# Case Study - Furniture Production Line Layout

Topics: Graph theory, Genetic algorithm, Algorithm Pages: 12 (3768 words) Published: November 12, 2012
Layout Design of a Furniture Production Line Using Formal Methods

Case Study

Table of Contest
1.0 Introduction…………………………………………………………………………. 2.0 Modeling Approaches………………………………………………………………. 3.1 Graph Theory……………………………………………………………….. 3.2 CRAFT ……………………………………………………………………… 3.3 Optimum Sequence …………………………………………………………. 3.4 BLOCKPLAN ……………………………………………………………… 3.5 Genetic Algorithm ………………………………………………………….. 3.0 Application of the Modeling Approaches…………………………………………… 4.6 Using Graph Theory………………………………………………………….. 4.7 Using CRAFT………………………………………………………………… 4.8 Using Optimum Sequence………………………………………………….. 4.9 Using BLOCPLAN……………………………………………………….. 4.10 Using Genetic Algorithm…………………………………………………… 4.0 Comparisons of experimentation results by AHP………………………………….. 5.0 Conclusion………………………………………………………………………….. 6.0 References………………………………………………………………………….

1.0 Introduction
In any manufacturing company there is many issues and problem that is affected by different situation. So, the companies need to have method to solve and adapt to these situation. In this case study, the furniture company faces a lot of layout problem which needs to methods to reduce manufacturing costs, improve quality. It came up with many approaches that will help it to solve this problem. The case experiments application of different heuristic approaches to real facility layout problem at a furniture manufacturing company. All these approaches help also to know the productivity for this company.

2.0 Modeling Approaches
Graph Theory
Bloc Plan
Craft
Optimum Sequence
Genetic Algorithm
So, the company decided to apply a number of layout modeling techniques to generate a near optimal layout based on formal methods that are rarely used in practice.

2.1 Graph Theory
In the branch of mathematics called Graph Theory, a graph bears no relation to the graphs that chart data, such as the progress of the stock market or the growing population of the planet. Graph paper is not particularly useful for drawing the graphs of Graph Theory. In Graph Theory, a graph is a collection of dots that may or may not be connected to each other by lines. It doesn't matter how big the dots are, how long the lines are, or whether the lines are straight, curved, or squiggly. The "dots" don't even have to be round! All that matters is which dots are connected by which lines. Two dots can only be connected by one line. If two dots are connected by a line, it's not "legal" to draw another line connecting them, even if that line stretches far away from the first one.

2.2 CRAFT
CRAFT (Computerized Relative Allocation of Facilities Technique) uses a pair wise exchange to develop a layout CRAFT does not examine all possible pair wise exchange before generating an improved layout. This is a program designed to physically arrange the departments in a facility layout. It uses a path-oriented improvement routine based on pair-wise and three-wise exchanges of departments. The final layout is dependent on the initial layout. For this reason, it is suggested to try different initial layouts. The goal of the CRAFT program is to minimize the total transportation cost. The transportation cost for a particular move between two departments is defined as the product of the number of trips by the corresponding distance and then by a specified cost per unit distance. As a result of this, transportation costs are not directly associated with the material handling equipment used. The CRAFT procedure makes the following assumptions: (1) the facility has a rectangular or squared shape, and (2) the facility has no interior void spaces. These assumptions can actually be satisfied in most cases by creating dummy departments in the desired layout.

2.3 Optimum Sequence Algorithm
A solution method starts with layout and tries to improve by switching 2 departments in the sequence (Heragu, 2006). In each step, the...