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
