Solving the Cubic Cell Formation Problem Using Simulated Annealing

Introduction

The Group Technology (GT) is a manufacturing concept that seeks to identify and group similar parts to take advantage of their similarities in system manufacturing and design. It has been practiced for many years around the world as part of good engineering practice. A Cellular Manufacturing System (CMS) is an application of the group technology; it is used to design the layouts of production systems. The problem of cell formation (CFP) in cellular manufacturing systems (CMSs) is an important problem in the operational research literature (Joines, King, & Culbreth, 1996), (Nourie, Tang, Tuah, Ariffin, & Samin, 2013). It consists on decomposing an entire production system into a set of manufacturing cells, and assigning the machines and allocating the parts, to be produced, to these production cells. During this decomposition, some constraints and objectives must be considered to produce most manageable and independent cells.

Considering only the minimization of inter-cell moves without constraints on the number of the cells produces a design with a single cell for the production system. By this way, the advantages of cellular manufacturing system will be lost. It is well known that when designing a cellular manufacturing system, the objective is to set up manageable cells by assigning to them parts and machines at a manageable level. To obtain manageable cells, two objectives are considered in this study: the minimisation of inter-cell moves of parts and workers, and the maximisation of machine use within cells by minimising heterogeneity of cells. These two objectives are considered as conflicting objectives because when trying to reduce the inter-cell moves, many machines are regrouped in a small number of cells. This contributes into incrementing the heterogeneity within cells. On the other hand, the maximum inter-cellular moves will be created at a minimum value of heterogeneity because the minimum value of heterogeneity is obtained when each cell is dedicated for each type of machines, and thus a part to be processed needs to visit a new cell at each processing operation.

Real situations are, generally, constrained by some limitations which are often difficult to quantify. These limitations make difficult the implementation to reach the best solution. Having alternative configurations and giving the decision-maker the ability to control the best trade-off between the two conflicting objectives is a great advantage in such conditions (Shiyas & Pillai, 2014). In this study, to let the decision-maker produces such configurations a weight parameter is used to regulate the importance of heterogeneity.