Abstract
Cutting production costs is a crucial instrument for companies to increase profitability and remain competitive. However, companies aim to cut costs without compromising performance requirements of the products. Commonality between components reduces the costs, while diversity between them differentiates the key attributes of the products in a product family. This commonality-diversity trade-off is the essence of the product family design optimization. Current model-based methodologies consider optimizing the design for commonality rather than cost. This article proves that higher commonality does not always amount to minimal cost and, therefore, a simple commonality index cannot replace a cost model. A tunable cost model that includes simplified formulas for standardization benefits is introduced to be used by cost optimization techniques. Current product family optimization methods are often combinatorial and perform inefficiently due to searching large design space. These methods also optimize the product family design from scratch. This limits the applicability of the current methods in industrial settings that are typically complex and brownfield. This article proposes a model-based cost optimization methodology that accelerates the cost optimization by starting from an existing design. The proposed methodology is a two-stage nested optimization algorithm, in which the commonality matrix is optimized with sensitivity analysis on component types in the outer loop and the associated design variables are optimized in the inner loop. The methodology is numerically demonstrated on an industrial example and benchmarked against state-of-the-art cost optimization methods. The proposed methodology ensures a gradual improvement in cost reduction with a significant acceleration in performance.
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Data availability
Data are provided within the manuscript or supplementary information files. The data from the numerical results of the cost optimization methods are published on Zenodo https://doi.org/10.5281/zenodo.5573621. The data contains the design variables and the commonality matrices of the results obtained in.mat file format.
References
Adanur S (2020) Handbook of weaving. CRC Press, Boca Raton
Alizon F, Shooter SB, Simpson TW (2006) Assessing and improving commonality and diversity within a product family. In: International design engineering technical conferences and computers and information in engineering conference, vol 4255, pp 899–909
Eichstetter M, Müller S, Zimmermann M (2015) Product family design with solution spaces. J Mech Des 137(12):121401
Fellini R, Kokkolaras M, Papalambros P, Perez-Duarte A (2005) Platform selection under performance bounds in optimal design of product families. J Mech Des 127(4):524–535
Fujita K, Yoshida H (2004) Product variety optimization simultaneously designing module combination and module attributes. Concurr Eng 12(2):105–118
Gonzalez-Zugasti JP, Otto KN (2000) Modular platform-based product family design. In: International design engineering technical conferences and computers and information in engineering conference, vol 35128, pp 677–687. American Society of Mechanical Engineers
Inci EO, Vermaut M, Gadeyne K, Claeys C, Desmet W (2023) Data for cost optimization of shedding mechanisms as a product family. Zenodo. https://doi.org/10.5281/zenodo.5573621
Khajavirad A, Michalek JJ (2008) A decomposed gradient-based approach for generalized platform selection and variant design in product family optimization. J Mech Des 10(1115/1):2918906
Khajavirad A, Michalek JJ, Simpson TW (2009) An efficient decomposed multiobjective genetic algorithm for solving the joint product platform selection and product family design problem with generalized commonality. Struct Multidisc Optim 39(2):187–201
Martin MV, Ishii K (1996) Design for variety: a methodology for understanding the costs of product proliferation. In: International design engineering technical conferences and computers and information in engineering conference, vol 97607, pp 004-04008. American Society of Mechanical Engineers
MathWorks (2019) MATLAB optimization toolbox. Natick, Massachusetts. https://www.mathworks.com/products/optimization.html
McCarthy JM, Soh GS (2010) Geometric design of linkages, vol 11. Springer, New York
Mezo I (2011) The r-Bell numbers. J Integer Seq 14(1):11
Michalek JJ, Ceryan O, Papalambros PY, Koren Y (2005) Balancing marketing and manufacturing objectives in product line design. J Mech Des 128(6):1196–1204
Moon SK, Park KJ, Simpson TW (2014) Platform design variable identification for a product family using multi-objective particle swarm optimization. Res Eng Des 25:95–108
Niazi A, Dai JS, Balabani S, Seneviratne L (2006) Product cost estimation: technique classification and methodology review. J Manuf Sci Eng 10(1115/1):2137750
Nocedal J, Wright S (2006) Numerical optimization. Springer, New York
Pacheco P (2011) An introduction to parallel programming. Elsevier, Burlington
Rötzer S, Thoma D, Zimmermann M (2020) Cost optimization of product families using solution spaces. In: Proceedings of the design society: design conference, vol 1, pp 1087–1094. Cambridge University Press, Cambridge
Rötzer S, Le Bourgeois M, Thoma D, Zimmermann M (2021) Two-level optimization of product families: application to a product family of water hose boxes. Proc Des Soc 1:3259–3268
Simpson TW (2006) Methods for optimizing product platforms and product families. In: Product platform and product family design, pp 133–156. Springer, New York
Simpson TW, D’souza BS (2004) Assessing variable levels of platform commonality within a product family using a multiobjective genetic algorithm. Concurr Eng 12(2):119–129
Simpson TW, Maier JR, Mistree F (2001) Product platform design: method and application. Res Eng Des 13(1):2–22
Simpson TW, Seepersad CC, Mistree F (2001) Balancing commonality and performance within the concurrent design of multiple products in a product family. Concurr Eng 9(3):177–190
Zapico M, Eckert C, Jowers I, Earl C (2015) Towards product platform introduction: optimising commonality of components. In: DS 80-7 proceedings of the 20th international conference on engineering design (ICED 15) vol 7: product modularisation, product architecture, systems engineering, product service systems, Milan, Italy, 27-30.07. 15, pp 023–032
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The Internal Funds KU Leuven are gratefully acknowledged for their support. The Flanders Innovation & Entrepreneurship Agency is gratefully acknowledged for its support.
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E.O.I wrote the main manuscript text. E.O.I., M.V. and P.E. achieved the results. E.O.I created the figures and tables. All authors reviewed the manuscript.
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Inci, E.O., Vermaut, M., Eremeev, P. et al. Guided optimization: a fast model-based nested cost optimization technique for existing product family designs. Struct Multidisc Optim 67, 111 (2024). https://doi.org/10.1007/s00158-024-03829-4
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DOI: https://doi.org/10.1007/s00158-024-03829-4