Balancing Supply and Demand in PaaS Markets: A Framework for Profitability, Cost Optimization, and Sustainability

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Dear Authors,

I will not get into the content of this paper, because there is a critical flaw: You have clearly selected the wrong outlet for this work. You state sustainability as one of the optimization goals, but checking in a bit more detail, it becomes clear, that there is no sustainability-centric optimization present. As a result, I will recommend the editor to reject this paper and I encourage you to resubmit to a journal that is explicitly centered on the topic at hand, such as IJOPM, Journal of Service Management (etc. pp.), maybe, if you can substantially strengthen the sustainablity aspect, BSE.

All the best!

Comments on the Quality of English Language

Language quality is fine.

Author Response

Dear Reviewer, we are very sorry that you were not able to “get into the content” of our article. However, if you had checked the content of our contribution in more detail, as well as the sources of literature in the field of sustainability [for instance: Sadollah, A., Nasir, M., & Geem, Z. W. (2020). Sustainability and optimization: From conceptual fundamentals to applications. Sustainability, 12(5), 2027. https://doi.org/10.3390/su12052027; Ma, D., Qin, H., & Hu, J. (2022). Achieving triple sustainability in closed-loop supply chain: The optimal combination of online platform sales format and blockchain-enabled recycling. Computers & Industrial Engineering, 174, 108763, https://doi.org/10.1016/j.cie.2022.108763; Dash, S. (2025). Green AI: Enhancing Sustainability and Energy Efficiency in AI-Integrated Enterprise Systems. IEEE Access], you would have easily noticed that:

• the challenges of balancing supply and demand in PaaS markets (see the paper’s title) have been the subject of numerous studies, with Pareto-based approaches dominating, seeking optimal trade-offs between mutually exclusive criteria, i.e solutions where no objective can be improved without worsening at least one other objective,
• sustainability problems and Pareto optimization are closely related because sustainability typically involves balancing multiple, often conflicting objectives. It means that multi-objective optimization, is a natural framework for addressing such trade-offs, i.e. balanced solutions that optimize multiple goals simultaneously,
• the fact that the Pareto frontier represents a set of optimal trade-offs in which improving one sustainability indicator worsens another means that decision-makers can analyze different points on the frontier to choose the optimal solutions that best suit them,
• in contrast to above mentioned methods, the proposed model employs a single criterion that evaluates how closely the proposed contract aligns with the local optima expected by both the customer and the provider (see Section 4). In other words, the proposed approach seeks a global trade-off among locally determined trade-offs, which individually influence the decision-making processes of the customer and the provider (see response to remark 1 of the Reviewer #3).

We therefore recommend that you read our text more carefully once again.

Reviewer 2 Report

Comments and Suggestions for Authors

This study presents a declarative modeling framework designed to balance supply and demand in PaaS markets by optimizing three key pillars: profitability, cost efficiency, and sustainability. The developed approach integrates financial viability with operational efficiency, allowing both provider and customers to identify trade-offs between leasing offers and requests for quotations. The results of the computational experiments demonstrate the practical applicability and effectiveness of the approach in addressing real-world scenarios. 

The idea of this paper is innovative.  The analysis is comprehensive and sound. The experiment results show that the method of this paper is effective and it can be applied in practice.

There serveral problem in the manuscript.

1. I would suggest that the authors add discussions about how to apply their modeling framework to different kinds enterprises. Does it fit all kinds of enterprises? If not, why?
2. Is  the asset liability ratio of the enterprise important when the model issed by this paper is applied to in practice?

So I would suggest the manuscript be published after revision.

 

Author Response

Reviewer #2: This study presents a declarative modeling framework designed to balance supply and demand in PaaS markets by optimizing three key pillars: profitability, cost efficiency, and sustainability. The developed approach integrates financial viability with operational efficiency, allowing both provider and customers to identify trade-offs between leasing offers and requests for quotations. The results of the computational experiments demonstrate the practical applicability and effectiveness of the approach in addressing real-world scenarios.

The idea of this paper is innovative.  The analysis is comprehensive and sound. The experiment results show that the method of this paper is effective and it can be applied in practice.

There serveral problem in the manuscript.

So I would suggest the manuscript be published after revision.

Remark 1: I would suggest that the authors add discussions about how to apply their modeling framework to different kinds enterprises. Does it fit all kinds of enterprises? If not, why?

Response: A key strength of the proposed modeling framework is its flexibility, enabled by its declarative modeling approach. This flexibility allows it to be adapted to various types of enterprises across industries, each with different operational constraints and strategic objectives. For instance, manufacturing enterprises can use the framework to optimize spare parts logistics and equipment servicing, ensuring a balance between cost efficiency and uptime reliability. Similarly, technology companies offering cloud-based services or subscription-based hardware (e.g., SaaS or Hardware-as-a-Service) can leverage the framework to fine-tune service contracts, dynamically adjusting pricing based on resource usage and infrastructure costs.

However, while the model is broadly applicable, it may not be equally effective across all enterprise types. Highly standardized, low-margin industries, such as fast-moving consumer goods (FMCG) or bulk commodities, may find limited benefit in applying a complex trade-off-driven contract structure, as their operations prioritize volume over customization. Additionally, in sectors where regulatory constraints impose fixed pricing structures (e.g., healthcare or utilities), the adaptability of the model may be constrained by external policies.

To reflect this intuition we have added a fragment in Conclusions, as follows:

Page 24, lines 637-647: Due to its declarative nature, the framework remains highly adaptable, allowing enterprises to tailor its parameters and constraints to their specific needs. Organizations operating in dynamic, service-oriented environments – such as mobility services, industrial leasing, or renewable energy systems – are particularly well-suited for its application, as they can leverage its flexibility to balance cost, performance, and sustainability. For instance, manufacturing enterprises can use the framework to optimize spare parts logistics and equipment servicing, ensuring a balance between cost efficiency and uptime reliability. Similarly, technology companies offering cloud-based services or subscription-based hardware (e.g., SaaS or Hardware-as-a-Service) can leverage the framework to fine-tune service contracts, dynamically adjusting pricing based on resource usage and infrastructure costs.

Remark 2: Is the asset liability ratio of the enterprise important when the model issed by this paper is applied to in practice?

Response: The research conducted has ignored the threads related to assets and liabilities related to establishing contracts, as well as elements that may be reflected in financial reporting and accounting. Instead, it focuses on managing the supply and demand balance within the Product-as-a-Service (PaaS) model, emphasizing the optimization of pricing strategies, risk-sharing mechanisms and sustainable resource management (see response to remark 1 of the Reviewer #3).

Reviewer 3 Report

Comments and Suggestions for Authors

The paper suggests a quantitative (empirical?) product-as-a-service (PaaS) equilibrium model based on constrained optimization logic, filling the gap in the existing literature. The authors describe the specifics of such a market under sustainability efforts (circular economy) and use standard constrained-optimization methodology (sets, constraints, etc.), followed by an empirical case study to test the model. Overall, the scientific rigor of the paper is high, but, in the reviewer's opinion, specific improvements are necessary before it can be published.

First of all, in its current form, the framework appears almost devoid of an economic theory foundation (it seems to be designed to fit the constrained optimization (COP) algorithms rather than constrained optimization being used to estimate it). If this is not the case, the authors must add additional paragraphs in section 2 (related works) and section 3.1 (problem formulation) explaining which microeconomic theories (standard/non-standard/tied to PaaS or similar markets) and what methodology to describe the market (comparative statics/dynamics/something else) were used to derive the framework and explaining the process of obtaining Fig. 2 (how and why the individual variables were selected). So far, the framework – from the theoretical side – is a "black box," which makes sense in constrained optimization terms but is vaguely intuitive otherwise. On the other hand, if the paper's goal is to suggest a COP model, it is necessary to explicitly state this fact and avoid the theoretical topics of equilibrium.

Regarding section 2, the reviewer also thinks that the choice of CDSC (closed decentralized supply chain) and CDSC equilibrium and their relation to PaaS need to be explained in more detail.

Finally, concretizing the abstract in terms of potential uses of the framework and adding an annex with the IBM ILOG CPLEX (or Gurobi compatible) code for potential readers to be able to use the model in their estimations would also improve the quality of the paper.

Author Response

Reviewer #3: The paper suggests a quantitative (empirical?) product-as-a-service (PaaS) equilibrium model based on constrained optimization logic, filling the gap in the existing literature. The authors describe the specifics of such a market under sustainability efforts (circular economy) and use standard constrained-optimization methodology (sets, constraints, etc.), followed by an empirical case study to test the model. Overall, the scientific rigor of the paper is high, but, in the reviewer's opinion, specific improvements are necessary before it can be published.

Remark 1: First of all, in its current form, the framework appears almost devoid of an economic theory foundation (it seems to be designed to fit the constrained optimization (COP) algorithms rather than constrained optimization being used to estimate it). If this is not the case, the authors must add additional paragraphs in section 2 (related works) and section 3.1 (problem formulation) explaining which microeconomic theories (standard/non-standard/tied to PaaS or similar markets) and what methodology to describe the market (comparative statics/dynamics/something else) were used to derive the framework and explaining the process of obtaining Fig. 2 (how and why the individual variables were selected). So far, the framework – from the theoretical side – is a "black box," which makes sense in constrained optimization terms but is vaguely intuitive otherwise. On the other hand, if the paper's goal is to suggest a COP model, it is necessary to explicitly state this fact and avoid the theoretical topics of equilibrium.

Response: The challenges of balancing Supply and Demand in PaaS markets have been the subject of numerous studies [Sadollah, A., Nasir, M., & Geem, Z. W. (2020). Sustainability and optimization: From conceptual fundamentals to applications. Sustainability, 12(5), 2027. https://doi.org/10.3390/su12052027; Ma, D., Qin, H., & Hu, J. (2022). Achieving triple sustainability in closed-loop supply chain: The optimal combination of online platform sales format and blockchain-enabled recycling. Computers & Industrial Engineering, 174, 108763, https://doi.org/10.1016/j.cie.2022.108763; Wicaksono, P.A.; Hartini, S.; Sutrisno; Nabila, T.Y. Game Theory Application for Circular Economy Model in Furniture Industry. IOP Conf Ser Earth Environ Sci 2020, 448, 012061, doi:10.1088/1755-1315/448/1/012061]. Among existing methods, Pareto-based approaches dominate, seeking optimal trade-offs between mutually exclusive criteria.

In contrast to previously explored methods, the proposed model employs a single criterion that evaluates how closely the proposed contract aligns with the local optima expected by both the customer and the provider. In other words, the proposed approach seeks a global trade-off among locally determined trade-offs, which individually influence the decision-making processes of the customer and the provider. This results in a "trade-off of trade-offs," where the final solution represents a balanced contract that globally minimizes the total losses of both the provider and the customer with respect to their local expectations.

It is important to emphasize that, unlike previous approaches, the constructed contracts are also evaluated in terms of their robustness (i.e., the impact on costs incurred due to failures of leased equipment) and the applied technology. The inclusion of these parameters allows for a holistic treatment of the customer-provider system, enabling the formulation of sustainable contract based on a unified criterion.

The developed model considers only the fundamental parameters of leasing offers, which, in general, can be extended or refined for specific use cases. For this reason, among others, the problem addressed in this study is formulated as a Constraint Optimization Problem (COP), solved using declarative environments, which facilitates adaptation and modification to different scenarios. Consequently, the model proposed in this approach should be regarded as a reference model for further extensions.

Remark 2: Regarding section 2, the reviewer also thinks that the choice of CDSC (closed decentralized supply chain) and CDSC equilibrium and their relation to PaaS need to be explained in more detail.

Response: Closed-loop supply chains (or Circular Supply Chains, or Closed-loop Decentralized Supply Chain system) in which resources move along the forward Supply Chains, originally separated, and the reverse Supply Chains are of configuration typical for self-regenerative ecosystems integrating a high number and variety of stakeholders in a connected network to extract new value from end-of-life resources, extend product life, and increase resource efficiency [A, B, C, D]. Such solution leverages decentralized networks of suppliers, manufacturers, warehouses, and distribution centers to improve flexibility, resilience, and efficiency. This means that CDSC has a significant impact on the PaaS market, influencing key aspects such as cost efficiency, service reliability, sustainability, and customer satisfaction. In particular, it enables: faster delivery of spare parts, which reduces downtime; local service, which ensures faster implementation and repairs, thus facilitating local refurbishment and recycling (i.e. supporting the sustainability goals of PaaS) as well as prevents dependence on single suppliers, which reduces the risks associated with long-term PaaS contracts.

To expand on this, we have added the following text:

Page 5, lines 177-189: In general case a closed-loop distributed supply chain (CDSC) (hypothetical part of which pictures Fig. 1) leverages decentralized networks of suppliers, manufacturers, warehouses, and distribution centers to improve flexibility, robustness, and efficiency shareholders of PaaS market [25,28–30]. This means that CDSC has a significant impact on the PaaS market, influencing key aspects such as cost efficiency, service reliability, sustainability, and customer satisfaction. In particular, it enables: faster delivery of spare parts, which reduces downtime; local service, which ensures faster implementation and repairs, thus facilitating local refurbishment and recycling (i.e. supporting the sustainability goals of PaaS) as well as prevents dependence on single suppliers, which reduces the risks associated with long-term PaaS contracts. In this context, by seeking solutions that balance supply and demand, we ensure that resource loops are closed and sustainability is embedded in the business model resulting in more robust, cost-effective, and environmentally responsible economic system.

[25] Difrancesco, R. M., & Huchzermeier, A. (2016). Closed-loop supply chains: a guide to theory and practice. International Journal of Logistics Research and Applications, 19(5), 443-464. https://doi.org/10.1080/13675567.2015.1116503

[28] Massari, G. F., Nacchiero, R., & Giannoccaro, I. (2023). Digital technologies for resource loop redesign in circular supply chains: A systematic literature review. Resources, Conservation & Recycling Advances, 20, 200189. https://doi.org/10.1016/j.rcradv.2023.200189.

[29] Jing, Y., & Li, W. (2018). Integrated recycling-integrated production-distribution planning for decentralized closed-loop supply chain. Journal of Industrial and Management Optimization, 14(2), 511-539. https://doi.org/10.3934/jimo.2017058

[30] Mustafee, N., Katsaliaki, K., & Taylor, S. J. (2014). A review of literature in distributed supply chain simulation. In Proceedings of the Winter Simulation Conference 2014 (pp. 2872-2883). IEEE. https://doi.org/10.1109/WSC.2014.7020128.

Remark 3: Finally, concretizing the abstract in terms of potential uses of the framework and adding an annex with the IBM ILOG CPLEX (or Gurobi compatible) code for potential readers to be able to use the model in their estimations would also improve the quality of the paper.

Response: Thank you for this remark. We have re-arranged the abstract to take into account the potential use of the proposed solution.

Page 1, lines 10-28: Efficient supply-demand management in Product-as-a-Service (PaaS) markets requires tools to evaluate pricing strategies while integrating sustainability goals like reuse, efficiency, and carbon footprint reduction. This paper introduces a declarative modeling framework aimed at balancing the three pillars of profitability, cost optimization, and sustainability in PaaS markets. The framework addresses risks such as equipment failure, usage variability, and economic fluctuations, helping providers optimize pricing and operating costs while enabling customers to manage expenses. A declarative model is developed to assess PaaS market balance to determine optimal leasing offers and requests for quotations. A case study is used to validate the framework, involving devices with specific rental prices and failure rates, as well as customer expectations and budget constraints. Computational experiments demonstrate the model’s practical applicability in real-world scenarios and it can be used by PaaS providers to develop competitive leasing strategies, policymakers to assess market stability, and enterprises to optimize procurement decisions. The findings show that the framework can guide decision-making, offering insights into the impact of new technologies, compatibility conditions for leasing offers, and strategies for balancing providers’ profits and customers’ costs. The proposed framework has broad applicability across industries such as manufacturing, healthcare, logistics, and IT infrastructure leasing, where efficient resource allocation and lifecycle management are crucial.

In relation to the second part of the remark, in accordance with our policy, we do not publicly share the source code. We prefer direct contact with the authors to discuss the details and provide potential support in reproducing the results.

Reviewer 4 Report

Comments and Suggestions for Authors

Dear authors,

Greetings, and thank you for your efforts in preparing this manuscript. However, the following comments can enhance the quality of your manuscript:

1. ABSTRACT: The abstract should include a clear study aim, methodology, findings, and recommendations. Please rewrite it to ensure the availability of all the mentioned aspects.
2. The research gap is not clear, and at the same time, the justification for this study is also not clear and needs strong evidence. The author should clearly clarify the research gap and justification for this study in the introduction.
3. The "Related Works" section can be renamed "Literature Review," as its purpose is to clarify previous studies and identify the research gap that this study aims to fill.
4. The methodology section (10 pages) is too long. Usually the purpose of methodology is simply to show the reader how the research was conducted, not to provide excessive detail. It should focus on the method used and how the authors will validate the results.
5. The structure of the manuscript needs to be reconsidered. I suggest to make slight improvements it the structure to ensure the availabiltiy of the following sections: Introduction, Literature Review, Research Methodology, Proposed Model/Framework, Case Study/Empirical Analysis, Results and Discussion, Conclusion and Future Research.

All the best,

 

Comments on the Quality of English Language

English needs proofreading. 

Author Response

Reviewer #4: Greetings, and thank you for your efforts in preparing this manuscript. However, the following comments can enhance the quality of your manuscript:

Remark 1: The abstract should include a clear study aim, methodology, findings, and recommendations. Please rewrite it to ensure the availability of all the mentioned aspects.

Response: Thank you. We re-arranged the abstract as follows.

Page 1, lines 10-28: Efficient supply-demand management in Product-as-a-Service (PaaS) markets requires tools to evaluate pricing strategies while integrating sustainability goals like reuse, efficiency, and carbon footprint reduction. This paper introduces a declarative modeling framework aimed at balancing the three pillars of profitability, cost optimization, and sustainability in PaaS markets. The framework addresses risks such as equipment failure, usage variability, and economic fluctuations, helping providers optimize pricing and operating costs while enabling customers to manage expenses. A declarative model is developed to assess PaaS market balance to determine optimal leasing offers and requests for quotations. A case study is used to validate the framework, involving devices with specific rental prices and failure rates, as well as customer expectations and budget constraints. Computational experiments demonstrate the model’s practical applicability in real-world scenarios and it can be used by PaaS providers to develop competitive leasing strategies, policymakers to assess market stability, and enterprises to optimize procurement decisions. The findings show that the framework can guide decision-making, offering insights into the impact of new technologies, compatibility conditions for leasing offers, and strategies for balancing providers’ profits and customers’ costs. The proposed framework has broad applicability across industries such as manufacturing, healthcare, logistics, and IT infrastructure leasing, where efficient resource allocation and lifecycle management are crucial.

Remark 2: The research gap is not clear, and at the same time, the justification for this study is also not clear and needs strong evidence. The author should clearly clarify the research gap and justification for this study in the introduction.

Response: The research gaps indicated in the article, such as: "... the gap related to the lack of a model (framework) enabling the assessment of the financial performance and viability of PaaS leading to the supply-demand balance…” see lines 62-64, “…gap in models that enable comprehensive financial assessments, which are necessary for providing a holistic understanding and improving operational strategies for both providers and users…” see lines 209-211, and “… need for tools that facilitate the determination of real-time pricing strategies tailored to diverse customer segments and service tiers within PaaS..."  see lines 211-213, point to the need for the development of scalable, platform-agnostic models that allow for cross-provider leasing, automated contract negotiation, and seamless integration. This is because there is a need to develop „…flexible financial assessment models for PaaS that can help practitioners identify conditions necessary for financial viability from the perspectives of providers, users, and market administrators, including governmental entities…” see lines 219-221, and because most of the research concerns models focus on profitability from the provider’s perspective [A, B, C] without attempting to propose a reference model that would comprehensively address the issues raised in the above-mentioned gaps.

The expectations expressed in the presented gaps indicate the need to develop appropriate interactive DSS tools. The prototype of declarative equilibrium model of the PaaS market presented in this paper responds to these expectations. It is a reference model covering trade-off issues among locally determined trade-offs, which individually influence the decision-making processes of the customer and the provider (see response to remark 1 of the Reviewer #3).

[A] Vishkaei, B. M. (2024). Optimal ordering for Product-as-a-Service models with circular economy practices. International Journal of Production Research, 1-20. https://doi.org/10.1080/00207543.2024.2434949

[B] Annarelli, A., Battistella, C., Costantino, F., Di Gravio, G., Nonino, F., & Patriarca, R. (2021). New trends in product service system and servitization research: A conceptual structure emerging from three decades of literature. CIRP Journal of Manufacturing Science and Technology, 32, 424-436. https://doi.org/10.1016/j.cirpj.2021.01.010.

[C] Hidalgo-Crespo, J., Riel, A., Duberg, J. V., Bunodiere, A., & Golinska-Dawson, P. (2024). An exploratory study for product-as-a-service (PaaS) offers development for electrical and electronic equipment. Procedia CIRP, 122, 521-526. https://doi.org/10.1016/j.procir.2024.01.076.

Remark 3: The "Related Works" section can be renamed "Literature Review," as its purpose is to clarify previous studies and identify the research gap that this study aims to fill.

Response: Thank you for this suggestion. Of course, the section title "Literature Review" is more appropriate, so we have changed it accordingly.

Remark 4: The methodology section (10 pages) is too long. Usually the purpose of methodology is simply to show the reader how the research was conducted, not to provide excessive detail. It should focus on the method used and how the authors will validate the results.

Response: The section "Framework and modeling methodology" has been consciously constructed. In order to clearly describe the essence of the proposed solution, a structure was adopted in which the problem is first formulated (section 3.1. “Problem formulation”), then its example is presented (section 3.2. “Illustrative example”) and then the formal model (section 3.3. “Declarative framework”). In these three sub-sections, the adopted assumptions of the process of searching for a trade-off between the provider and the customer are presented, new definitions are introduced (technological level of devices, cost of losing functionality, robustness, etc.) and a mathematical model of the considered problem is presented. Shortening this section can therefore only be done at the cost of losing readability and making the description hermetic and incomprehensible. In addition, the size of the section is a consequence of the use of large figures (Figs. 2 and 3) and many tables (1-5).

Remark 5: The structure of the manuscript needs to be reconsidered. I suggest to make slight improvements it the structure to ensure the availabiltiy of the following sections: Introduction, Literature Review, Research Methodology, Proposed Model/Framework, Case Study/Empirical Analysis, Results and Discussion, Conclusion and Future Research.

Response: Thank you for your interesting suggestion. After carefully reading the manuscript, it is easy to see that the structure proposed by the Reviewer corresponds to the one adopted in the article:

1. Introduction => Introduction,
2. Related works => Literature Review (see answer to remark 3),
3. Framework and modeling methodology => Research Methodology; Proposed Model/Framework (see answer to remark 4),
4. Case study => Case Study/Empirical Analysis, Results and Discussion,
5. Conclusions => Conclusion and Future Research.

The adopted structure seems to be more compact and readable.