Preventive Planning of ‘Product-as-a-Service’ Offers Using Genetic Population-Driven Stepping Crawl Threads

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The proposed approach, utilizing Genetic Population Stepping Crawl Threads (GPSCT), presents a novel way to handle preventive planning in Product-as-a-Service environments by integrating a genetic algorithm with a unique method of exploring the Cartesian product of functional offerings. This innovation allows for the dynamic recreation of allocation variants for leased devices, effectively aligning service offerings with customer expectations while navigating complex constraints such as budget and risk levels. Using stepping crawl threads (SCTs) that involve the solution space enhances adaptability and responsiveness to customer needs. It distinguishes itself from traditional precise methods used in constraint programming, which often lack flexibility and scalability. However, the GPSCT approach has notable shortcomings, particularly its reliance on problem-specific parameters and computational efficiency. The effectiveness of the genetic algorithm is highly contingent on the characteristics of each problem instance, which can lead to variable performance and solution quality. Additionally, while the method aims for scalability, the inherent complexity of genetic algorithms can result in significant computation times, especially for complex configurations. This may limit its practical application in real-time scenarios where rapid decision-making is crucial. Furthermore, the sensitivity of the results to initial population selection underscores the need for careful parameter tuning, which can be a barrier to the widespread adoption of the methodology. There are a few mistakes that need to be carefully revised before being accepted, as follows:

1.      In Abstract, “in constraints” should be modified to “in constrained”, “by the means of” should be modified to “by means of”. In addition, it is suggested that the author should carefully check the grammar and related expressions in the paper to describe it more accurately.

2.      The format of the paper is wrong, and please refer to the template to modify

3.      It is suggested that sections 1 and 2 be streamlined and the innovations of the paper be proposed rather than just pointing out the gaps in the current research.

4.      In Section 3.1, the definitions of the collections are somewhat confusing, and authors are advised to check carefully for duplicate definitions. Since it is matrix multiplication, please give a specific explanation of Eq. (2).

5.      In lines 288-290, the process for preparing a set of offers that meet the constraints for a given set of customers should be specified.

6.      Flow charts are suggested for describing the solution process (Section 3.2). Eq.(5) should be explained.

7.      The font in the box in Figure 9 should be changed.

Author Response

The authors thank the reviewers for their very helpful comments and suggestions. The authors have incorporated the reviewers’ comments in the revised manuscript. Some of the comments from Reviewer #1 concerned mathematical formulas that are difficult to address and present the corrections made in this form, so we are attaching a PDF file that details our responses.

 

Remark 1: In Abstract, “in constraints” should be modified to “in constrained”, “by the means of” should be modified to “by means of”. In addition, it is suggested that the author should carefully check the grammar and related expressions in the paper to describe it more accurately.

Response: Thank you for the remark and comment. The phrase "by the means of" has been corrected. However, the phrase "in constraints" has remained unchanged because it refers to the term "constraints programming", i.e. a Constraint Programming Paradigm (Gabbrielli, M., Martini, S. (2023). Constraint Programming Paradigm. In: Programming Languages: Principles and Paradigms. Undergraduate Topics in Computer Science. Springer, Cham. https://doi.org/10.1007/978-3-031-34144-1_13) implemented for solving combinatorial problems.

Additionally, the entire article has been verified once again.

 

Remark 2: The format of the paper is wrong, and please refer to the template to modify.

Response: The manuscript was prepared according to the styles and template file prepared by the editors. We have corrected the format of references to figures and tables. Of course, we are ready to correct any other indicated cases of incorrect formatting and noticed errors.

 

Remark 3: It is suggested that sections 1 and 2 be streamlined and the innovations of the paper be proposed rather than just pointing out the gaps in the current research.

Response:

Thank you for this suggestion. As already mentioned in Section 1, the motivation for our research is the expectation related to the development of a PaaS model enabling the construction of algorithms that take into account preventive resource allocation to address uncertainties and preemptively handling potential disruptions. We tried to identify the relevant research gap in the presented literature review (sections 2.1-2.3). Moreover, in section 2.4 we pointed to the results of our previous research [7,14] emphasizing the issues of robustness of rental offers to disruptions, pointing out to the shortcomings of exact methods (e.g. constraint programming), limiting their applications to small-scale problems that rarely occur in practice. We also referred to our recent research [56], in which we improved the scale of our approach by implementing a genetic algorithm. However, taking into account the reviewer suggestion, we have included an additional paragraph in section 2.3 emphasizing the innovative features of our solution:

Page 5, lines 204-212: As discussed in Sections 2.1, planning Platform-as-a-Service (PaaS) offerings under conditions of disruption, such as the failure of leased equipment, has been extensively addressed through various preventive and predictive strategies (see Section 2.2). However, existing approaches in the literature concerning the maintenance of leased devices often fall short of meeting the expectations of both providers and customers. These studies primarily focus on specific aspects of the problem such as maintenance policy for leased equipment [45,46], prognosis & health management (PHM) in the leased manufacturing system [47] warranty for leased equipment from the lessor's perspective [48], leaving critical gaps unaddressed.

[45]   Schutz, J.; Rezg, N. Maintenance Strategy for Leased Equipment. Comput Ind Eng 2013, 66, 593–600, doi:10.1016/j.cie.2013.05.004.

[46]   Liu, B.; Pang, J.; Yang, H.; Zhao, Y. Optimal Condition-Based Maintenance Policy for Leased Equipment Considering Hybrid Preventive Maintenance and Periodic Inspection. Reliab Eng Syst Saf 2024, 242, 109724, doi:10.1016/j.ress.2023.109724.

[47]   Zhang, K.; Xia, T.; Si, G.; Pan, E.; Xi, L. An Edge-Based Framework for Real-Time Prognosis and Opportunistic Maintenance in Leased Manufacturing System. IEEE Transactions on Automation Science and Engineering 2024, 21, 4177–4187, doi:10.1109/TASE.2023.3292908.

[48]   Ben Mabrouk, A.; Chelbi, A. Joint Preventive Maintenance and Extended Warranty Strategy for Leased Unreliable Equipment Submitted to Imperfect Repair at Failure. IFAC-PapersOnLine 2022, 55, 1201–1206, doi:10.1016/j.ifacol.2022.09.553.

[49]   Strimovskaya, A.; Barykin, S. A Multidimensional Approach to the Resource Allocation Problem (RAP) through the Prism of Industrial Information Integration (III). J Ind Inf Integr 2023, 34, 100473, doi:10.1016/j.jii.2023.100473.

 

Remark 4: In Section 3.1, the definitions of the collections are somewhat confusing, and authors are advised to check carefully for duplicate definitions. Since it is matrix multiplication, please give a specific explanation of Eq. (2).

Response: Thank you very much for your substantive remarks. The formulas of section 3.1 have been checked again and provided with more precise commentary.

The intuition of equation (2) is reflected in the following example. For instance, if the prepared offer  is described with the sequence: , then customer  is offered 1 device of type , 2 devices  and 1 device .

Assuming that the matrix  is of the form: , the proposed functionalities  in the offer are described by the sequence  (2) of the form: . This means that as part of the leased devices, the customer has three functionalities , three functionalities , and two  functionalities . In this context, section 3.1 has been expanded to include the following paragraph:

Page 6, lines 280-289:  – product of matrices A and B. For example, if the prepared offer  is set according to the sequence: , then customer  is offered 1 device of type , 2 devices  and 1 device . Assuming that the matrix K is: , then  (i.e. device type  has functionality  and ),  (i.e. device type  has functionality  and )) and  (i.e. device type  has functionality  and ). The functionalities offered as part of the offer  are therefore described by the sequence  (obtained as the product of the matrix  – see (2)) of the form: . This means that as part of the presented offer, the customer will have 3 functionalities , 3 functionalities , and 2 functionalities .

 

Remark 5: In lines 288-290, the process for preparing a set of offers that meet the constraints for a given set of customers should be specified.

Response: Thank you for your very helpful comment. The process for preparing a set of offers for a given set of customers, which constitutes the essence of our article, is described in detail in the following sections 3 and 4. However, in order to dispel any doubts, the following additions have been made to the indicated place in the text.

Page 7, lines 307-317: The proposed approach to planning PaaS offerings addresses the main question: Given a set of customers , can a corresponding set of offers  be formulated to satisfy their requirements (detailed below)?

To fulfill the specified constraints, each offer must ensure the following:

1. Functionality: .
2. Budget: .
3. Device Availability: ​.
4. Robustness: ​.

The methodology for identifying offers that satisfy these constraints (I–IV) is outlined in Section 4. This approach is grounded in the "space of stepping crawl thread" concept introduced in Section 3.2

 

Remark 6: Flow charts are suggested for describing the solution process (Section 3.2). Eq.(5) should be explained.

Response: Thank you for your very helpful comment which introduced the following diagram in section 3.2.2 and following text:

Pages 12-13, lines 463-472:

Figure 7. Structure of subspaces making up the  space.

To sum up, in the space  we can distinguish the following subspaces (see Figure A):

• subspace of expected solutions (6),
• subspace of achievable solutions (7),
• subspace of feasible solutions which is intersection of  and  (8),
• subspace of robust solutions which is included in the subspace  (9),

The introduced concepts allow us to develop a method for determining SCTs representing robust offers  guaranteeing the fulfillment of constraints No. I-IV (see section 2). An example of such a method is presented in section 4.

 

The second part of this Reviewer remark, concerning the essence of equation (5) is presented in the following example. SCT  from Figure 2b) takes the form: , where: , . According to (5), the end point is equal to: . This point represents the functionalities made available to the customer, which means that the customer will have 6 functionalities and 2 functionalities . In this context, Figure 2 has been revised and section 3.1 has been extended with the following paragraph:

Page 9, lines 375-379: For example, SCT  from Figure 2b) takes the form:  where: , . According to (5), the end point is the point  representing the functionalities made available to the customer as part of the offer  presented by  – to the customer who will have 6 functionalities  and 2 functionalities .

 

Remark 7: The font in the box in Figure 9 should be changed.

Response: The font used for the description in Figure 9 (Figure 10 after revisions) is the same as in the remaining figures.

 

All our responses and provided changes to the manuscript are written in the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper discusses the integration of genetic algorithms and optimization techniques to improve resource allocation and preventive planning within the Product-as-a-Service (PaaS) model. Through the use of Genetic Population Stepping Crawl Threads (GPSCT), the authors aim to optimize the allocation of leased devices, addressing customer needs while accounting for budgetary and risk constraints. 

 

While the paper has some merits, there are some aspects to improve.

 

-Although Genetic Population Stepping Crawl Threads (GPSCT) is presented in the paper as a novel solution, it does not sufficiently explain why this specific strategy is required or better than alternative resource allocation or optimization methods. GPSCT is presented as competitive with existing constraint programming methods, but the rationale behind choosing GPSCT over other genetic or heuristic approaches remains underexplored. 

 

-While computational experiments are conducted, the paper lacks sufficient detail on the experimental setup and the criteria used to evaluate the effectiveness of the GPSCT approach. There is no clear baseline or control against which the results are measured, nor is there a thorough interpretation of the significance of the outcomes. 

 

-Although the paper mentions scalability as a benefit of the proposed model, it does not sufficiently address how the model would perform in real-world, large-scale PaaS environments. Many PaaS applications involve high variability in demand and more complex constraints than those considered. A discussion on how the model could adapt to these larger, dynamic systems or additional testing with realistic scenarios could provide insights into the practical utility of GPSCT.

 

-The literature review focuses primarily on PaaS models and maintenance strategies but does not adequately cover recent advancements in genetic algorithms or resource allocation methods.  Including a more comprehensive review of recent methodologies could improve the paper.

Author Response

Remark 1: Although Genetic Population Stepping Crawl Threads (GPSCT) is presented in the paper as a novel solution, it does not sufficiently explain why this specific strategy is required or better than alternative resource allocation or optimization methods. GPSCT is presented as competitive with existing constraint programming methods, but the rationale behind choosing GPSCT over other genetic or heuristic approaches remains underexplored.

Response: Thank you for your very helpful comment. In the presented GPSCT approach, an approximate method implementing a genetic algorithm was used for the first time. So far, the use of this type of approach has been limited to allocation problems, which ignore the aspect of the offered offer's robustness to disruptions occurring during leasing. Unfortunately, this limits the possibility of comparing the effectiveness of the approach we propose with the research results  available in the literature. In future research, we also plan to use other heuristics (e.g. Particle Swarm Optimization), which will allow for a comparison of several heuristics. In this context, in section 2.3 we have added the following paragraph:

Page 5, lines 204-212: As discussed in Sections 2.1, planning Platform-as-a-Service (PaaS) offerings under conditions of disruption, such as the failure of leased equipment, has been extensively addressed through various preventive and predictive strategies (see Section 2.2). However, existing approaches in the literature concerning the maintenance of leased devices often fall short of meeting the expectations of both providers and customers. These studies primarily focus on specific aspects of the problem such as maintenance policy for leased equipment [45,46], prognosis & health management (PHM) in the leased manufacturing system [47] warranty for leased equipment from the lessor's perspective [48], leaving critical gaps unaddressed. To address this limitation, our research extends the classic resource allocation problem (RAP) [49] by incorporating the concept of disruption-robust offers—those that ensure the continuity of expected functionalities even in the event of a device failure. By considering this form of robustness, it becomes possible to mitigate costs associated with the risk of equipment failure.

[45]   Schutz, J.; Rezg, N. Maintenance Strategy for Leased Equipment. Comput Ind Eng 2013, 66, 593–600, doi:10.1016/j.cie.2013.05.004.

[46]   Liu, B.; Pang, J.; Yang, H.; Zhao, Y. Optimal Condition-Based Maintenance Policy for Leased Equipment Considering Hybrid Preventive Maintenance and Periodic Inspection. Reliab Eng Syst Saf 2024, 242, 109724, doi:10.1016/j.ress.2023.109724.

[47]   Zhang, K.; Xia, T.; Si, G.; Pan, E.; Xi, L. An Edge-Based Framework for Real-Time Prognosis and Opportunistic Maintenance in Leased Manufacturing System. IEEE Transactions on Automation Science and Engineering 2024, 21, 4177–4187, doi:10.1109/TASE.2023.3292908.

[48]   Ben Mabrouk, A.; Chelbi, A. Joint Preventive Maintenance and Extended Warranty Strategy for Leased Unreliable Equipment Submitted to Imperfect Repair at Failure. IFAC-PapersOnLine 2022, 55, 1201–1206, doi:10.1016/j.ifacol.2022.09.553.

[49]   Strimovskaya, A.; Barykin, S. A Multidimensional Approach to the Resource Allocation Problem (RAP) through the Prism of Industrial Information Integration (III). J Ind Inf Integr 2023, 34, 100473, doi:10.1016/j.jii.2023.100473.

 

Remark 2: While computational experiments are conducted, the paper lacks sufficient detail on the experimental setup and the criteria used to evaluate the effectiveness of the GPSCT approach. There is no clear baseline or control against which the results are measured, nor is there a thorough interpretation of the significance of the outcomes.

Response:

Thanking you very much for your comment, we would like to emphasize once again that the computer experiments carried out distinguish two types of research: qualitative (see section 5.1) and quantitative (see section 5.2). In both cases, the developed genetic algorithm is characterized by the following parameters: Population size , maximum number of generations , mutation rate . The algorithm was implemented in C++ with the Google OR-Tools library, on an Apple M1 3,2 669 GHz, 16 GB RAM.

The tests were carried out for two variants using different methods of determining the initial population, implementing LPA and BBA, respectively. The effectiveness of the algorithm was assessed against the following criteria (see sections 5.1-5.2):

• time for determining the robust solution (i.e. one that meets limitations no. I-IV – section 3);
• the minimum value of for which there is the robust solution;
• the influence of on the time to obtain the robust solution.

The reference point for the obtained results were the results of experiments carried out for the exact methods presented in the works [14,56] (see summary of section 5.2 – lines 801-806). However, in order to improve the readability of this issue, section 5.2 has been supplemented with the following paragraph:

Page 21, lines 739-742: The calculations were performed in the environment described in section 5.1 assuming population size , maximum number of generations , mutation rate . The developed genetic algorithm was implemented in C++ with the Google OR-Tools library and ran on an Apple M1 3.2 GHz processor, 16 GB RAM.

 

Remark 3: Although the paper mentions scalability as a benefit of the proposed model, it does not sufficiently address how the model would perform in real-world, large-scale PaaS environments. Many PaaS applications involve high variability in demand and more complex constraints than those considered. A discussion on how the model could adapt to these larger, dynamic systems or additional testing with realistic scenarios could provide insights into the practical utility of GPSCT.

Response:

Thanking you for your insightful remark, we would like to point out that the results of the conducted quantitative experiments (see section 5.2) indicate that the presented approach is applicable in situations where the number of devices presented in offers does not exceed 450, i.e. the scale of real problems encountered in PaaS environments (we mentioned about it in Section 6). Of course, the developed model taking into account four constraints (requirements I-IV, page 7) including among others, the robustness of the prepared offer, can be easily extended with additional constraints adapting it to other types of needs related to, e.g. delivering the rented equipment, in particular route, and schedule limitations (including service visits). These types of extensions provide directions for future research. In this context, section 6 has been extended with additional paragraph:

Page 25, lines 832-851: The proposed model is distinguished by its open and flexible architecture, which facilitates the seamless incorporation of additional constraints to address the specific requirements of an offer or a particular customer. This adaptability ensures that any extensions or modifications involve merely augmenting the existing set of constraints, without adversely affecting the computational efficiency of the solution. Such a design is particularly advantageous in dynamic and rapidly evolving application contexts, where both PaaS providers and their customers must navigate an environment shaped by shifting operational guidelines, competitive dynamics, and regulatory changes. The model's inherent flexibility and responsiveness enable it to maintain relevance and effectiveness in the fluid landscape of the leasing industry.

Future research will focus on the development of methodologies for identifying and analyzing factors that influence the balance between supply and demand in PaaS-driven markets. A key area of investigation will center on the provider's perspective, specifically the trade-offs between the costs associated with equipment procurement by the primary PaaS provider and the expenses incurred for maintenance services outsourced to third-party vendors. By extending the model to capture trade-offs from both supply- and demand-side perspectives, this research aims to provide a comprehensive framework for understanding the dynamic interactions that underpin equilibrium in service-oriented industries, ultimately enhancing the ability to manage and sustain balance within the PaaS market.

 

Remark 4: The literature review focuses primarily on PaaS models and maintenance strategies but does not adequately cover recent advancements in genetic algorithms or resource allocation methods. Including a more comprehensive review of recent methodologies could improve the paper.

Response: Thank you for this comment. Noting the similarity to comment 1, we see the need to clarify our contribution to the field. It should be noted that the motivation of our research is the way of constructing PaaS models, in particular preventive resource allocation to address uncertainties and preemptively handle potential disruptions as it was briefly mentioned in the Introduction. We have indicated the related research gap in the presented literature review on the subject (section 2.1-2.3). In turn, the thread of research on the use of genetic algorithms in resource allocation problems was only briefly touched upon in section 2.4. This is due to the fact that genetic algorithms implemented in approximate methods make it possible to estimate the scalability of exact methods. The shortcomings of our previous approach to planning robust leasing offers based on exact methods (e.g. constraints programming) resulted from its limitations in allowing the analysis of small problems that rarely occur in practice. In our further research [56], we used heuristic methods (genetic algorithm), which showed better results in terms of scalability, but still insufficient for use in practice. Hence the need to conduct further research, which is reflected in this work.

 

All our responses and provided changes to the manuscript are written in the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The author presents a model leveraging Genetic Population Stepping Crawl Threads to establish "stepping crawl threads" for targeted resource allocation within preventive planning of "Product-as-a-Service". The model enables alignment with customer-defined risk levels, facilitating integration into computer-aided decision-support systems, also provides both qualitative and quantitative computational experiments assessing the scalability of the proposed approach. I would be willing to consider this manuscript for acceptance after the following points are addressed:

 

1. The SCT search begins at a starting point within the Cartesian product space. How this starting point is determined, and how does this choice influence the convergence or computational efficiency of the final results?

2. The effectiveness of the LPA algorithm is sensitive to the hru parameter. Whether a data-driven or adaptive mechanism could be implemented to optimize the hru value automatically?

3. Ensure consistency in the formatting of the references, as some entries contain DOI information while others do not.

Author Response

Remark 1: The SCT search begins at a starting point within the Cartesian product space. How this starting point is determined, and how does this choice influence the convergence or computational efficiency of the final results?

Response: Thank you very much for your interesting comment. In fact, in the adopted approach, each SCT product begins with the origin of the Cartesian product space - point (0,0, ...,0). This point represents an empty offer  of customer  (i.e. no device is leased). In other words, it is the starting point from which the construction of SCTs offers begins. Of course, it is possible to use offers appearing in other points (e.g. with coordinates different from zero). In practice, however, this would mean that the customer already has an initial offer, e.g. an extended one, which extends the existing leasing offer. These types of issues were not likely to occur in our work and may be introduced if the work occurs.

 

Remark 2: The effectiveness of the LPA algorithm is sensitive to the hru parameter. Whether a data-driven or adaptive mechanism could be implemented to optimize the hru value automatically?

Response: Thank you for your interesting observation. The LPA algorithm is sensitive to the hru parameter, which is why quantitative experiment II was devoted to it (chapter 5.2.). As a result, a trend was observed that "suggested" how to determine it. Thank you for your suggestion of automated generation of the value of this parameter for a given problem instance. As a consequence, we introduced the following sentence in the conclusions to one of the experiments:

Page 22, lines 769-771: It is worth noting that the possibility of automatically generating the value of this parameter, i.e. selecting it depending on the given scale of the problem, raises a promising topic for future research.

 

Remark 3: Ensure consistency in the formatting of the references, as some entries contain DOI information while others do not.

Response: Thank you for this remark. In accordance with the publisher's requirements, the References section was prepared using a program for automatic generation of a bibliography and reference list, based on the MDPI publishing style. Some omitted DOI numbers result from the mechanism used. Some literature items were supplemented with DOI numbers.

 

All our responses and provided changes to the manuscript are written in the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

The authors addressed my comments.