An Actual Case Study of a Deterministic Multi-Objective Optimization Model in a Defined Contribution Faculty Pension System

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper describes the startling revelation of the current pension systems around the world, which include the global south. It presents a model to determine the contributions, which is simple to implement by determining the numerical values of the parameters and how many years an employee wants to work or save.

The paper starts directly with the assumption of a contributory pension system as the only existing pension system of the world. Apart from the defined-contribution pension system, there are several countries and sub-national states continuing or reviving the defined-benefit pension system. For instance, in India (among the global south) there is a reformation in the defined-contribution pension system recently which ensures a defined pension. A better introduction to the different pension systems around the world in the introduction will make the paper clearer to a reader.

Author Response

• The full article was sent to a professional language review service, in addition, it did include in its additional information to make clear the objectives of the study with the realization of the scenarios considered.
• The literature review was considerably increased to include works that address analytical and operations research techniques, although it is important to highlight that a gap was found in the conjunction of multi-objective programming in educational pension systems.
• The corresponding text was introduced to explain why this study aims to work on a deterministic model, since it is mentioned that in a work previously published by the authors, the incorporation of stochastic elements in the pension model considered in the case of the university under study is analyzed. A future study of this work is to incorporate random variables such as interest rates and mortality rates into the single-target or multi-objective model.
• The text was introduced to justify and explain why the 3 scenarios are handled. These scenarios reflect the typical extreme cases that could occur in inflation rates in Mexico, and a variation in the percentage of the amount that a retiree might need to live in a way equivalent to how he or she has lived before retiring throughout the years. 
• Graphics have been improved by putting sharper colors and figure captions and captions have been updated, even Figure 5 was adjusted for better understanding.
• The environment in which this model can be applied is commented on and the sensitivity analysis is precisely done on the inflation rate, since it is the parameter of the model on which there is information from the government, while other factors such as the interest rate given by the banking institution is controlled by the educational institution when formalizing a contract.
• The paper discusses how interested parties can use this model in the educational environment, but also in other companies that try to implement their own pension systems.
• We now discuss what the extension of this model could be considering stochastic variables. Now this model does not incorporate anything particular from the demographic point of view for its application.

Reviewer 2 Report

Comments and Suggestions for Authors

Dear Authors,

Please address my comments as below:

1. Please separate introduction and literature review. Put introduction part that includes your motivation, gap, interests, organization of the paper. Then you put a literature review section that includes a summary of prior research related to your topic from latest years, only 2021, 2022, 2023, 2024.

2.  Regarding to the methodology, could you explain which modelling you are using, mention also is there any redundant variables.  

3. Results, the sensitivity analysis is missing of your results part.

4.  I don’t see any table in your paper, please add some tables for the results. You can develop many tables from your model like sensitivity analysis table…etc.

5. Please compare your results with what has been stated in the literature.

6. In conclusion, please add some policy implications, limitations and scope for future studies.

7. References
a) Authors should verify that all papers in the reference section are mentioned in the text and that all papers in the text are in the reference section.
b) Authors should verify whether the working papers cited in the article were published or not.
c) Authors should ensure that references are complete, written consistently, and reported following the journal guidelines.
8. before submitting the revised version of their paper, the authors have to proofread their manuscript by a native English professional.

Comments on the Quality of English Language

 Minor proofreading is required. 

Author Response

• The full article was sent to a professional language review service, in addition, it did include in its additional information to make clear the objectives of the study with the realization of the scenarios considered.
• The literature review was considerably increased to include works that address analytical and operations research techniques, although it is important to highlight that a gap was found in the conjunction of multi-objective programming in educational pension systems.
• The corresponding text was introduced to explain why this study aims to work on a deterministic model, since it is mentioned that in a work previously published by the authors, the incorporation of stochastic elements in the pension model considered in the case of the university under study is analyzed. A future study of this work is to incorporate random variables such as interest rates and mortality rates into the single-target or multi-objective model.
• The text was introduced to justify and explain why the 3 scenarios are handled. These scenarios reflect the typical extreme cases that could occur in inflation rates in Mexico, and a variation in the percentage of the amount that a retiree might need to live in a way equivalent to how he or she has lived before retiring throughout the years. 
• Graphics have been improved by putting sharper colors and figure captions and captions have been updated, even Figure 5 was adjusted for better understanding.
• The environment in which this model can be applied is commented on and the sensitivity analysis is precisely done on the inflation rate, since it is the parameter of the model on which there is information from the government, while other factors such as the interest rate given by the banking institution is controlled by the educational institution when formalizing a contract.
• The paper discusses how interested parties can use this model in the educational environment, but also in other companies that try to implement their own pension systems.
• We now discuss what the extension of this model could be considering stochastic variables. Now this model does not incorporate anything particular from the demographic point of view for its application.

Reviewer 3 Report

Comments and Suggestions for Authors

The study contributes to pension optimization research by focusing on the specific needs of academic staff in a faculty pension system, using three main scenarios to examine the impacts of inflation, contribution years, and desired coverage years. However, there are some issues that need attention:

The abstract provides a good overview but could benefit from refined wording to improve clarity, especially in describing the scenarios and objectives. Enhance the abstract by clearly specifying each scenario's purpose and differentiating the objectives more succinctly. In the introduction, better highlight the unique aspects of this study relative to prior work in pension modeling.

The literature review is extensive but lacks focus on recent studies specifically related to multi-objective optimization in pension systems. Narrow the literature review to emphasize recent optimization techniques and similar studies on pension systems, particularly within academic or institutional contexts.

The authors chose a deterministic model without addressing why it was preferred over a probabilistic or stochastic model, especially considering long-term financial uncertainties. Include a justification for the deterministic approach, explaining its advantages and limitations. Address whether a stochastic model might offer additional insights, especially given the inherent uncertainties in financial projections over decades.

The paper presents three scenarios but lacks detailed rationale for choosing these specific scenarios. Clearly explain the reasoning behind the selection of each scenario and its relevance to real-world pension planning. Clarify if these scenarios represent common financial conditions or are intended to model edge cases for stress-testing the model.

Some figures, such as Figures 4 and 8, lack optimal color contrast, making them difficult to interpret. Additionally, the context of each scenario is not fully explained in the captions. Enhance the readability of the figures by adjusting color contrasts and adding captions that briefly summarize the conditions each figure represents (e.g., inflation rates, contribution years). Consider simplifying or adding labels to make the results clearer for readers.

The paper does not adequately address potential limitations or the sensitivity of the model to changes in key assumptions, such as inflation or interest rates. Conduct and include a sensitivity analysis to show how varying key parameters (e.g., inflation, interest rate) impact the model’s outcomes. Additionally, discuss any limitations of the model, particularly regarding its assumptions and applicability to other economic environments or demographic groups.

While the paper mentions practical implications, there is limited discussion on how stakeholders might use the model's insights or adapt it for different institutional contexts. Expand on the practical implications of the findings, providing specific examples of how academic institutions or policymakers might use this model in decision-making. Address how adaptable the model is to other contexts or variations in institutional pension structures.

The conclusion summarizes the findings well but does not suggest avenues for future research. Include recommendations for future research, particularly the potential for extending the model to stochastic frameworks or applying it to broader demographic studies. Highlight areas where further work could enhance the model’s accuracy or applicability across different retirement systems.

Comments on the Quality of English Language

It should be checked and carefully revised, maybe by a native speaker.

Author Response

• The full article was sent to a professional language review service, in addition, it did include in its additional information to make clear the objectives of the study with the realization of the scenarios considered.
• The literature review was considerably increased to include works that address analytical and operations research techniques, although it is important to highlight that a gap was found in the conjunction of multi-objective programming in educational pension systems.
• The corresponding text was introduced to explain why this study aims to work on a deterministic model, since it is mentioned that in a work previously published by the authors, the incorporation of stochastic elements in the pension model considered in the case of the university under study is analyzed. A future study of this work is to incorporate random variables such as interest rates and mortality rates into the single-target or multi-objective model.
• The text was introduced to justify and explain why the 3 scenarios are handled. These scenarios reflect the typical extreme cases that could occur in inflation rates in Mexico, and a variation in the percentage of the amount that a retiree might need to live in a way equivalent to how he or she has lived before retiring throughout the years. 
• Graphics have been improved by putting sharper colors and figure captions and captions have been updated, even Figure 5 was adjusted for better understanding.
• The environment in which this model can be applied is commented on and the sensitivity analysis is precisely done on the inflation rate, since it is the parameter of the model on which there is information from the government, while other factors such as the interest rate given by the banking institution is controlled by the educational institution when formalizing a contract.
• The paper discusses how interested parties can use this model in the educational environment, but also in other companies that try to implement their own pension systems.
• We now discuss what the extension of this model could be considering stochastic variables. Now this model does not incorporate anything particular from the demographic point of view for its application.

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Authors addressed my points. 

Reviewer 3 Report

Comments and Suggestions for Authors

Thanks for considering my remarks.