Sustainable Economic Production Quantity Model Considering Greenhouse Gas and Wastewater Emissions
Round 1
Reviewer 1 Report
The paper addresses a relevant topic of sustainable economic development amid increasing carbon and wastewater emission. Although the topic is definitely relevant, the content is rather immature to be accepted in its current form. The author overfocuses on establishing and describing the model, while the results section and, most importantly, the discussion component are lacking. The methodology section is like a textbook - the extensive explanation with illustrations and lists of variables, while the critical approach to discussing the model is weak. The author should radically rethink the approach to establishing the narrative - trimm the methodology section and extend the results and discussion
Author Response
Please see attached file.
Author Response File: 
Author Response.docx
Reviewer 2 Report
This paper developed the economic production quantity (EPQ) inventory model considering carbon emission and wastewater costs to optimize the production quantity. It has some practical significance. However, I have some concerns.
1) In Literature Review, essentially, many papers have examined the decisions for the economic production quantity. For example：
Wee H.M., Huang Y.D.,Wang W.T.,Cheng Y.L., An EPQ model with partial backorders considering two backordering costs，Applied Mathematics and Computation，2014，232, 898-907.
Wang, C., Huang R., Wei Q., Integrated pricing and lot-sizing decision in a two-echelon supply chain with a finite production rate, International Journal of Production Economics, 2015, 161(3), 44-53.
It is suggested that author(s) introduce the papers related to the EPQ decision into the literature review, and identify the differences between the previous papers and current paper. Thus, the authors have to differentiate further and rethink about their work's innovativeness.
2) There are not enough managerial insights in this paper. Merely all the propositions or theorems are the presents of mathematical results. But authors should provide managerial insights to the manufacturers, Pulp and Paper Mill Industry
and sometimes government according to the background of the paper.
3) In Section 3.2.1, the process to proof that the total cost function is strictly convex with respect to Q is suggested to provide in Appendix. .
4) In Table 5 of page 24, why only the C1,C2,C4,C7,C10 and C12 in cost components were considered in Sensitivity analysis ?
Author Response
Please see attached file.
Author Response File: Author Response.docx
Reviewer 3 Report
The authors aim to develop an Economic Production Quantity (EPQ) inventory modelling that takes into account carbon emissions and waste water costs.
The authors present their work with clarity, starting with a relatively thorough literature review showcasing the necessity for their model. The mathematical model, and the results, are presented in a way that facilitates a better understanding, while the results are supported by a complementary sensitivity analysis. Furthermore, the development of the three different scenarios for examination provides an effective overview of the generated costs.
The authors state that the model could also consider the product life cycle. It would be interesting to expand on that statement on future research.
Author Response
Please see attached file.
Author Response File: Author Response.docx
Round 2
Reviewer 2 Report
Comments:
I reviewed the revised paper. Part of my comments were addessed. However, the following comments were still not addressed. I suggest the authors to revise it
again.
1) In Literature Review, essentially, many papers have examined the decisions for the economic production quantity. For example：
Wee H.M., Huang Y.D., Wang W.T., Cheng Y.L., An EPQ model with partial backorders considering two backordering costs, Applied Mathematics and Computation, 2014, 232, 898-907.
Wang, C., Huang R., Wei Q., Integrated pricing and lot-sizing decision in a two-echelon supply chain with a finite production rate, International Journal of Production Economics, 2015, 161(3), 44-53.
It is suggested that author(s) introduce the papers related to the EPQ decision into the literature review, and identify the differences between the previous papers and current paper. Thus, the authors have to differentiate further and rethink about their work's innovativeness.
2) In Section 3.2.1, the process to proof that the total cost function is strictly convex with respect to Q is suggested to provide in Appendix.
Author Response
Dear Editor and reviewer,
Enclosed please find a cover letter to explain, point by point, the details of the revisions to the manuscript and our responses to the editor and reviewers’ comments and suggestions.
Comments and Suggestions for Authors
Comments:
I reviewed the revised paper. Part of my comments were addressed. However, the following comments were still not addressed. I suggest the authors to revise it again.
1) In Literature Review, essentially, many papers have examined the decisions for the economic production quantity. For example：
Wee H.M., Huang Y.D., Wang W.T., Cheng Y.L., An EPQ model with partial backorders considering two backordering costs, Applied Mathematics and Computation, 2014, 232, 898-907.
Wang, C., Huang R., Wei Q., Integrated pricing and lot-sizing decision in a two-echelon supply chain with a finite production rate, International Journal of Production Economics, 2015, 161(3), 44-53.
It is suggested that author(s) introduce the papers related to the EPQ decision into the literature review, and identify the differences between the previous papers and current paper. Thus, the authors have to differentiate further and rethink about their work's innovativeness.
Our response: Thanks for the constructive comments. We have dealt with the above issues in the revised manuscript. Please see the track file.
2) In Section 3.2.1, the process to proof that the total cost function is strictly convex with respect to Q is suggested to provide in Appendix.
Our response: Thanks for your suggestions. We have created Appendix A & B to prove the total cost function is strictly convex as follows:
Appendix A
Proof for convexity of the Total Cost
Substituting Eqs. (2), (7), (12), (15), and (18) to Eq. (1), the total cost function per unit time is:
|
|
(A1) |
|
|
Taking the first derivative of Eq. (A1) using Maple15, yields:
|
(A2) |
Taking the second derivative of Eq. (A1) with respect to Q, it is shown to be strictly positive as follows:
|
(A3) |
Thus, since the second derivative is definitely positive, the total cost is proved to be strictly convex.
|
Equating Eq. (A2) to zero at minimum total cost, Q can be derived. Therefore, the optimal Q* resulting in the optimal solution is |
(A4) |
Appendix B
Referring to Cambini and Martein [38], we illustrate thatis a positive, differentiable, and (strictly) joint convex function with respect to the variables T and . To create the Hessian matrix for the function, compute all the second-order partial derivatives with respect to the decision variables T and as follows:
Substituting, in terms of T and T2, using the expressions from the first model and those of Eqs. (2), (12), (15), and (18), into (32), one has:
|
(
((B1) |
To solve for T and T2, take the first derivative using Maple15, one has:
|
((B2) |
|
|
((B3) |
Taking the second derivative, the convexity property of the total cost function can be proven.
|
((B4) |
|
|
((B5) |
Taking the derivative of Eq. (37) concerning T and T2 results in the following equation:
|
((B6) |
To test if the model is convex, a convexity test is performed.
The Hessian matrix for the function can be written as:
|
((B7) |
The result is negative in nature since production rate, P, is always greater than demand rate, D. The test result proves that the total cost function is strictly convex.
Author Response File: 
Author Response.pdf
