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

Jose Joaquin del Pozo-Antúnez, Francisco Fernández-Navarro, Horacio Molina-Sánchez, Antonio Ariza-Montes and Mariano Carbonero-Ruz
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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

Mathematics, 2021, vol. 9, issue 15, 1-16

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.

Keywords: machine-part cell formation problem; fractional 0–1 programming; mixed-integer linear programming; human resources management (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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