Simulated annealing for machine layout problems in the presence of zoning constraints

One of the assumptions behind the Quadratic Assignment Problem (QAP) formulation for machine layout problems is that any machine could be located to any of the available sites. However, it is quite common in manufacturing environments to find restrictions on the arrangement of machines (zoning constraints). Positive zoning constraints require that machines are located next to each other, while negative zoning constraints force certain machines not to be in close proximity. In this paper the authors address the machine layout problem in the presence of zoning constraints. The QAP formulation is appropriately modified to account for the existence of such constraints. Two distinct implementations of the Simulated Annealing (SA) algorithms, the Compulsion and the Penalty procedures, are proposed for the solution of the problem. Sensitivity analysis on the control parameters of the above procedures is performed. The computational results on the comparison of the above two methods favor the Compulsion procedure. The Penalty method, however, might still be appealing to layout designers due to the easiness of implementation for any type of zoning constraints. Finally, the present computational results indicate that imposing cleverly generated restrictions (for example, machines with exceptionally large flow between them to be close together) on SA procedures for QAP formulations (i.e., machine layout problems with no zoning constraints) can signficantly improve the solution effectiveness (i.e., lower total layout cost) of the SA algorithm for such problems.