Solving the Cubic Cell Formation Problem Using Simulated Annealing

The Cubic Cell Formation Problem (CCFP) in cellular manufacturing systems consists in decomposing a production system into a set of manufacturing cells, and assigning workers to cells besides parts and machines. The major objective is to obtain manageable cells. Manageable cells mean cells with a minimum value of inter-cell moves of parts and workers and a minimum value of heterogeneity within cells. In this paper, a solution methodology based on a modified simulated annealing heuristic with a proposed neighbourhood search procedure is proposed. The methodology allows building multiple configurations by giving to the decision-maker the ability to control some parameters. Experimental results show that the proposed algorithm gives a promising performance for all problem instances found in the literature.

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

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.