Application of Positive Mathematical Programming (PMP) in Sustainable Water Resource Management: A Case Study of Hetao Irrigation District, China

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

General Remarks

The manuscript addresses a highly relevant and timely issue by examining the dual challenges of water scarcity and soil salinization in arid and semi-arid regions, with specific application to the Hetao Irrigation District in China. The integration of Positive Mathematical Programming (PMP) with multi-stress factors such as water constraints, pricing policies, and salinity thresholds is an innovative approach that strengthens the study’s contribution both methodologically and practically.

Specific comments:

Strengths

• The study addresses two pressing global issues—water scarcity and soil salinization—that are particularly critical in arid and semi-arid regions.
• Use of a multi-stress factor integrated PMP model is novel, especially incorporating crop-specific salinity tolerance thresholds alongside water pricing and supply constraints.

Weakness:

There is no weakness in the manuscript.

Abstract: Provides a good and adequate summary of the study.

Key words: I suggest revising the keywords. Usually, keywords should not repeat words already included in the title; instead, they should capture other frequently used terms in the text or relevant concepts related to the topic.

Introduction

Provides a good and relevant background for the study.

Materials and Methods

Line 200 add appropriate reference

Please provide flow diagram of methodology

Results and Analysis

• The results are clearly presented; headings and subheadings are well chosen. The authors have carried out a thorough analysis. The explanations are clear and logically structured, and the arguments are convincing.
• Figure 2-6 it is suggested to revise the figures so that these may be clearly legible.

Discussion: The article effectively discussed the research findings.

Conclusions and suggestions: They are structured and easy to follow.

Recommendation: The manuscript has potential and requires a minor revision to meet the standards for publication.

Please address these points for the improvement of the manuscript. Thank you.

Best regards

Author Response

Please see the attachment

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper, "Water Allocation Based on Positive Mathematical Programming under Conjunctive Use of Surface Water and Groundwater," addresses a relevant problem in the agriculture of arid and semi-arid areas. This problem relates to maximizing crop yield while facing salinity exceedance in irrigation water and water availability (surface and groundwater). At the same time, it addresses the economic dimension in the optimization process using Positive Mathematical Programming (PMP).

The paper represents a well-structured case study in the Hetao Irrigation District (HID), located in Bayannur City, Inner Mongolia Autonomous Region, China. It is a useful study that has its main value in implementing PMP in problems related to high salinity of irrigation water, and therefore, the work is mostly important as decision-making support. However, the model would profit most from incorporating the dynamic nature of salinity (not only a threshold of 2.5 dS/m) connected to crop tolerance, growth stage, and final yield, as well as groundwater dynamics mirroring hydrological settings and technical capabilities. The three-dimensional scenario does not entirely capture the dynamic behavior of the model. Nevertheless, the paper is publishable as it is; the authors should consider the introduction of groundwater dynamics (climate change impact) in further research work.

As for the research stage presented in the paper, with some minor interventions, the clarity of the work and the presentation of the findings could be improved prior to publication. Here are some of the suggestions:

P06

Main crop phenological information given in Table 2 could be represented in a Gantt chart for each crop, also specifying the percentage of each crop represented in HID. That way, the information would be conveyed to the reader more clearly.

P10

Figure 4, "Impact of Water Price on Crop Cultivation Area in HID," should have a dual y-axis with different scales so the values for crops besides Corn and Wheat are visible. As it is now, the figure suggests that for the rest of the crops, the cultivated area is not decreasing with the increase of water pricing.

There is no specific suggestion for representing findings, but some tables, as described for Table 2, would be more informative if transformed into charts, especially the table with the evaluation of three scenarios (bar or radar chart). The main advice is to represent the findings in the paper so the methods and the model can be reproduced by other members of the scientific community for HID or any other irrigation area.

To conclude, the paper can be published if minor revisions are conducted. Congratulations to the authors.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

Water

 This study applies Positive Mathematical Programming (PMP) to analyze agricultural water resource management in the Hetao Irrigation District (HID), China. The research constructs a comprehensive multi-stress factor integrated PMP model to evaluate the compound impacts of water resource constraints, pricing policies, and environmental stress on agricultural production systems. The model incorporates crop-specific salinity tolerance thresholds and simulates farmer decision-making behaviors under various scenarios including water supply reduction (0-100%), water pricing increases (0.2-1.0 CNY/m3), and soil salinity stress (0-10 dS/m). Results reveal that the agricultural system exhibits significant vulnerability characteristics with critical thresholds concentrated in the 60-70% water resource utilization interval. The subject addressed is interesting and within the scope of the Water. However, the following drawbacks have been found:

1. In a table, add the decision variable names and their corresponding ranges.
2. The Methods section is too short. Add more details about the methodology used.
3. Please explain PMP in more detail for readers. The main equations and algorithms of PMP should be added to Section 2.
4. Why were metaheuristic algorithms not used to analyze water resource management?
5. Please mention which software was employed to run PMP.
6. What could be the impact of climatic parameters on this issue? The quality of Figure 2 is low; please provide more details.
7. In the first paragraph of the conclusion, add more details about the methods used.
8. Please add a flowchart and a graphical abstract.
9. The quality of the figures is low.Considering the mentioned points, this study in the current version needs major revisions.

With kind regards,

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

Dear Editor,

 Water

This manuscript is previously carefully evaluated. The current version of the manuscript is being suggested to be published in this admir journal.