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 Facility Layout Design using Genetic Algorithm

Any major industry's success depends invariably on the location of its bases, production centers and warehouses. Thus locating the sites before establishing these units is done by facility location and planning unit of the industry. For greater profits the facilities should be located at an optimum distance from the market , raw material procurement sites utilities like water , sand etc. For these problems involving layout a number of algorithms are in use like ALDEP,CORELAP, CRAFT etc. But since the location of facilities have become very complex due to greater constraints these days a determined search of a good algorithm begins. This can be achieved by using GENETIC ALGORITHMS. This type of evolutionary algorithms have made the computational effort fast and accurate.

Introduction
Material handling and layout related costs have been estimated to be about 20%-50% of the total operating expenses in manufacturing. To stay competitive in the market these high overhead costs have to be reduced considerably. One way of doing this is to develop an efficient facility layout. The secondary benefit of doing so is in reducing the large Work-In-Process inventory and justifying the costly long-term investment. Developing an efficient layout is primarily finding the most efficient arrangement of n facilities in m locations (m >= n).

Traditionally the layout problem has been presented as a Quadratic Assignment problem (QAP). The layout problem can also be termed as one-dimensional or two-dimensional problem corresponding to the single-row or multi-row patterns of layout. It is well known that QAP is NP-complete category due to the combinatorial function involved and cannot be solved for large layout problems. An alternative model for the QAP that consists of absolute values in the objective function and constraints that can be used for continuous formulations instead of discrete. The efficiency of these models however depends upon the efficient integer programming algorithms.

PROBLEM FORMULATION
The facility layout problem has been termed as Quadratic Assignment Problem (QAP) because the objective function is a second-degree polynomial function of the variables, and the constraints are identical to the constraints of the assignment problem. The objective of the QAP is to find the optimal assignment of n facilities to n sites in order to minimize the material handling cost expressed as the product of workflow and the travel distance. The QAP can be formally stated as where wij is the workflow between the facilities i and j, a(i) denotes the location to which i has been assigned. The distance function d is anyone of the lp distance between the facilities i and j and is defined as where (xi, yj )and (xi, yj ) are the geometric centers for the locations a(i) and a(j) . If p = 1 the distances are the rectilinear distances whereas when p = 2 the distances are Euclidean.

Each position can be occupied by only one facility and no facilities overlap each other. The Algorithms are based on those aforementioned statements and assumptions taking care of both the Rectilinear and the Euclidean distances while minimizing the objective.

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