Case Study – Furniture Production Line Layout
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 method computes the flow multiplied by the distance changes for all the possible switches of two departments and the most effective one is the one to be chosen. This method (switching two departments) is repeated until no further switches process can be made.
The input required to generate a layout using Optimum Sequence are mainly dimensions of the building and facilities, the material flow or frequency of trips between facility pairs and cost per unit load per unit distance. This technique of optimum sequence is used to apply the supply chain which is a total of activities involved in producing goods and services.
Uploading operation management to optimum method we used the transmission process by converting the input, transmission, and the output into information, processing the switch of two departments, and having the final result of goods and services.
The figure below will show the whole transmission process. 2. 4 BLOCPLAN Layout design can be done with various methods. One of them is by using software BLOCPLAN.
It is a program used to develop and improve single and multi layout, made by Donaghey and Pire, which can develop the layout of single story and multistory. This program offer heuristic algorithm to solve the layout problem, and can handle quantitative which is numerical information which can be formatted as a diagram as well as qualitative data which is a descriptive information that can be formatted as a matrix.
Users can enter data routing products. BLOCPLAN can calculate the flow and frequency of the trip matrix although the two previous alternatives are used, the main advantage of this program are: adequate facilities for the user, it provides an opportunity to edit the data that has been added previously according to the crises circumstances, fix the position of the facility, and manually enter them into the desired location. BLOCPLAN also prints the table layout that has been ranked, which shows the location of the value of relationships with some of the information.
In addition to single-story layout, BLOCPLAN can produce multistory layout. Eighteen facilities can be handled by the BLOCPLAN program. BLOCPLAN is similar to CRAFT in that departments are arranged in bands; it may be used both as a construction algorithm and an improvement algorithm. In an improvement algorithm, as with CRAFT, it may not be possible to capture the initial layout accurately. Nevertheless, improvements in the layout are sought through (two-way) department exchanges.
Although the program accepts both a “relationship chart” and “from-to chart” as input, the two charts can be used only one at a time when evaluating a layout.
There are certain differences between the two algorithms (CRAFT and BLOKPLAN). BLOCPLAN uses a relationship chart as well as a “from-to chart” as input data for the “flow”. Layout “cost” can be measured either by the distance-based objective or the adjacency-based objective. In BLOCPLAN, the number of bands is determined by the program and limited to two or three bands.
However, the band widths are allowed to vary.
In BLOCPLAN since each department occupies exactly one band, all departments are rectangular in shape. Lastly, unlike CRAFT, BLOCPLAN uses the continuous representation. 2. 5 Genetic Algorithm Genetic Algorithm is another way of modeling approaches that used to solve the unequal area facility layout problem with geometric constraints. Each facility has a different rectangular shape specified by its area and aspect ratio.
It requires formulating many alternatives solutions to decide on the best layout from the given solution.
The steps of how to assign many alternatives solutions to this approach is relative to as we took in chapter 5 about the Steps in Capacity Planning: Estimate future capacity requirements, Evaluate existing capacity and facilities; identify gaps, Identify alternatives for meeting requirements, Conduct financial analyses, Assess key qualitative issues, Select the best alternative for the long term, Implement alternative chosen, and Monitor results. Genetic Algorithm is inspired by Darwin’s theory about evaluation. There are many advantages of genetic algorithm. One advantage is that this approach can solve problems ith multiple solutions. Another advantage is that Genetic algorithm is a method, which is very easy to understand, and it practically does not demand the knowledge of mathematics.
One more advantage is that Genetic algorithms are easily transferred to existing simulations and models. However, genetic algorithm is parameter sensitive. To formulate facilities layout problems through genetic algorithms, we can use the slicing tree structure (STC) method. It looks like the family tree but with differences in the contests. The slicing tree structure contains of leaves and nodes.
Every leaf of a tree represents a demand rectangle and an interior node of a tree represents a meta rectangle. Two nodes have the same father if the rectangles represented by these nodes are paired. In every node the shape function of the corresponding meta rectangle is stored. 3. 0 Application of Modeling Approaches 3.
1 Using Graph Theory If you look at a graph and your eyes want to zip all around it like a car on a race course, or if you notice shapes and patterns inside other shapes and patterns, then you are looking at the graph the way a graph theorist does. 3. 2 Using CRAFT
Input 1. Number of departments (up to 40). 2. Plant area, length, and width.
3. Number of bays. 4. Department areas. 5.
Number of trips and cost per unit distance between departments. 6. Initial layout as a sequence of departments (some can be fixed in the sequence). 7. Selection of rectilinear or Euclidean distances to compute the cost.
Output 1. Graphical display of the arrangement. 2. Total cost. Outline of Procedure 1.
Compute centroids for departments in the initial layout. 2. Create distance matrix between centroids. 3. Compute transportation cost of initial layout. .
Consider interchanges of department with equal area of with common borders. 5. Select the interchange with the greatest cost reduction. 6. Compute cost and repeat the procedure until no further reductions in cost are obtained 3.
3 Using Optimum Sequence Algorithm Input data is the same as CRAFT but it follows a different set by using operation functions such as using forecasting, capacity planning, scheduling, and managing inventories. As in operation management, product and services life stage contain a huge part in productivity, and by using this figure below.
The introduction stage is where the input is and in this case which is the information, the growth stage is where the processing of switching two department is, the maturity is where the output is and in this case which is goods and service, and in the decline stage is where the output reaches a deadline that has to be saved which in this case BLOCPLAN has to be used. According to Paul A. Jensen (2004) The sequential layout is defined by the department width and the sequence used to layout the departments.
The optimum sequence method of solution starts with an arbitrary initial sequential solution and tries to improve the layout by switching two departments in the sequence. At each step, the method computes the cost changes for all possible switches of two departments and chooses the most effective pair. The two departments are switched in the sequence and the method repeats. The process stops when no switch results in a reduced cost. To illustrate we start with the departments sequenced in order of department index as below. | | During the program there are two buttons when clicking on solving button.
And as the figure below. The top button stops at each repetition to show the new layout. The second button stops when there is no further improvement. | | Starting from the initial sequence, the program finds the best switch and presents its conclusion as the figure below. Noting that the departments 9 and 10 are switched in sequence and in location. | | | | The next best switch is departments 1 and 3.
Noting that the change in sequence affects the relative locations of the departments switched. When the departments are of different size, the locations of all departments between are also adjusted. | We restarted the process with the initial sequence and chose the Do Not Stop option. The process stopped with no further improvement after one additional switch of departments 6 and 7. The result is shown below.
| | To the right of the layout appears a summary of the switches made during the process. | | Above the layout there are several additional buttons. The Random Layout button generates a random sequence of departments and places them on the layout. Since the switch heuristic does not guarantee optimality, it is useful to start at several different solutions and select the best.
The Evaluate button evaluates the current sequence placed in column G of the worksheet.
The user can manually change the sequence. The Switch button allows the user to force the program to switch two departments. The Change Facility button allows the user to change features of the facility, such as length, width or department width, or change the solution options. The Show Flows button draws lines between c centroids to show the flows. We discuss the Opt.
Form and Optimize buttons later. | For the example we generated a random sequence using the Random Layout button and performed the switch procedure until no improvement was possible.
The resulting layout is shown below with the summary results. Note that this layout is much different than the one previously discovered. Its cost is slightly larger than before. | | | We initiated the layout with a department width of 4 with the resultant sequential layout as below.
| | After a sequence of switches we obtain the final layout shown with its summary below. | | | Clicking the Show Flows button shows the flow lines between departmental centroids. The thickness of a line shows the relative magnitude of the flow-cost between two of the departments.
Four different thicknesses are used with a thin line indicating a relative small flow-cost between two departments and a thick line indicating a large flow-cost. | | The sequential layout can be easily automatically generated. The sequential layout method quickly finds good layouts for alternative facility designs.
The Traditional Craft method is an alternative. It is described on the next page. | 3. 4 Using BLOCPLAN According to operation management, when there are some changes in economics, legal, politics, social, cost, technological, or availability, product should be re-designed.
In BLOCPLAN re-designed are used to help the product when reaching into the deadline stage.
As known previously, the user has three ways to provide data flow that can be done with qualitative relationships in the form of diagrams, data can be provided by quantitative flow in the form of a matrix, and the user can easily specify the type and number of parts to be processed as well as the flow of information for each section. To use BLOCPLAN there are certain steps has to be done too. Step one is to assigns each department to one of the two (or three) bands.
Then give all the departments assigned to a particular band, BLOCPLAN computes the appropriate band width by dividing the total area of the departments in that band by the building length. Stage three is to complete layout is formed by computing the appropriate width for each band as described above and arranging the departments in each band according to a particular sequence. Fourth, to consider the two-way (pair wise) exchanges, identifies the best exchange and updates the layout according to the best exchanges.
Last stage is the process continues until no further reduction in layout cost can be obtained. As shown is the figure below 3. 5 Using Genetic Algorithm Gene structures of the genetic algorithm are used to represent layout of departments. The algorithm involved deriving an initial assignment of departments to the given floor plan and then, possibly, improving the solution quality through genetic algorithm mechanisms. A slicing tree is built bottom up. At the beginning of the algorithm all slicing trees consist of only one node (the root) representing the demand rectangles.
In every iteration step, some of the trees are combined by a common father, which is the root of a new slicing tree representing the new meta rectangle. The iteration stops, if no more suitable pairs can be matched. Since all nodes contain a shape function and every shape function describes all possible layouts of a meta rectangle, the slicing trees contain an exponential number of possible layouts for the stock rectangles. When the algorithm has ended, we can detect how the demand rectangles should be cut out of the stock rectangles. Therefore, a tree is traversed in top down order.
Since every node stores a shape function we can detect how the first cut in the stock rectangle has to be made by considering the shape function in the root of a tree and searching for the first slicing instruction whose -value is smaller or equal to the width of the stock rectangle. Due to the property of the shape functions mentioned above, we automatically get the slicing instruction, which describes the layout with the minimal length according to the made pairings. If the first cut has been carried out, the stock rectangle is split into two parts.
The shape functions in the sons of the root describe how these two parts efficiently have to be split further. This proceeding is shown in Figure bellow.
By the traversal of all slicing trees (one slicing tree for every layout) the demand rectangles can be produced. If two facilities are exchanged in the tree, a pair of facilities combined adjacently is changed. If the tree structure is changed, the facility grouping process is changed. An example is shown bellow. Here is a tree structure and its layout before doing any changes: And here is a figure that shows how the same layout that shown above became after modifying the tree structure: .
0 Comparisons of experimentation results by AHP In the paper of Chan and Abhary (1996) titled as “Design and evaluation of automated cellular manufacturing systems with simulation modeling and AHP approach” perform an AHP multi-attribute analysis by using AUTOMAN, a decision support software package. This package evaluates and combines the qualitative and quantitative factors for different configuration designs (2). According to Operations Management 4th Edition by Russell and Taylor III it is a quantitative method for ranking decision alternatives and selection the one given multiple criteria.
AHP is a process for developing a numerical score to rank each decision alternative based on how well each alternative meets the decision maker’s criteria. The question “Which one do we choose? ” or “Which one is best? ” by selecting the best alternative that matches all of the decision maker’s criteria.
It uses Simple mathematics criteria (set by the decision maker), preferences of that criteria , also set by the decision maker, and the standard preference table. As Russell, Roberta, Taylor III, and Bernard (2003) said in operation management. Cost and quality for product A ;amp; B.
The cost for A= $60 and the quality is above average. The cost for B=$15 and the quality is right at average.
Which do you choose? By making a matrix the price of B is very strongly preferred to A and A is only moderately preferred to B. The matrices of these preferences would look like Since price B is very strongly preferred to the price of A. The score of B to B is 7 and A to B is the reciprocal or inverse of 1/7. Now to apply AHP according to Smith, bush, and schmoldt (2003), there are certain steps to be done. The first step is shown in the figure below.
The second step is shown in the figure below. The third step is shown in the figure below. The fourth step is shown in the figure below. The fifth step is shown in the figure below. The steps 6, 7, 8, and 9 is shown in the figure below. The last step is the final calculation to find the result.
5. 0 Conclusion In every problem solving, we need to set many alternatives solutions to choose the best one that satisfy our needs and wants. These solutions might results from many way of thinking. In designing a layout, the different solutions result from many modeling approaches.
As we discussed the five different modeling approaches, the best layout for the furniture company was using BLOCPLAN. This approach followed by Graph Theory then Genetic Algorithm.
The other solutions, CRAFT and Optimum sequence algorithm, are far worse. There are many reasons of choosing the BLOCPLAN approach as the best layout design. One of the reasons is because it deals with quantitative and qualitative data. In addition, as this approach is a software program, it gives the users the ability to edit the data easily until they reach the layout that satisfies their requirements.
It also gives the user the opportunity to fix the position of the facility, and manually enter them into the desired location.
More reasons of choosing BLOCPLAN as the best modeling approach are: providing readable information by printing the table layout that has been ranked, which shows the location of the value of relationships with some of the information, and handling eighteen layout facilities. After all these advantages of BLOCPLAN approach, doesn’t it deserve to be on the top of modeling approach list? 6. 0 References Arifinfo. (2012). Facility Layout design by BLOCPLAN.
Opetation manament. Engineering and industrial management http://arifinfo. com/2012/02/13/facility-layout-design-by-using-blocplan/ Heragu, S. (2006). Facilities design secondth edition.
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(December, 2004). Tree Structure Modeling and Genetic Algorithm-based Approach to Unequal-area Facility Layout Problem. IMES, vol. 3, no. 2, Pg. 123-128.
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