of supply chain participants on decision-making and their own profits, but no research has analyzed its impact on the bullwhip effect. For example, Ji et al. [8] constructed game-theoretic models considering the overconfidence of suppliers and retailers, respectively. They considered the overconfidence of suppliers in overestimating the impact of their emission reduction efforts on product demand and the overconfidence of retailers in underestimating the variability of random demand. They analyzed the impact on joint decisions regarding carbon emission reduction and inventory replenishment, as well as the impact on their own profits. Yu & Sun [9] constructed a supply chain model including manufacturers and retailers and used a Stackelberg game model to explore the role of carbon trading pricing and overconfidence in the decision-making and profits of supply chain members. They found that overconfidence is always detrimental to manufacturers, especially when carbon trading prices rise. In the research on sustainable supply chains, no studies have yet considered the impact of retailers' overconfidence on the bullwhip effect. Therefore, this study starts from this perspective and focuses on the impact of retailers' overconfidence on the bullwhip effect in sustainable supply chains.”
The revised introduction will more clearly present "why this study is important" (practical value) and "why this study is necessary" (theoretical gap), ensuring that the research motivation is both practically penetrating and academically well-positioned. We believe that this revision will significantly enhance the problem-oriented nature of the paper and lay a more solid foundation for the subsequent chapters.
Thank you again for your valuable suggestions, which are crucial for improving the quality of the paper!
Comments 2:
Second, the paper lacks a dedicated literature review section.
Response 2:
Thank you for your constructive feedback. We fully recognize the importance of a dedicated literature review section in establishing the theoretical foundation and contextualizing our research within the broader scholarly conversation. Your observation highlights a critical area for improvement, and we appreciate the opportunity to address this gap.
In our current draft, while we integrated some literature within the introduction and methodology sections, we acknowledge that this approach lacks the systematic depth and organization expected of a standalone literature review. To strengthen the paper, we plan to:
Add a dedicated "Literature Review" chapter that synthesizes and critiques existing research relevant to our study’s core themes. In order to enhance the relevance of the description in the research background section, I have split the content of the introduction. The content related to the research background has been retained in the introduction, while the analysis of the current research status has been moved to the second section, the literature review. This makes the content of the literature review clearer and more detailed. I have also added 8 highly relevant latest references to make the literature review section more up-to-date and reflective of the current research progress. You can find the "Literature Review" paragragh on Page 4 of 27- Page 6 of 27.
“The traditional economic theory system is based on the assumption of "economic man," which holds that individual behavior is driven by self-interest and can make fully rational decisions. However, decision-making behavior in reality often deviates from this assumption. Psychological research has revealed that there are widespread cognitive biases in the decision-making process of individuals. In recent years, scholars have begun to explore the impact mechanism of incomplete rational cognitive biases on economic behavior from the perspective of behavioral economics. The concept of "overconfidence" originates from research findings in the field of cognitive psychology. Numerous cognitive psychology studies have pointed out that humans generally have a tendency to be overconfident, especially in overestimating the accuracy of their own knowledge.Wolosin et al. [10] found that people tend to overestimate their abilities and contributions to their work, often attributing their success to their skills and capabilities. Mahajon [11] argued that overconfidence refers to the behavior of individuals who overestimate the probability of certain events during decision-making. After these events occur, individuals believe their previous estimates were correct, thus reinforcing this psychological factor. Moore et al. [12] reviewed over 350 articles on overconfidence and confirmed its influence on decision-making. Their research found that decision-makers may exhibit overconfident irrational behavior across various fields and environments, and they identified three main manifestations of overconfidence behavior: overestimation, overplacement, and overprecision. Overestimation typically refers to the overestimation of one's own abilities to handle tasks, believing that one's skills are superior to others in managing situations. Overplacement refers to the belief that one's position or platform is higher than others, i.e., above the average level. Overprecision involves making more accurate predictions based on one's perceived understanding of the actual situation.
Traditional perspectives often attribute the widespread inefficiencies in supply chains (such as the bullwhip effect) to information asymmetry, but traditional theoretical frameworks have limitations in explaining the bullwhip effect. Against this backdrop, scholars have begun to focus on the impact of decision-makers' irrational behavior on supply chain fluctuations. Lu et al.[13] explored the impact of information errors in inter-channel information sharing on decision-making and supply chain operational efficiency in omnichannel operations. Pournader et al.[14] explored the impact of risk preferences on decision biases and the bullwhip effect in multi-stage supply chains from a risk preference perspective.Pillai and Min [15] introduced the concept of knowledge calibration into supply chain management, emphasizing the role of matching confidence with the accuracy of knowledge in decision-making. If confidence and accuracy do not match (such as overestimating or underestimating the value of knowledge), it may lead to supply chain inefficiencies (such as the bullwhip effect).
Among supply chain entities, downstream retailers may exhibit overconfidence due to incomplete information or insufficient self-awareness, which can lead to decision errors and trigger the bullwhip effect. However, research that considers the overconfidence biases of retailers in the context of the bullwhip effect is still insufficient. Existing studies mainly explore the impact of retailer overconfidence on the supply chain from the perspectives of supply chain coordination and decision-making. Wang et al. [16] discussed the efficiency of supply chain contracts in coordinating the supply chain with overprecision-type retailers. Ren and Croson [17] assumed that retailers over-precisely interpret demand information and analyzed their ordering decisions from the supply chain decision-making perspective, while correcting overconfidence through pricing strategies, repurchase contracts, and other methods to stimulate optimal decision-making behavior. Xu et al. [18] investigated the optimization of pricing and overconfidence issues in a duopoly supply chain, analyzing the impact of retailer overconfidence on supply chain performance, with the results highlighting that overconfidence does not necessarily harm supply chain performance.
With the expansion and deepening of supply chain research, scholars have gradually introduced the concept of overconfidence into the study of supply chains to analyze the bullwhip effect. Ancarani et al. [19] found through the beer game research that overconfidence can lead to biases in supply chain ordering decisions, triggering the bullwhip effect. In experimental settings, even experts familiar with supply chain management may have their decisions affected by overconfidence. Shee and Kaswi [20] discovered through surveys of local and multinational supermarket managers in India that these managers are overly confident in their decisions, which leads to increased order variability and the bullwhip effect. Yang et al. [21] demonstrated that behavioral and psychological factors play a critical role in generating the bullwhip effect. Their research on overconfidence shows that it is an important behavioral factor affecting supply chain decisions and may lead to the bullwhip effect.
However, in the research literature on sustainable supply chain management, there is limited research on the bullwhip effect in sustainable supply chains. Existing research literature mainly focuses on the green collaboration across the entire supply chain, including green procurement, low-carbon logistics, and supplier social responsibility management [22]. Metwally et al. [23] empirically demonstrated based on the Egyptian manufacturing industry that digital technology indirectly improves the environmental performance of sustainable supply chains by enhancing supply chain resilience and robustness. Li et al. [24] focused on the joint impact of lead time uncertainty (LTU) and carbon cost on the bullwhip effect in sustainable supply chains. Shaban et al. [25] explored how to reduce the bullwhip effect while maintaining service levels under demand-related scenarios to enhance supply chain sustainability.Some studies have also focused on the impact of irrational behaviors, such as overconfidence, on supply chain performance and stability, indirectly affecting the bullwhip effect.
Research on overconfidence in sustainable supply chain remains insufficient. Some scholars still only focus on the impact of overconfidence on decision-making and coordination in sustainable supply chains, with limited research on its impact on the bullwhip effect in sustainable supply chains. Moreover, the bullwhip effect has only been studied as a reference factor for measuring the efficiency of sustainable supply chain systems, and no systematic research has been found on the impact of retailers' overconfidence on the bullwhip effect of order quantities and inventory levels. Therefore, this paper analyzes the impact of retailers' overconfidence on the bullwhip effect of order quantities and inventory levels in sustainable supply chains from the perspective of retailers' overconfidence. It not only supplements the research on the bullwhip effect from the behavioral operations aspect but also further extends the application research of overconfidence theory in the field of sustainable supply chains.”
This revision will not only fulfill the structural expectation of a literature review but also deepen the paper’s theoretical rigor by providing readers with a comprehensive understanding of where our work stands in relation to existing knowledge. We sincerely appreciate your guidance, which is instrumental in improving the quality and completeness of our manuscript.
Comments 3: Third, the conclusion should compare the findings of this study with related literature.
Response 3:
We sincerely appreciate the reviewer’s constructive suggestion. To address this point, we have revised the Conclusion section to explicitly compare our findings with key studies in the existing literature. The revised text can be found in the Conclusion section (Page 19 of 27, the 4th paragragh of the updated manuscript).
“The conclusions of this study on the impact of lead time and demand autocorrelation coefficient on the bullwhip effect are basically consistent with those of other researchers[24-25]. Meanwhile, this study characterizes the overconfidence of retailers from two aspects: overestimation and overprecision. The analysis of the impact of overestimation coefficient and overprecision coefficient on the bullwhip effect fills the gap in existing research. The conclusion that overestimation exacerbates the bullwhip effect is consistent with intuitive judgment. However, contrary to intuitive judgment, overprecision has a certain mitigating effect on the bullwhip effect, although this mitigating effect is relatively weak.”
Thank you once again for your professional suggestions! We believe these revisions significantly strengthen the scholarly contribution of the paper, ensuring that the conclusions are both summative and theoretically extendable.
Comments 4:
Moreover, the authors assume that demand follows an AR(1) model. They need to clarify the application scenarios for this assumption and specify which types of products are suitable for this assumption.
Response4:
Thank you for your professional advice. We strongly agree with your comments. Your professional advice has prompted us to seriously consider the choice of demand model. The AR(1) model, namely the first-order autoregressive model, as a special form of the ARMA model, is widely used in time series analysis. The AR(1) (first-order autoregressive) model assumes that the current market demand Dt is linearly correlated with the demand of the previous period Dt-1. This model is suitable for market scenarios where demand has short-term persistence but is stable in the long run, that is, demand fluctuates around the mean, there is correlation between demands in adjacent periods, but there is no significant trend or seasonality. In the study of the bullwhip effect in sustainable supply chains focused on , demand is consistent with stationarity, there is no long-term upward or downward trend in market demand, and the fluctuation range is controllable. At the same time, demand also has short-term dependence, with the demand of the current period being directly affected by the demand of the previous period (such as consumer purchasing habits, replenishment cycles, etc.).
Overall, the AR(1) assumption is suitable for market environments where demand is stable, has strong short-term correlation, and is subject to minimal random disturbances. This is typical for products such as everyday consumer goods and basic industrial products. Combined with research on retailers' overconfidence, the model can effectively simulate the amplification of the bullwhip effect caused by forecasting bias.
Therefore, this study assumes that the current market demand conforms to the AR(1) model, which is widely used in bullwhip effect research and is well-suited to the characteristics of sustainable supply chains.
Following your suggestion, we have supplemented the following content in the third paragraph on page 6 of 27:
“ For the demand process, the ARMA model has been widely applied, especially the special form of the ARMA model, the AR(1) model. Lee et al. [18] were the first to systematically analyze the bullwhip effect in the supply chain and its countermeasures using the AR(1) demand model. The AR(1) model is widely used in time series analysis.”
Comments 5:
And the study focuses on a single-stage supply chain, which may not fully reflect the characteristics of multi-stage supply chains.
Response 5:
Thank you for pointing this out. We agree with this comment. This article is based on the analysis of a single-stage supply chain structure, focusing on the overconfidence of retailers in a single-stage supply chain to analyze the impact on the bullwhip effect on product orders and inventory. Your comments is very accurate. The single-stage supply chain model, as a typical supply chain structure, cannot represent the characteristics of a multi-stage supply chain model. Therefore, we later expanded the supply chain structure to study the overconfidence of retailers in both two-stage supply chains and two parallel supply chain structures, analyzing the impact on the bullwhip effect. The research conclusions are essentially consistent with those derived from the single-stage supply chain structure. On this basis, I completed my doctoral dissertation. This article, as a part of my doctoral dissertation, fully elaborates on the single- stage supply chain structure. However, due to space limitations, it is indeed impossible to cover the research content of the two-stage supply chain structure and the two parallel supply chain structures from the subsequent studies at the same time. Therefore, I explained this in the first point of the research limitations section at the end of the article, which can serve as a direction for future research to continue expanding. The explanation in the research limitations section can be found in the last paragraph on page 20 of 27:
“Firstly, in terms of model design, a single-stage simplified model is used, without considering the complex interactions in multi-echelon supply chains.”
The above modifications have been highlighted in yellow in the revised draft and we sincerely ask you to review it again. It is hoped that a thorough elaboration of the research limitations can address the issue you have pointed out.
Comments 6: Lastly, some figures, such as Figure 4, are of poor quality.
Response 6:
Thank you for your professional advice. We strongly agree with your comments. Following your suggestion, we have revised Figure 4, which was not very clear, and made the following changes:
We have replaced Figure 4 with a higher-quality and clearer original image. To ensure clarity, we have split the original Figure 4, titled “Figure 4. Relationship Between the BWEinventory and ρ for Different α, β Values (L = 2)” into two separate figures, “Figure 4(a). Relationship Between the BWEinventory and ρ for Different β Values (L = 2, α= 0.4)” and “Figure 4(b). Relationship Between the BWEinventory and ρ for Different α Values (L = 2,β=5 )” The revised figures are as follows(Page 17 of 27):
Figure 4(a). Relationship Between the BWEinventory and ρ for Different β Values (L = 2, α= 0.4)
Figure 4(b). Relationship Between the BWEinventory and ρ for Different α Values (L = 2,β=5 )
Finally, we once again express our gratitude to the reviewers for your valuable suggestions. Your comments have provided us with good inspiration for improving and revising the paper. We have further supplemented relevant data discussions and detailed explanations in the paper based on your suggestions.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe introduction in the submitted manuscript is quite general and rather vague. Is the problem of Retailers' Overconfidence typical for all industries and do the authors solve it for all industries in their study? If the solution is not general, then it is necessary to reflect what specific problem the authors want to solve in their study. Is it typical for a specific industry or a specific retailer? It is necessary to more clearly and reasonably present the problem under consideration in the article in order to justify the relevance of the study.
My main complaints about Section 5. Simulation Analysis follow from the unclear justification of relevance. I did not see in this section where the data for the modeling was obtained. Are the input data synthesized or obtained from the Internet. What is the structure of the input data? Is it possible to provide an example of the output data? How do these initial data reflect the problem of Retailers' Overconfidence? I also did not see what software was used for the modeling. It would be good if the authors presented a diagram or chart of data processing during the experiment. Accordingly, the results of the study should reflect whether the authors managed to solve the formulated problem by analyzing the initial data.
Author Response
Dear Reviewer 2：
Thank you very much for taking the time to review this manuscript. We strongly agree with your comments. Next, we reply to your comments and suggestions one by one. Meanwhile, we mark all the modifications made to the original paper in red. Your advice provides us with great inspiration and good guidance.
Reviewer #2: The introduction in the submitted manuscript is quite general and rather vague.
Accordingly, the results of the study should reflect whether the authors managed to solve the formulated problem by analyzing the initial data.
Point-by-point response to Comments and Suggestions for Authors
Comments 1:
Is the problem of Retailers' Overconfidence typical for all industries and do the authors solve it for all industries in their study? If the solution is not general, then it is necessary to reflect what specific problem the authors want to solve in their study. Is it typical for a specific industry or a specific retailer? It is necessary to more clearly and reasonably present the problem under consideration in the article in order to justify the relevance of the study.
Response 1:
Dear Reviewer, thank you for your insightful comments on the scope of the study. The issues you raised are of great significance.According to your suggestion, I further discuss the problem of industry adaptability in my paper.We have further clarified the boundaries and applicability of the study based on the original text. The specific explanations are as follows:
1.The Ubiquity and Industry-Specificity of Retailers' Overconfidence
Overconfidence, as a behavioral decision bias, is a widespread phenomenon in supply chain management, but its intensity and impact vary across industries. For example: In industries with stable demand and frequent information updates (such as fast-moving consumer goods), retailers are more likely to over-rely on their own forecasts with historical demand information. In industries with high demand volatility and high supply chain transparency (such as fashion products and highly seasonal goods), the negative impact of overconfidence may be relatively weak.
This study focuses on the former scenario and does not claim to be applicable to all industries. However, by extracting key drivers (such as demand autocorrelation and level of overconfidence), it can provide an analytical framework for other industries. The applicable industries have also been supplemented in the model-building section.
The specific modifications can be found in page 6 of 27 , Paragragh 3 “3.1 Demand Model” section as follows:
“The AR(1) model is widely used in time series analysis, and it is suitable for market environments where demand is stable, has strong short-term correlation, and is subject to minimal random disturbances.”
2.Specificity of Research Questions and Industry Orientation
The core objective of this study is to reveal "how overconfidence exacerbates the bullwhip effect through demand signal distortion," rather than to provide a universal solution. To enhance the clarity of the problem and the applicability of the conclusions, we have revised the conclusion section and supplemented the practical implications:
For industries with low demand volatility (such as everyday consumer goods and basic industrial products), the conclusions of this study's model can be applied to optimize order decisions.
For industries with high demand volatility, parameters need to be recalibrated based on industry data, but the analytical logic of behavioral bias remains of reference value.
We have revised the conclusion section, strengthening and supplementing the relevance of the study and the scope of the conclusions. The newly added content has been highlighted in red in the third paragraph on Page 20 of 27. We sincerely thank you to review it again.
“In supply chain practice, for industries with low demand volatility (such as everyday consumer goods and basic industrial products), the conclusions of the model in this paper can be applied to optimize order decisions. For industries with high demand volatility, parameters may need to be recalibrated based on industry data, but the analytical logic of overconfidence behavioral bias in this study still has reference value.”
Comments 2:
My main complaints about Section 5. Simulation Analysis follow from the unclear justification of relevance. I did not see in this section where the data for the modeling was obtained. Are the input data synthesized or obtained from the Internet. What is the structure of the input data?
Response 2:
Dear Reviewer, Thank you very much for your valuable comments on the thesis. In response to your concerns regarding the data source and the correlation demonstration in Section 5, "Simulation Analysis", the following is our reply.
1.The source of the input data
The simulation data in this paper is not directly derived from the Internet or external datasets, but is generated based on theoretical models. The core objective is to verify the logical consistency, convergence, and parameter sensitivity of the model derivation. Specifically:
In the simulation analysis of this paper, all input data are generated through numerical calculations with the aim of verifying the validity and accuracy of the results derived from the model. To ensure the consistency between the theoretical derivation of the model and its actual numerical performance, we used the scientific computing software Wolfram Mathematica 13.3 for programming to perform numerical calculations and generate data according to the model assumptions and parameter settings, so as to construct the simulation scenarios. Since the core function of the data is to verify the model logic within the theoretical framework, there is no involvement of data collection from the Internet or the use of external actual datasets for the time being.
2.The structure of the input data
Regarding the data structure, we generate multiple sets of input data under different conditions based on the variables and parameters involved in the model. Each set of data includes the set values of key variables, the parameter values involved in the model derivation, etc., which are stored in the form of a matrix and called and processed in an orderly manner through programming codes. In the subsequent revision, we will supplement the specific methods of data generation and the example data structure in the paper to make the generation logic and usage of the data more transparent and clear. Meanwhile, we will strengthen the demonstration of the correlation between the data and the results derived from the model to ensure that readers can accurately understand the logical chain of the simulation analysis.
Therefore, we have marked the revised content in red font in the third paragraph of the “Simulation Analysis” section on Page 11 of 27. The specific supplementary revisions are as follows:
“To further verify the results and determine the critical threshold, this paper conducted numerical simulations using the scientific computing software Wolfram Mathematica 13.3. To examine the effects of overconfidence coefficients (α,β), demand autocorrelation coefficient (?), and lead time (?) on the bullwhip effect on product orders and inventory under lead times of ? = 1,2,4.”
Therefore, in the simulation analysis, the data input were all based on the relevant literature on the bullwhip effect, using numerical simulation data.
In Section “6.1 Simulation Analysis of the Bullwhip Effect on Product Orders”, the input data were lead time L=1, L=2, and L=4. The overestimation coefficient β∈{1,3,5,7,9} and the demand autocorrelation coefficient ρ∈{0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9}. After calculating the numerical values of using Mathematica software, the results were output in graphical form. The output data results are shown in Table 2.
In Section “6.2 Simulation Analysis of the Bullwhip Effect on Inventory”, the input data were lead time L = 2 and L = 4. the overestimation coefficient = 3 and = 5, the overprecision coefficient , and the demand autocorrelation coefficient . After calculating the numerical values of using Mathematica software, the results were output in graphical form. The output data results are shown in Table 3.
Thank you again for your meticulous review and professional suggestions, which are of great significance for improving the quality of the thesis!
Comments 3:
Is it possible to provide an example of the output data? How do these initial data reflect the problem of Retailers' Overconfidence?
Response3:
Thank you to the reviewers for your in-depth attention to the research logic of this paper and your valuable comments. In response to the two questions you raised, we provide detailed explanations as follows:
- Output Data Example and Explanation
Table 1 and Table 2 are the actual output data from our simulation analysis. We have not made any modifications to the output data results. We have only organized and presented them in graphical form for clarity in the article. To ensure consistency in presentation, we have rounded the output results to two decimal places. The original data tables for Table 1 and Table 2 will be attached here:
Table 2 Analysis of the Impact of Different Parameter Combinations on the for L=1,2, and 4
|
L=1 |
ρ |
|||||||||||
|
|
β |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
ρ* |
BWEorder max |
|
BWEorder |
1 |
1.21978 |
1.47616 |
1.75894 |
2.04832 |
2.31250 |
2.50528 |
2.56366 |
2.40544 |
1.92682 |
0.68335 |
2.56650 |
|
3 |
1.79002 |
2.98144 |
4.55446 |
6.40288 |
8.31250 |
9.93952 |
10.78894 |
10.19296 |
7.28938 |
0.71678 |
10.81080 |
|
|
5 |
2.53450 |
5.22400 |
9.05350 |
13.76800 |
18.81250 |
23.27200 |
25.81150 |
24.61600 |
17.33050 |
0.72564 |
25.94520 |
|
|
7 |
3.45322 |
8.20384 |
15.25606 |
24.14368 |
33.81250 |
42.50272 |
47.63134 |
45.67456 |
32.05018 |
0.72976 |
47.97530 |
|
|
9 |
4.54618 |
11.92096 |
23.16214 |
37.52992 |
53.31250 |
67.63168 |
76.24846 |
73.36864 |
51.44842 |
0.73192 |
76.90190 |
|
|
L=2 |
ρ |
|||||||||||
|
|
β |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
ρ* |
BWEorder max |
|
BWEorder |
1 |
1.22198 |
1.49521 |
1.82724 |
2.21605 |
2.64063 |
3.04718 |
3.32985 |
3.30492 |
2.67754 |
0.74697 |
3.37141 |
|
3 |
1.79900 |
3.07606 |
4.94240 |
7.45166 |
10.51563 |
13.77983 |
16.44988 |
17.05949 |
13.17110 |
0.77147 |
17.21600 |
|
|
5 |
2.55345 |
5.44416 |
10.00511 |
16.42528 |
24.51563 |
33.36352 |
40.85034 |
43.00704 |
33.18260 |
0.77716 |
43.27880 |
|
|
7 |
3.48531 |
8.59951 |
17.01539 |
29.13691 |
44.64063 |
61.79826 |
76.53122 |
81.14756 |
62.71207 |
0.77978 |
81.56390 |
|
|
9 |
4.59460 |
12.54212 |
25.97321 |
45.58655 |
70.89063 |
99.08404 |
123.49253 |
131.48105 |
101.75948 |
0.78123 |
132.07200 |
|
|
L=4 |
ρ |
|||||||||||
|
|
β |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
ρ* |
BWEorder max |
|
BWEorder |
1 |
1.22222 |
1.49981 |
1.85444 |
2.31427 |
2.90723 |
3.63764 |
4.42559 |
4.96860 |
4.45383 |
0.81956 |
4.99032 |
|
3 |
1.79999 |
3.09904 |
5.09868 |
8.07762 |
12.35254 |
18.09860 |
24.84207 |
30.26315 |
27.66179 |
0.83387 |
30.82200 |
|
|
5 |
2.55553 |
5.49776 |
10.39008 |
18.02070 |
29.30566 |
44.80714 |
63.34562 |
78.70083 |
72.60346 |
0.83695 |
80.53580 |
|
|
7 |
3.48885 |
8.69597 |
17.72863 |
32.14352 |
53.76660 |
83.76326 |
119.93626 |
150.28163 |
139.27885 |
0.83833 |
154.13400 |
|
|
9 |
4.59995 |
12.69366 |
27.11435 |
50.44607 |
85.73535 |
134.96697 |
194.61397 |
245.00556 |
227.68796 |
0.83902 |
251.61600 |
|
Table 3. Analysis of the Impact of Different Parameter Combinations on the for L=2 and 4
|
L=2 |
β=3 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
1.798720 |
2.104320 |
2.566720 |
3.243520 |
4.200000 |
5.509120 |
7.251520 |
9.515520 |
12.397100 |
|
|
0.4 |
1.361140 |
1.635840 |
2.077140 |
2.746240 |
3.712500 |
5.053440 |
6.854740 |
9.210240 |
12.221900 |
||
|
0.6 |
0.923560 |
1.167360 |
1.587560 |
2.248960 |
3.225000 |
4.597760 |
6.457960 |
8.904960 |
12.046800 |
||
|
0.8 |
0.485980 |
0.698880 |
1.097980 |
1.751680 |
2.737500 |
4.142080 |
6.061180 |
8.599680 |
11.871600 |
||
|
L=2 |
β=5 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
1.94392 |
2.79552 |
4.39192 |
7.00672 |
10.95000 |
16.56830 |
24.24470 |
34.39870 |
47.48630 |
|
|
0.4 |
1.50634 |
2.32704 |
3.90234 |
6.50944 |
10.46250 |
16.11260 |
23.84790 |
34.09340 |
47.31110 |
||
|
0.6 |
1.06876 |
1.85856 |
3.41276 |
6.01216 |
9.97500 |
15.65700 |
23.45120 |
33.78820 |
47.13600 |
||
|
0.8 |
0.63118 |
1.39008 |
2.92318 |
5.51488 |
9.48750 |
15.20130 |
23.05440 |
33.48290 |
46.96080 |
||
|
L=2 |
β=7 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
2.18592 |
3.94752 |
7.43392 |
13.27870 |
22.20000 |
35.00030 |
52.56670 |
75.87070 |
105.96800 |
|
|
0.4 |
1.74834 |
3.47904 |
6.94434 |
12.78140 |
21.71250 |
34.54460 |
52.16990 |
75.56540 |
105.79300 |
||
|
0.6 |
1.31076 |
3.01056 |
6.45476 |
12.28420 |
21.22500 |
34.08900 |
51.77320 |
75.26020 |
105.61800 |
||
|
0.8 |
0.87318 |
2.54208 |
5.96518 |
11.78690 |
20.73750 |
33.63330 |
51.37640 |
74.95490 |
105.44300 |
||
|
L=4 |
β=3 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
3.75310 |
4.50016 |
5.54947 |
7.08474 |
9.41250 |
13.03230 |
18.73720 |
27.75410 |
41.93330 |
|
|
0.4 |
2.82717 |
3.43742 |
4.34281 |
5.73553 |
7.93828 |
11.47880 |
17.19680 |
26.39270 |
41.02960 |
||
|
0.6 |
1.90124 |
2.37468 |
3.13616 |
4.38633 |
6.46406 |
9.92533 |
15.65640 |
25.03140 |
40.12590 |
||
|
0.8 |
0.97530 |
1.31194 |
1.92950 |
3.03712 |
4.98984 |
8.37185 |
14.11600 |
23.67000 |
39.22220 |
||
|
L=4 |
β=5 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
3.90122 |
5.24776 |
7.71799 |
12.14850 |
19.95940 |
33.48740 |
56.46380 |
94.67990 |
156.88900 |
|
|
0.4 |
2.97529 |
4.18502 |
6.51133 |
10.79930 |
18.48520 |
31.93390 |
54.92340 |
93.31860 |
155.98500 |
||
|
0.6 |
2.04935 |
3.12228 |
5.30468 |
9.45009 |
17.01090 |
30.38040 |
53.38300 |
91.95720 |
155.08200 |
||
|
0.8 |
1.12342 |
2.05954 |
4.09802 |
8.10089 |
15.53670 |
28.82690 |
51.84260 |
90.59580 |
154.17800 |
||
|
L=4 |
β=7 |
ρ |
|||||||||
|
|
α |
0.1 |
0.2 |
0.3 |
0.4 |
0.5 |
0.6 |
0.7 |
0.8 |
0.9 |
|
|
BWEinventory |
0.2 |
4.14808 |
6.49377 |
11.33220 |
20.58810 |
37.53750 |
67.57920 |
119.34200 |
206.22300 |
348.48200 |
|
|
0.4 |
3.22215 |
5.43103 |
10.12550 |
19.23890 |
36.06330 |
66.02570 |
117.80100 |
204.86200 |
347.57800 |
||
|
0.6 |
2.29622 |
4.36829 |
8.91888 |
17.88970 |
34.58910 |
64.47230 |
116.26100 |
203.50000 |
346.67500 |
||
|
0.8 |
1.37029 |
3.30555 |
7.71222 |
16.54050 |
33.11480 |
62.91880 |
114.72000 |
202.13900 |
345.77100 |
||
Considering the length and conciseness of the article, the original table data are not listed. In the revised manuscript, we have added supplementary explanations of the output data, including the typical structure and content of the output data, to help readers better understand the nature of our results. The revised content is as follows:
“To unify the format of the output results, the calculation results are rounded to two decimal places.”
The newly added explanatory content is respectively added to paragraph 1 on page 12 of 27 and paragraph 1 on page 15 of 27, and is displayed in red font.
2.How the Data Reflects the "Retailer Overconfidence" Issue
Thank you for your valuable feedback. To further clarify how our output data reflect retailers' overconfidence, we'd like to elaborate on the following points:
In our output results, we utilize two key coefficients - the overestimation coefficient β and the overprecision coefficient α - to measure retailers' overconfidence. Specifically, as the value of β increases, it directly indicates a higher level of overestimation by retailers. This relationship is clearly demonstrated in the output tables, where we observe a significant increase in both the bullwhip effect of product orders and inventory level. These findings are consistent with the theoretical propositions derived earlier in the paper, and have been further validated through numerical simulations.
In addition, we have included Figures 1 - 4 to provide a more intuitive visual representation of these relationships. The figures clearly show upward - trending curves, indicating that both the bullwhip effect of order quantity and inventory level rise significantly as the value of β increases. This visual evidence further supports our theoretical analysis and findings, offering a more comprehensive understanding of how retailers' overconfidence impacts supply chain dynamics.
In Section 6.2 Simulation Analysis of the Bullwhip Effect on Inventory, the impact of retailer over-precision on the bullwhip effect in inventory levels is also observed by adjusting the value of α simultaneously. As can be seen from Table 3, with the increase in the value of α representing the level of retailer over-precision, the bullwhip effect value in inventory levels decreases slightly, but the decline is not very significant. This change can be more intuitively observed from Figure 4(b), where the four curves with different values of α almost overlap. As the value of α increases, only a small decrease in the bullwhip effect in inventory levels can be seen.
Thank you once again for your suggestions! We are more than happy to provide further explanations regarding specific examples or details of the analysis.
Comments 4:
I also did not see what software was used for the modeling. It would be good if the authors presented a diagram or chart of data processing during the experiment. Accordingly, the results of the study should reflect whether the authors managed to solve the formulated problem by analyzing the initial data.
Response 4:
Dear Reviewer, Thank you for your constructive feedback. Regarding your concerns, we sincerely apologize for the lack of clarity in the manuscript.
1.Software was used for the modeling
In our study, we employed Mathematica as the primary software for modeling. Mathematica's powerful symbolic and numerical computation capabilities, along with its extensive built - in functions and visualization tools, provided an ideal platform for implementing our theoretical models and conducting in - depth simulations. Its ability to handle complex equations and generate accurate results efficiently made it the perfect choice for our research requirements.
To address your suggestion, we will definitely add a detailed description in the revised version. We have marked the revised content in red font in the third paragraph of the “Simulation Analysis” section on Page 11 of 27. The specific supplementary revisions are as follows:
“To further verify the results and determine the critical threshold, this paper conducted numerical simulations using the scientific computing software Wolfram Mathematica 13.3.”
2.The software code for the data processing procedure.
To more clearly demonstrate the data processing procedure, I will provide a detailed display of the running code for Figures 2 and 3 as examples. However, considering the length limitation of the article and the need for proper expression, the software code has not been placed in the appendix. I hope you can understand this. If you believe that the data processing code should be included, I can upload the code file as supplementary material. Thank you again for your suggestion.
(1)The Mathematica software running code for calculating the bullwhip effect on product orders for Table 2:
(* Define the function *)
BWEorder[β_, ρ_, L_] := (2 β^2 ρ^2 (1 - ρ^(L + 1))^2 + 2 β ρ (1 - ρ^(L + 1)) (1 - ρ) + (1 - ρ))/(1 - ρ);
(* set the parameters *)
L = 2;
βValues = {1, 3, 5, 7, 9};
ρValues = {0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9};
(* calculate the value of BWE_order *)
results = Table[BWEorder[β, ρ, L], {β, βValues}, {ρ, ρValues}];
(* output the result *)
TableForm[results, TableHeadings -> {βValues, ρValues}]
(2)The Mathematica software running code for calculating the bullwhip effect on inventory for Table 3:
"(*" Define the function "*)"
BWEinventory[ρ_,α_,L_,β_]:=1⁄((1-ρ)^2)*(ρ^2*(β-1)^2*(1-ρ^L)^2+(1-α)*L*(1-ρ^2)-2*(1-α)*ρ*(1-ρ^L)*(1+ρ)+(1-α)*ρ^2*(1-ρ^(2*L)))"
(*"parameters"*)"
L=1;β=3;αValues={0.2,0.4,0.6,0.8};ρValues={0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9};"
(*" calculate the value” *)"
results=Table[BWEinventory[ρ,α,L,β],{α,αValues},{ρ,ρValues}];"
(*"output the result"*)"
resultsTable=TableForm[results,TableHeadings->{αValues,ρValues}];" Print[resultsTable]
3.Summary
To sum up, through the simulation analysis above, we used Mathematica software to perform calculations and generated results of the bullwhip effect on product orders and inventory level under different parameter combinations. We also employed Mathematica software to draw three-dimensional and two-dimensional function images for visualization. The final simulation analysis results fully validated the propositions derived in the model analysis stage. The data simulation analysis more intuitively shows the impact of parameters such as overestimation coefficient, overprecision coefficient, demand autocorrelation coefficient, and lead time on the bullwhip effect on product orders and inventory. It addressed the main issues we wanted to discuss in the introduction and led us to the final conclusions.
Your feedback is invaluable in helping us enhance the transparency and comprehensibility of our research. We greatly appreciate your time and effort in reviewing our work.
Finally, we once again express our gratitude to the reviewers for your valuable suggestions. Your comments have provided us with good inspiration for improving and revising the paper. We have further supplemented relevant data discussions and detailed explanations in the paper based on your suggestions.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsDear Author,
Thank you for the opportunity to review your manuscript titled “Research on the Bullwhip Effect Based on Retailers.” I found your study to be a thorough, detailed, and carefully constructed piece of research.
The title and abstract are both well-formulated. The abstract is informative without being overly lengthy and clearly communicates the key aspects of your work.
The introduction and literature review effectively identify a research gap and present three well-defined research proposals. While the review is based on a relatively concise but in-depth analysis, one issue is that most of the cited literature is over ten years old. I recommend incorporating more recent references to strengthen the relevance of your background section.
The model description is highly professional and detailed. The appendix at the end supports the validity of your model. However, I have one question:
The formula N(0, (1 − alpha)δ²) is unclear — it is not obvious where it fits within the model or what its exact purpose is. Please clarify its context or intended use.
The biggest problems are formatting issues:
- In Chapters 2 and 3, the main formulas need to be clearly separated from the body text, as the current formatting makes them difficult to read.
- Please avoid placing limitations and conditions within the main body text. For readability, these should be placed directly below the formulas they refer to.
- The notation delta* should not be used in this form. Please replace the asterisk with a superscript apostrophe, as the current form can be easily misinterpreted as a multiplication symbol.
The figures are generally well-prepared, and the experiments and sensitivity analyses are comprehensive. The results are valid and clearly support your conclusions. The overall presentation of data is effective.
However, one issue: the caption of Figure 1 contains an error — it shows only the analysis for L = 2, which should be stated clearly in the caption.
The conclusion provides a strong summary of the study, clearly outlining the contributions, limitations, and directions for future research.
In terms of language and style, the manuscript is well-written and free from major grammatical or typographical errors.
Congratulations on an excellent and insightful piece of work. With the suggested minor corrections and an expansion of the literature review with newer research, I believe the manuscript is suitable for acceptance.
Author Response
Dear Reviewer 3：
Thank you very much for taking the time to review this manuscript. We strongly agree with your comments. Next, we reply to your comments and suggestions one by one. Meanwhile, we mark all the modifications made to the original paper in red. Your advice provides us with great inspiration and good guidance.
Reviewer #3: I found your study to be a thorough, detailed, and carefully constructed piece of research.
The conclusion provides a strong summary of the study, clearly outlining the contributions, limitations, and directions for future research.
In terms of language and style, the manuscript is well-written and free from major grammatical or typographical errors.
Congratulations on an excellent and insightful piece of work. With the suggested minor corrections and an expansion of the literature review with newer research, I believe the manuscript is suitable for acceptance.
Point-by-point response to Comments and Suggestions for Authors
Comments 1:
The title and abstract are both well-formulated. The abstract is informative without being overly lengthy and clearly communicates the key aspects of your work.
Response 1:
Thank you for your positive evaluation of the title and abstract of the article. We strive to ensure that the title and abstract can accurately convey our main conclusions. The abstract of the paper is rich in information and conforms to the word count requirements and writing requirements of the journal for abstracts. Firstly, we explained the core characteristics of the bullwhip effect. Then, we discussed the main research variables of this paper, namely the retailer's cognitive bias (i.e., overconfidence) and the relationship between the bullwhip effect and sustainable supply chain. At the same time, we also studied the moderating effect and the results of numerical simulation analysis. Finally, we discussed the important management implications and policy significance of the research conclusions of this paper.
Comments 2:
The introduction and literature review effectively identify a research gap and present three well-defined research proposals. While the review is based on a relatively concise but in-depth analysis, one issue is that most of the cited literature is over ten years old. I recommend incorporating more recent references to strengthen the relevance of your background section.
Response 2:
Thank you for your thoughtful feedback. We greatly appreciate your insight regarding the currency of our literature review. You are absolutely correct that incorporating more recent references is essential to strengthen the relevance of the background section, especially in a field where theoretical and empirical advancements continue to evolve rapidly.
We acknowledge that while the foundational theories and concepts discussed in our current draft rely on seminal works from earlier decades, updating the literature to include more recent studies (particularly from the past five years) will enhance the manuscript’s alignment with contemporary research trends.
In order to enhance the relevance of the description in the research background section, I have split the content of the introduction. The content related to the research background has been retained in the introduction, while the analysis of the current research status has been moved to the second section, the literature review. This makes the content of the literature review clearer and more detailed. I have also added the following highly relevant latest references to make the literature review section more up-to-date and reflective of the current research progress:
[1] Lu J , Nageswaran L , Xu J ,et al.Horizontal Information Sharing in Omnichannel Operations: Impact of Information Errors[J]. Social Science Electronic Publishing[2024-10].
[2] Pournader M, Narayanan A, Keblis M F, et al. Decision Bias and Bullwhip Effect in Multiechelon Supply Chains: Risk Preference Models[J]. IEEE Transactions on Engineering Management, 2024, 71: 9229-9243.
[3] Yang Y, Lin J, Liu G, et al. The behavioural causes of bullwhip effect in supply chains: A systematic literature review[J]. International Journal of Production Economics, 2021, 238: 108120.
[4] Shaban, A.; Shalaby, M.A.; Di Gravio, G.; Patriarca, R. Analysis of Variance Amplification and Service Level in a Supply Chain with Correlated Demand. Sustainability 2020, 12, 6470.
[5] Li, Z.; Fei, W.; Zhou, E.; Gajpal, Y.; Chen, X. The Impact of Lead Time Uncertainty on Supply Chain Performance Considering Carbon Cost. Sustainability 2019, 11, 6457.
[6] Metwally, A.B.M.; Ali, H.A.A.; Aly, S.A.S.; Ali, M.A.S. The Interplay between Digital Technologies, Supply Chain Resilience, Robustness and Sustainable Environmental Performance: Does Supply Chain Complexity Matter? Sustainability 2024, 16, 6175
[7] Theeraworawit, M.; Suriyankietkaew, S.; Hallinger, P. Sustainable Supply Chain Management in a Circular Economy: A Bibliometric Review. Sustainability 2022, 14, 9304.
[8] Ji, S.; Zhao, D.; Peng, X. Joint Decisions on Emission Reduction and Inventory Replenishment with Overconfidence and Low-Carbon Preference. Sustainability 2018, 10, 1119.
[9] Yu, J.; Sun, L. Supply Chain Emission Reduction Decisions, Considering Overconfidence under Conditions of Carbon Trading Price Volatility. Sustainability 2022, 14, 15432.
[10] Pillai K G , Min S .A firm's capability to calibrate supply chain knowledge—Antecedents and consequences[J].Industrial Marketing Management, 2010, 39(8):1365-1375.
This revision will not only address the timeliness of our references but also deepen the theoretical contribution by situating our study within the latest scholarly conversations. We sincerely appreciate your guidance, which will significantly improve the rigor and relevance of our work.
Comments 3:
The model description is highly professional and detailed. The appendix at the end supports the validity of your model. However, I have one question:
The formula N(0, (1 − alpha)δ²) is unclear — it is not obvious where it fits within the model or what its exact purpose is. Please clarify its context or intended use.
Response 3:
Thank you for your careful review and for your affirmation of my research model. The issue you pointed out is indeed due to my unclear expression, which can easily cause misunderstandings for readers. I will make serious corrections. The reasons for using in my research model are mainly as follows:
- The need to define over-precision.
In the general demand model where retailers are not overconfident, following the demand model defined by Lee et al. (1997), where is an i.i.d. (independent and identically distributed) random variable used to describe the error in demand across different periods, and it follows a normal distribution . Based on the three main manifestations of overconfidence behavior proposed by Moore et al. (2008): overestimation, overplacement, and overprecision. To describe the overprecision level of retailers, we consider adding an overprecision coefficient α to the model. Since retailers have the cognitive bias of overprecision, in the overprecise retailer's forecast, the demand error is , and, that is, is an i.i.d. random variable following . Here, we consider the expected value of to be 0, and the variance of to be . Since , the larger the value of α, the smaller the value of （1-α）, and thus the smaller the variance of , meaning the lower the volatility of the retailer's forecasted demand error and the higher the precision; conversely, the smaller the value of α, the larger the variance of , meaning the greater the volatility of the retailer's forecasted demand error and the lower the precision. The use of here is mainly to describe the size of the retailer's error volatility, thereby describing the retailer's overprecision bias. However, in the original article's descriptive assumptions, my expression was not clear enough. Therefore, I have marked the modified place in red in the second paragraph on page 5 of 25, and changed the description to " ", making the description more precise.
- In the proof of Lemma 2, refer to Appendix A.6.
In the calculation of ， the value of is used. Since in the previous model assumptions, is defined, it follows that . Here, is used to calculate the variance of ， thereby calculating . In the subsequent calculation of the bullwhip effect in inventory levels, the numerator is ， which incorporates the over-precision coefficient into the calculation of the bullwhip effect. When analyzing the factors affecting the bullwhip effect, the role of the over-precision coefficient α can be further analyzed, thereby achieving the research objective of this paper to analyze the impact of the retailer's level of over-precision.
Comments 4:
The biggest problems are formatting issues:
- In Chapters 2 and 3, the main formulas need to be clearly separated from the body text, as the current formatting makes them difficult to read.
- Please avoid placing limitations and conditions within the main body text. For readability, these should be placed directly below the formulas they refer to.
- The notation delta* should not be used in this form. Please replace the asterisk with a superscript apostrophe, as the current form can be easily misinterpreted as a multiplication symbol.
Response4:
We highly value your comments, we will follow your suggestions to seriously modify the format, which about the format of the formula of the problem, we through the use of the body and the formula of the form of an empty line between the body and the formula to distinguish between the body and the formula. We also center important formulas. In terms of the limitations and conditions of the formula, we also try our best to listen to your suggestion to place it below the formula, and try not to affect the reading of the main text. Since the specific method of the conclusion derivation in this paper is derived from the mathematical formula derivation, the formula appears to be more, and we will seriously modify it to make the article better readable in the main text. Thanks to the reviewers for their suggestions.
If two letters are connected in the main text *, in order to avoid * being mistaken for a multiplication symbol, we have replaced “ρ*” with a superscript apostrophe, all revised to “ρ’ ” thank you for your careful advice.
During the subsequent layout process, we will also meticulously complete the format improvement and revision in accordance with the requirements of the journal, the editors and the reviewers to meet the publication standards. We sincerely appreciate your suggestions.
Comments 5:
The figures are generally well-prepared, and the experiments and sensitivity analyses are comprehensive. The results are valid and clearly support your conclusions. The overall presentation of data is effective.
However, one issue: the caption of Figure 1 contains an error--it shows only the analysis for L = 2, which should be stated clearly in the caption.
Response 5:
Thank you for your careful review and pointing out this error. It was indeed a mistake in my writing, and I failed to notice it during the proofreading. I appreciate your correction again. I have revised the title of Figure 1 as follows:
“Figure 1 Analysis of the Impact of Different Parameter ? and ? Combinations on the for ? = 2” (page 14 of 27).
Figure 1 illustrates the impact of different values of parameters ? and ? on the bullwhip effect on product orders when the lead time L = 2. Figure 1 uses a three-dimensional image to show the relationship between the bullwhip effect of order quantity and the two parameters. The two horizontal axes represent the values of parameters ? and ?, respectively, while the vertical axis indicates the results of the bullwhip effect on product orders.
Finally, we once again express our gratitude to the reviewers for your valuable suggestions. Your comments have provided us with good inspiration for improving and revising the paper. We have further supplemented relevant data discussions and detailed explanations in the paper based on your suggestions.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsOverall, the revisions made to the paper are acceptable. However, there is still a need for more careful language refinement. For example, the statement “Research on overconfidence in sustainable supply chain remains insufficient” seems somewhat arbitrary.
Author Response
Dear Reviewer 1：
Thank you for your constructive feedback and for acknowledging the revisions to our manuscript. We greatly appreciate your time and meticulous review, which has helped us refine our work further. Next, we reply to your comments and suggestions one by one. At the same time, in order to distinguish the modifications made in the previous round, all the changes made to the original paper in this round are highlighted with a yellow background. Your advice provides us with great inspiration and good guidance.
Reviewer #1: Overall, the revisions made to the paper are acceptable.
Point-by-point response to Comments and Suggestions for Authors
Comments 1:
However, there is still a need for more careful language refinement. For example, the statement “Research on overconfidence in sustainable supply chain remains insufficient” seems somewhat arbitrary.
Response 1:
Dear Reviewer,
We sincerely appreciate your acknowledgment that the overall revisions to our paper are acceptable, and we are grateful for your astute observation regarding the need for language refinement.
In response to your note on language refinement, we have conducted a rigorous proofreading of the entire manuscript to enhance clarity, precision, and academic tone. Specifically, regarding the statement “Research on overconfidence in sustainable supply chain remains insufficient”, we agree that this phrasing could appear overly generalized. To make the expression more rigorous and accurate, we have revised the statement in paragraph 4 on page 5 of 27 as follows:
“Although existing studies have focused on the impact of overconfidence of supply chain members on the decision-making and profits of sustainable supply chains [8-9], the role of overconfidence in the bullwhip effect in sustainable supply chains has not yet been fully explored.”
This adjustment better aligns the claim with existing evidence and mitigates potential arbitrariness.
In addition, in light of your suggestions, we have also reviewed the overall expression of the article and revised and improved the following statements:
（1）On page 3 of 27, in paragraph 2, the revised sentence is highlighted with a yellow background.
Before:
“In the research on sustainable supply chains, no studies have yet considered the impact of retailers' overconfidence on the bullwhip effect.”
Revised:
“In the research on sustainable supply chains, the study of the impact of retailers' overconfidence on the bullwhip effect is not yet in-depth and sufficient.”
（2）On page 4 of 27, in the end of paragraph 3, the revised sentence is highlighted with a yellow background.
Before:
“However, research that considers the overconfidence biases of retailers in the context of the bullwhip effect is still insufficient. Existing studies mainly explore the impact of retailer overconfidence on the supply chain from the perspectives of supply chain coordination and decision-making.”
Revised:
“However, existing research mainly explores the impact of retailers' overconfidence on supply chains from the perspective of supply chain coordination and decision-making. Studies on the impact of retailers' overconfidence on the bullwhip effect in supply chains are still relatively rare.”
All language-related revisions, including grammatical corrections and improved sentence structure, have been implemented throughout the manuscript. Tracked changes and a clean version are provided for your convenience. Should further refinements be needed, we are fully prepared to address them promptly.
Once again, we sincerely value your insightful suggestions, which have strengthened the rigor and readability of our work. Thank you for your continued support in advancing this research.
Author Response File: 
Author Response.docx
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors have provided comprehensive explanations for my comments. I am satisfied with them and recommend the manuscript for publication.
Author Response
Dear Reviewer 2：
Thank you very much for taking the time to review our manuscript and for your positive feedback.On behalf of our entire research team, I am writing to express our heartfelt gratitude for your thorough review of our manuscript and your thoughtful recommendations.
We were truly delighted to learn that you were satisfied with the explanations we provided in response to your comments. Your endorsement of the manuscript for publication means a great deal to us and serves as a significant validation of our research efforts.
Your insightful feedback has been instrumental in helping us refine and strengthen our work. The suggestions you offered were both constructive and invaluable, enabling us to address key areas for improvement and enhance the overall quality of the manuscript. We are confident that the revisions made as a result of your input have significantly elevated the clarity, rigor, and impact of our study.
Once again, thank you for your time, expertise, and dedication to the review process. Your contributions have been essential in shaping this manuscript, and we are incredibly grateful for your support.
Should you have any further thoughts or suggestions, please do not hesitate to reach out. We value your perspective and would welcome the opportunity to continue our dialogue.
With sincere appreciation,
Dr. Shan Lu
Central University of Finance and Economics
E-mails:0020120021@cufe.edu.cn
Author Response File: Author Response.docx
