A Review of Optimization for Corrugated Boards
Abstract
:1. Introduction
- RQ1.
- What is the current landscape of optimization methodologies in the corrugated board industry, and how do these methodologies contribute to the economic and environmental outcomes?
- RQ2.
- How have these methodologies evolved, and what are the key drivers behind these changes?
- RQ3.
- What current state-of-the-art limitations may lead to potential trends that can be anticipated in optimizing corrugated boards?
- The early stages of optimization of corrugated boards.
- Advances of optimization in the design and manufacturing of corrugated boards.
- Design optimization of the structure.
- Optimization objectives.
- Numerical optimization algorithms used in the context of corrugated boards.
2. Background of Concepts
2.1. Optimization—Definition and Strategies
2.2. Corrugated Boards—An Overview
3. Methodology and General Overview
3.1. Databases and Keywords
3.2. Limitations
- It is possible that more English terms similar to those mentioned are being discarded.
- There might exist other libraries and databases that consider other papers that are not detected by Google Scholar, Scopus, Web of Science, and ULB.
- Despite the capability of the considered databases to detect papers written in languages other than English but using English keywords, this paper is limited by these databases’ own limitations of not finding other non-English written papers.
- It is also possible that “optimization”-related keywords are present in the body of the papers despite not being mentioned in the title. However, the authors are considering that optimization must be mentioned in the title so that it can be considered an optimization-related paper.
- Words such as “minimization” and “maximization” that are related to the optimization topic are not used, not only because there are multiple combinations of such words but also because they are not so widely used as “optimization”.
3.3. First Analysis of the Available Literature
- Five publications are excluded because they are not related to the scope of the current review, despite having the necessary keywords.
- Seven other publications are excluded because they are not complete or not accessible (due to policies that do not allow public consultation).
- One other publication is duplicated (i.e., with double reference) from another publication that is already considered in the final set of papers.
4. Literature Review on the Optimization of Corrugated Boards
4.1. Early Stages
4.2. Design vs. Manufacturing and Distribution
4.3. Design Optimization of the Corrugated Boards
4.4. Optimization Objectives
4.5. Numerical Optimization
5. Discussion of the Results Found
5.1. What Are the Main Common Findings throughout the Literature?
5.2. The Research Questions
5.3. The Gaps—And Research Directions
- It is clear that researchers have yet to fully explore the potential of corrugated boards in terms of weight reduction and safety enhancement. Despite a handful of studies on the subject, there appears to be a lack of consensus and focus on design optimization. Highlighting the benefits of corrugated boards could prove invaluable in establishing them as a reliable alternative to other materials in various structures and physical products. Therefore, it is imperative that more research is conducted in this area to realize the potential of corrugated boards fully. Future research directions: to establish new optimization strategies to reduce corrugated boards’ weight and enhance the design safety.
- There has been a significant amount of research conducted on weight minimization through different optimization approaches in applications such as composite structures [18]. These approaches include size, shape, and topology optimization. However, studies related to corrugated boards only focus on size and material optimization, and shape and topology optimization are not explored. Future research directions: to establish and tackle shape and topology optimization problems.
- The No Free Lunch Theorem [39] underscores the importance of a diversified optimization approach. Yet, the trend in corrugated board optimization research often showcases a heavy leaning toward expert-driven knowledge and a singular optimization strategy. This narrow approach potentially overlooks innovative solutions that a multifaceted, adaptive strategy could yield. Future research directions: to explore applying other optimization approaches by changing the algorithm or seeking surrogate models.
- While the FEM has proven invaluable in many engineering applications, its dominance in the realm of corrugated board weight minimization research is a double-edged sword. Sole reliance on FEM implies that the accuracy and reliability of optimization solutions are contingent upon the precision of the model. Exploring alternative or supplementary modeling techniques could enhance the robustness of the findings and their applicability in real-world scenarios. Future research directions: to explore the robustness of the simulation models and optimized solutions by exploring techniques in robust optimization.
- A discernible gap in the literature is the lack of emphasis on identifying future research directions. Such omissions might stifle the continuity and progression of knowledge in the field. Addressing limitations and articulating future research avenues not only fosters academic rigor but also galvanizes further exploration, ensuring the subject remains dynamic. Future research directions: to describe guidelines for future improvements.
- Given the complexity of real-world applications, it is often imperative to juggle multiple design objectives simultaneously. The noticeable absence of multi-objective design optimization in the literature suggests a missed opportunity. Incorporating such methodologies, especially in the context of customized solutions and robust optimization, could elevate the practical utility and adaptability of corrugated board designs. Future research directions: to more accurately apply and discuss such application of multi-objective optimization techniques.
- Factors such as environmental conditions, fire risks, and manufacturing defects profoundly influence the efficacy of any material in practical applications. The oversight of these critical variables in many studies indicates a somewhat myopic research perspective. Addressing these overlooked factors could not only bridge the prevailing research gap but also enrich the holistic understanding of corrugated board optimization in diverse conditions. Future research directions: to address new objectives that can also improve the sustainability related to the corrugated boards.
- One of the overarching gaps is the lack of a consolidated research framework. Such a framework would encompass standardized problems, methodologies, and assessment metrics, promoting consistency across studies. By working within a unified paradigm, researchers can build upon previous findings more effectively, propelling the field forward with cumulative knowledge. Future research directions: to enhance collaboration between the scientific community working in the field of the optimization of corrugated boards in order to work on standard problems instead of specific cases.
- Lastly, while theoretical advancements are crucial, there is an impending need to bridge the gap between theoretical research and its practical implications. Translational research, which focuses on turning academic findings into tangible, real-world applications, is vital. Such an approach would ensure that innovations in corrugated board optimization find their rightful place in industries and commercial products, maximizing their societal impact. Future research directions: to manage and monitor problems occurring from the application of the optimized solution or potential changes occurring in the objective function over time.
6. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Ref. | Authors (Year) | Novelty | Objectives (Category) | Design Variables | Lifecycle |
---|---|---|---|---|---|
[61,62] | Langaard (1968) | Optimization of corrugated boards based on the McKee equation (first approach) | Mechanical Properties | Type and quality of the corrugated board | Design |
[63] | P. Seyffert (1978) | Introduction of VERWEL | Time | Product order-related data | M&D |
[64] | M. W. Johnson et al. (1979) | Formulation of a theory for short-column strength of the local buckling, Empirical stress–strain analysis | Mechanical Properties | Strain of the material | Design |
[65] | Goldschmidt AG (1981) | Increase glue quality to achieve minimum defects | Mechanical Properties | Chemical concentrations; shear forces applied during mixing; temperature during the gelatinization process | M&D |
[66] | Durinda and Obetko (1982) | Design of experiments for adhesives, with the purpose of saving manufacturing costs, while increasing efficiency in production and quality of the products | Cost | Gelatination temperature, apparent viscosity | Design |
[67] | Kainulainen (1986) | Maximization of the compression resistance | Mechanical Properties | Basis weight, properties of fluting | Design |
[68] | Vogelpohl and Hohmann (1987) | Maximization of the grooveability, bending resistance, and uniformity of moisture content in storage and minimization of cover damage during grooving, variability in grooving outcomes, and moisture loss during storage | Mechanical Properties | Gap width in relation to board thickness, type of corrugated board, groove profile used, storage conditions, especially humidity levels, creasing tool profile and the gap width | M&D |
Ref. | Authors (Year) | Novelty | Objectives (Category) | Design Variables | Lifecycle |
---|---|---|---|---|---|
[69] | Cho and Um (2007) | Changing operation conditions in manufacture to improve physical properties of the product | Mechanical Properties | Operational conditions | M&D |
[70] | Tian et al. (2021) | Cutting methodology to reduce cutting waste | Cost | Raw material | M&D |
[71] | Kubera and Tyczyński (2009) | Fitting packages in a corrugated box | Volume | Production process and storage | M&D |
[72] | Mahakalkar et al. (2015) | Use of Buckling Pis for an application in the production process | N/A | Buckling Pis | M&D |
[73] | Musielak (2014) | Usage of ANN for minimization of electricity consumption for a corrugator | Cost | Corrugated board plant modules, corrugator speed and flute type | M&D |
[74] | Karabacakoğlu and Tezakıl (2023) | Added energy consumption as an objective beyond Chemical Oxygen Demand (COD) related to corrugated board production | Cost | Current density, time, stirring speed | M&D |
[75] | Wang et al. (2021) | Improvement of the procedure for selecting a corrugated board by measuring shock absorption characteristics | Mechanical Properties | Prediction model (hyperparameters)—input: drop height; static stress; cushion thickness; output—impact strength | Design |
Ref. | Authors (Year) | Novelty | Objectives (Category) | Design Variables | Design Opt. (Category) |
---|---|---|---|---|---|
[78] | Mikami et al. (2005) | Maximum strength by considering several design parameters | Mechanical Properties | Geometric values (radius of curvature, glue width, flute weight, take-up factor, angle between liner and medium theta) | Size |
[79] | Litovski et al. (2003) | Consideration of D-optimal experimental design for optimization | Mechanical Properties | Amount of chemical-mechanical pulp, freeness level of the fiber material | Topology (Material) |
[80] | Ihwah et al. (2021) | Usage of the response surface methodology for material selection by optimizing the proportion of raw material | Mechanical Properties | Proportion of raw material | Topology (Material) |
[81] | Park et al. (2009) | Development of a suitable design for corrugated board for archival quality containers | N/A | Types of corrugating adhesives used and the conditions of storage and curing temperatures | Topology (Material) |
[82] | Song et al. (2017) | FEM element optimization for modelling corrugated boards | N/A | N/A | N/A |
Ref. | Authors (Year) | Novelty | Objectives (Category) | Design Variables | Lifecycle |
---|---|---|---|---|---|
[83] | Neidoni et al. (2009) | Experimental approach to optimize perforations | Mechanical Properties | Type, dimensions, position of the perforations on the corrugated board boxes | Design |
[84] | Li et al. (2012) | Minimize the mass transfer of honeycomb panels and the frequent handling of semi manufacturers | Time | Workshop layout by using parameters | M&D |
[85] | Yuan et al. (2014) | Use of numerical simulation and mathematical modeling to optimize the structure size of UV-type corrugated board | Weight | Dimensions, structural parameters of the corrugated board | Design |
[87] | Kalyankar et al. (2015) | Minimization of box size and clearance by using FEM | Volume | Box design parameters | Design |
[5,88] | Mrówczyński et al. (2022) | Sensitivity analysis for the optimal selection of the components of a five-layer corrugated board was studied | Cost | Edge crush resistance, critical load of the packaging walls, and packaging load capacity | Design |
Ref. | Authors (Year) | Numerical Algorithm Used | Objectives (Category) | Design Variables | Lifecycle |
---|---|---|---|---|---|
[89] | Rodríguez and Vecchietti (2006) | MINLP and MILP | Cost | Cutting patterns | M&D |
[90] | Daxner et al. (2007) | COBYLA and Brent’s method | Weight | Width of the board, the height of the unit cell, and the thickness of the liners and fluting. | Design |
[91] | Protalinskii and Kokuev (2009) | Local descent; a penalty is proposed to handle violated constraints | Cost | Dimensions, structural parameters of the corrugated board | M&D |
[92] | Daxner et al. (2011) | COBYLA and Brent’s method | Weight | Width of the board, the height of the unit cell, and the thickness of the liners and fluting | Design |
[93] | Zhang et al. (2022) | Finite Differences | Mechanical Properties | Sine wave parameters amplitude and the period, thicknesses of the inner, outer and sine layers | Design |
[94] | Kalita et al. (2022) | Genetic Algorithm (and RSM as a surrogate model) | Mechanical Properties | Length, width, height, size of length stiffener, size of width stiffener | Design |
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Fitas, R.; Schaffrath, H.J.; Schabel, S. A Review of Optimization for Corrugated Boards. Sustainability 2023, 15, 15588. https://doi.org/10.3390/su152115588
Fitas R, Schaffrath HJ, Schabel S. A Review of Optimization for Corrugated Boards. Sustainability. 2023; 15(21):15588. https://doi.org/10.3390/su152115588
Chicago/Turabian StyleFitas, Ricardo, Heinz Joachim Schaffrath, and Samuel Schabel. 2023. "A Review of Optimization for Corrugated Boards" Sustainability 15, no. 21: 15588. https://doi.org/10.3390/su152115588