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The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession

Author

Listed:
  • Jose Joaquin del Pozo-Antúnez

    (Department of Financial Economics and Accounting, Universidad Loyola Andalucía, 41704 Sevilla, Spain)

  • Francisco Fernández-Navarro

    (Department of Quantitative Methods, Universidad Loyola Andalucía, 41704 Sevilla, Spain)

  • Horacio Molina-Sánchez

    (Department of Financial Economics and Accounting, Universidad Loyola Andalucía, 41704 Sevilla, Spain)

  • Antonio Ariza-Montes

    (Social Matters Research Group, Universidad Loyola Andalucía, 41704 Sevilla, Spain)

  • Mariano Carbonero-Ruz

    (Department of Quantitative Methods, Universidad Loyola Andalucía, 41704 Sevilla, Spain)

Abstract

The traditional machine-part cell formation problem simultaneously clusters machines and parts in different production cells from a zero–one incidence matrix that describes the existing interactions between the elements. This manuscript explores a novel alternative for the well-known machine-part cell formation problem in which the incidence matrix is composed of non-binary values. The model is presented as multiple-ratio fractional programming with binary variables in quadratic terms. A simple reformulation is also implemented in the manuscript to express the model as a mixed-integer linear programming optimization problem. The performance of the proposed model is shown through two types of empirical experiments. In the first group of experiments, the model is tested with a set of randomized matrices, and its performance is compared to the one obtained with a standard greedy algorithm. These experiments showed that the proposed model achieves higher fitness values in all matrices considered than the greedy algorithm. In the second type of experiment, the optimization model is evaluated with a real-world problem belonging to Human Resource Management. The results obtained were in line with previous findings described in the literature about the case study.

Suggested Citation

  • Jose Joaquin del Pozo-Antúnez & Francisco Fernández-Navarro & Horacio Molina-Sánchez & Antonio Ariza-Montes & Mariano Carbonero-Ruz, 2021. "The Machine-Part Cell Formation Problem with Non-Binary Values: A MILP Model and a Case of Study in the Accounting Profession," Mathematics, MDPI, vol. 9(15), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1768-:d:602013
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    References listed on IDEAS

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    1. Feng, Yanling & Li, Guo & Sethi, Suresh P., 2018. "A three-layer chromosome genetic algorithm for multi-cell scheduling with flexible routes and machine sharing," International Journal of Production Economics, Elsevier, vol. 196(C), pages 269-283.
    2. Jose Joaquin Pozo-Antúnez & Horacio Molina-Sánchez & Antonio Ariza-Montes & Francisco Fernández-Navarro, 2021. "Promoting work Engagement in the Accounting Profession: a Machine Learning Approach," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 157(2), pages 653-670, September.
    3. Dekkers, Rob, 2018. "Group technology: Amalgamation with design of organisational structures," International Journal of Production Economics, Elsevier, vol. 200(C), pages 262-277.
    4. Erfan Mehmanchi & Andrés Gómez & Oleg A. Prokopyev, 2019. "Fractional 0–1 programs: links between mixed-integer linear and conic quadratic formulations," Journal of Global Optimization, Springer, vol. 75(2), pages 273-339, October.
    5. M. Grunspan & M. E. Thomas, 1973. "Hyperbolic integer programming," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 20(2), pages 341-356, June.
    6. Sarker, Bhaba R., 2001. "Measures of grouping efficiency in cellular manufacturing systems," European Journal of Operational Research, Elsevier, vol. 130(3), pages 588-611, May.
    7. J. E. King, 1999. "Introduction," Review of Political Economy, Taylor & Francis Journals, vol. 11(3), pages 251-255.
    8. Wu, Tai-Hsi, 1997. "A note on a global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 101(1), pages 220-223, August.
    9. Espinosa-Pike, Marcela & Barrainkua, Itsaso, 2016. "An exploratory study of the pressures and ethical dilemmas in the audit conflict," Revista de Contabilidad - Spanish Accounting Review, Elsevier, vol. 19(1), pages 10-20.
    10. Li, Han-Lin, 1994. "A global approach for general 0-1 fractional programming," European Journal of Operational Research, Elsevier, vol. 73(3), pages 590-596, March.
    11. B. Pierce & B. Sweeney, 2004. "Cost-quality conflict in audit firms: an empirical investigation," European Accounting Review, Taylor & Francis Journals, vol. 13(3), pages 415-441.
    12. Reza Raminfar & Norzima Zulkifli & Mohammadreza Vasili, 2013. "A Mathematical Programming Model for Cell Formation Problem with Machine Replication," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, May.
    13. S Lozano & B Adenso-Díaz & I Eguia & L Onieva, 1999. "A one-step tabu search algorithm for manufacturing cell design," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 50(5), pages 509-516, May.
    14. Juan S. Borrero & Colin Gillen & Oleg A. Prokopyev, 2017. "Fractional 0–1 programming: applications and algorithms," Journal of Global Optimization, Springer, vol. 69(1), pages 255-282, September.
    15. William T. McCormick & Paul J. Schweitzer & Thomas W. White, 1972. "Problem Decomposition and Data Reorganization by a Clustering Technique," Operations Research, INFORMS, vol. 20(5), pages 993-1009, October.
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