Two-phase approach to GT cell formation using efficient p-median formulations

Abstract

The purpose of this paper is to develop an efficient p-median approach applicable to large cell formation (CF) problems. A two-phase methodology that seeks to minimize the number of exceptional elements is proposed. In phase I, two efficient p-median formulations which contain fewer binary variables than existing p-median formulations are constructed. For a CF problem with m machines existing p-median formulations contains m2 or more binary variables, whereas the new formulation proposed in phase I contains not more than 5m binary variables at the expense of a slightly increased number of continuous variables and constraints for practical values of p less than 32. This makes it possible to implement large CF problem within reasonable computer runtime with commercially available linear integer programming codes. Given the initial cell configuration found with the new p-median formulation, in phase II bottleneck machines and parts are reassigned to reduce the number of exceptional elements. This procedure has the flexibility of providing the cell designer with alternative solutions. Test results on large CF problems show a substantial increase in the efficiency of the new p-median formulations compared with existing p-median formulations.