Idea Transcript
INEN 416 Facility Location, Layout, and Material Handling
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Computerized Layout Planning • Focus on how computers can aid the facility layout process. • Designer must interact with multiple design databases and provide the integration between them to translate information and ensure consistency. • We will concentrate on decision aids for block layout planning. – Information required – Common elements – “Classical” layout programs » Craft, Corelap, Aldep, and Planet
– “Newer” layout programs » M-Craft, LayOpt, FactoryPlan
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Computerized Layout Planning • Information in layout planning – Numeric information » Space required for an activity » Total flow between two activities
– Logic information » Preferences of the designer, i.e., activity relationship chart
– Graphical information » Drawing of the block plan
• Key element of computerized layout planning is the representation and manipulation of these three types of information. – Graphical representation is most challenging. A method suitable for display is not suitable for manipulation and vice-versa.
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Computerized Layout Planning • Graphical Representation – “Points and lines” representation is not convenient for analysis
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Computerized Layout Planning • Graphical Representation (cont.) – Most procedures employ a “unit area square” representation as an approximation » Space available and space required for each activity are expressed as an integer multiple of the unit area.
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Computerized Layout Planning • Graphical Representation (cont.) – Unit Square Area approximation can also be represented by a two dimensional array or matrix of numbers » Easy to manipulate (e.g., determine adjacency) but difficult to visually interpret 1
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Computerized Layout Planning • Layout Evaluation – Algorithm needs to distinguish between “good” layouts and “bad” ones – Develop scoring model, s = g(X) – Adjacency-based scoring » Based on on the relationship chart and diagram
s=
6
∑ wi Xi i =1
» Aldep uses A=64, E=16, I=4, O=1, U=0, and X=-1024 » Scoring model has intuitive appeal; the ranking of layouts is sensitive to the weight values. Layout “B” may be preferred to “C” with certain weights but not with others. » Therefore, correct specification of the weights is very important -- but how do you do that? Texas A&M INEN 416
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INEN 416 Facility Location, Layout, and Material Handling
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Computerized Layout Planning • Layout Evaluation (cont.) – Distance-based scoring » Approximate the cost of flow between activities » Requires explicit evaluation of the flow volumes and costs
s=
m −1 m
∑ ∑ cij Dij i =1 j = i + 1
» cij covers both the i to j and the j to i material flows » Dij can be determined with any appropriate distance metric • Often the rectilinear distance between department centroids
» Assumes that the material flow system has already been specified » Assumes that the variable flow cost is proportional to distance » Distance often depends on the aisle layout and material handling equipment Texas A&M INEN 416
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Computerized Layout Planning – Layout Evaluation -- Distance-based scoring Example Initial Layout
B
A
C
Flow Data From/To A B C A 2 4 B 1 1 C 2 1 D 4 1 0
D 4 3 2 -
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Distance Data From/To A B C D A - 40 25 55 B 40 - 65 25 C 25 65 - 40 D 55 25 40 Texas A&M
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From/To A B C D Total
Total Cost A B C - 80 100 40 - 65 50 65 220 25 0 310 170 165
D 220 75 80 375
Total 400 180 195 245 1020
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Computerized Layout Planning • Layout Evaluation (cont.) – Distance-based scoring – Impact of aisle layout and direction of travel
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D
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Computerized Layout Planning • Layout Evaluation (cont.) – Distance-Weighted Adjacency-Based Scoring s=
6
6
∑ ∑ w ij X ij i =1 j =1
» A smaller score is better » As before, the scoring model is sensitive to the adjacency class weights, wij
– More Complex Scoring Methods » Could employ simulation to determine material handling equipment utilization, etc. » Would probably better reflect the preferences of the layout planner » Certainly more difficult to compute and could effect the number of alternatives considered Texas A&M
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Computerized Layout Planning • Layout Generation – Construction Algorithms » Start with basic SLP data and build a block layout by iteratively adding activities to a partial layout until all activities have been placed.
– Improvement Algorithms » Require an initial block layout which they then attempt to improve.
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Computerized Layout Planning • Construction Algorithms – For i = 1 to n SELECT an activity to be placed PLACE the selected activity in the layout End For – Selection rules » Choose the next activity having the largest number of “A” (“E”, “I”, etc.) relationships with the activities already in the layout. Break ties randomly. » Supplement above procedure with TCR for choosing first department and breaking ties. » Consider “flow cost chart” and user specified placement priorities.
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Computerized Layout Planning • Construction Algorithms – Placement Rules » Contiguity Rule • If an activity is represented by more than one unit area square, every unit area square representing the activity must share at least one edge with at least one other unit area square representing the activity.
» Connectedness Rule • The perimeter of an activity must be a single closed loop that is always in contact with some edge of some unit area square representing the activity.
» The following are infeasible shapes for activities.
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Computerized Layout Planning • Construction Algorithms (cont.) – Placement Rules (cont.) » Five “basic” shapes for an activity represented by 4 unit area squares.
» Determining possible shapes becomes nontrivial for activities with more than 5 unit area squares, and some of the shapes have bizarre configurations.
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Computerized Layout Planning • Construction Algorithms (cont.) – Placement Rules (cont.) » Therefore, additional rules are often used. » Enclosed Voids Rule • No activity shape shall contain an enclosed void.
» Shape Ratio Rule • The ratio of a feasible shape’s greatest length to its greatest width shall be constrained to lie between specified limits.
» Corner Count Rule • The number of corners for a feasible shape may not exceed a specified maximum.
» Given an activity’s shape there are a large number of alternative placements for it in a layout, including different locations and mirror images and rotations.
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Computerized Layout Planning • Construction Algorithms (cont.) – Bounded placement procedures » Accept a specified facility configuration and fit the activities into the facility. » May not be able to enforce all of the activity shape rules. » E.g., ALDEP
– Free placement procedures » Create a layout without regard to the resulting facility configuration. » May produce layouts requiring considerable adjustment to conform to conventional building configurations. » E.g., CORELAP
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Computerized Layout Planning • Improvement Algorithms – “Moves” activities around within the block plan, much like a jigsaw puzzle except that the shapes of the pieces are not fixed. – Too many degrees of freedom to devise a good method for modifying the block plan. – Most all improvement algorithms limit the kinds of changes that are permitted. – Basic procedure » CHOOSE a pair (or triple) of activities ESTIMATE the effect of exchanging them EXCHANGE if the effect is to reduce the total cost CHECK to be sure the new layout is better Repeat Until no more improvements are possible.
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Computerized Layout Planning • Improvement Algorithms (cont.) – To CHOOSE a pair of activities » Activities that have the same area, or » Activities that share a common boundary.
– There are many possibilities for EXCHANGE when the areas are not equal. » Generally, the shape ratio and corner count rules are violated, therefore, manual adjustment is sometimes required.
– ESTIMATE the value of the exchange by comparing the cost if the two centroids are switched. » However, this estimate will not necessarily be correct for unequal area activities.
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Computer-Aided Layout • Computer-aided layout techniques are classified by – Method of recording flows between departments » Quantitatively in a from-to chart » Qualitatively in a relationship chart
– Method of generating layouts » Construction of a layout » Improvement of an existing layout
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Computer-Aided Layout Techniques Construction Routine Improvement Routine Quantitative Input
PLANET
CRAFT COFAD
CORELAP Qualitative Input
ALDEP PLANET
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CRAFT • Attempts to minimize transportation cost, where Transportation cost = flow * distance * unit cost
• Requires the assumptions that: – Move costs are independent of the equipment utilization. – Move costs are linearly related to the length of the move.
• Distance metric used is the rectilinear distance between department centroids.
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CRAFT • Procedure 1. 2. 3. 4.
Determine department centroids. Calculate rectilinear distance between centroids. Calculate transportation cost for the layout. Consider department exchanges of either equal area departments or departments sharing a common border. 5. Determine transportation cost of each departmental interchange. 6. Select and implement the departmental interchange that offers the greatest reduction in transportation cost. 7. Repeat the procedure for the new layout until no interchange is able to reduce the transportation cost. Texas A&M
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CRAFT • CRAFT is a path-oriented method so the final layout is dependent on the initial layout. • Therefore, a number of different initial layouts should be used as input to the CRAFT procedure. • CRAFT allows the use of dummy departments to represent fixed areas in the layout.
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CRAFT Example • Initial Layout
1 2 3 4 5 6 7 8 9 10
1 A A A B B B B D D D
2 3 4 5 6 7 8 9 10 A A A A A A A A A A A A A A A A A A A B B B B C C C C C B C C B C C C C C B B B B D D D D F D D D D D D F D F D D D D D D D H H
11 G G G E E E F
12 13 14 15 16 17 18 G G G G G G G G G G G E G G G G G G E E E E E E E E E E E E E E F F F F F E E F F F F F F F H H H F F F F F
Shipping Department
Dummy Department
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CRAFT Example • Distance Matrix A B C D E F G H
A B C D E F G H 6 5 6 13 16 6 11 14 7 10 6 12 3 4 14 3 7
• Cost Matrix A A B C D E F G H
B C D E F G 270 75 150 130 80 180 275 210 35 100 120 420 195 140 70 75 455
H
Total 705 665 135 540 335 600 0 0 2980
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CRAFT Example • Trial Distance Matrix A B C D E F G H
A B C D E F G H 6 5 6 16 13 6 14 11 10 7 6 9 3 7 11 3 4
• Trial Cost Matrix A A B C D E F G H
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B C D E F G 270 75 150 160 65 180 350 165 50 70 120 315 195 245 55 75 260
H
Total 720 695 120 435 440 390 0 0 2800
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CRAFT Example • New Layout
• Final Layout
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1 A A A B B B B D D D
2 3 4 5 6 7 8 9 10 11 A A A A A A A A A G A G A A A A A A A A A G B B B B C C C C C F B C C F B C C C C C F B B B B D D D D E E D D D D D D E D E E D D D D D D D H H H
12 13 14 15 16 17 18 G G G G G G G G G G G F G G G G G G F F F F F F F F F F F F F E E E E F F E F F E E E E F F H H E E F F F
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1 A A A C C C C D D D
2 3 4 5 6 7 8 9 10 11 A A A A A A A A A G A G A A A A A A A A A G C C B B B B B B B F C C B B F C B B B B B B F C C C B D D D D E E D D D D D D E D E E D D D D D D D H H H
12 13 14 15 16 17 18 G G G G G G G G G G G F G G G G G G F F F F F F F F F F F F F E E E E F F E F F E E E E F F H H E E F F F
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COFAD • A modification of CRAFT to allow for a variety of material handling equipment alternatives. • It attempts to select both the layout and the material handling system. • A special version, COFAD-F, allows the evaluation of varying the product volumes and mixes to analyze the flexibility of the design.
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PLANET • PLANET is a construction routine with the same basic input requirements as CRAFT. • Material Flow Input Methods – Specify a route or production sequence for each part. – From-to Chart. – Penalty Matrix -- quantitative representation of a relationship chart.
• Construction Algorithm Selection Methods – Choose based on individual flow-between costs. – Choose based on the sum of the flow-between costs with previously placed departments. – Choose based on the sum of the flow-between costs with all other departments. Texas A&M
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CORELAP • Constructs a layout for a facility by calculating the total closeness rating (TCR) for each department. • The total closeness rating is the sum of numerical values assigned to the closeness relationships from the relationship chart. – A = 6, E = 5, I = 4, O = 3, U = 2, X = 1
• Procedure (similar to one of the procedures for relationship diagramming) – Place department with the highest TCR in the center of the layout. – Scan the relationship chart for a department with an A (if none, then E, I, and so on) relationship with the selected department. Highest TCR is tie-breaker. – Continue until all departments are in the layout. Texas A&M
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ALDEP • Same basic input requirements and objectives as CORELAP. • Selection Procedure – Randomly select first department in the layout. – Scan the relationship chart for an A (then E, etc.) relationship with the selected department. Break ties randomly. – Repeat procedure until all departments are selected.
• Placement Procedure – Place first department in upper left corner and extend it downward. Width of the extension is determined by the sweep width. – Next department begins where the previous department ended and follows the serpentine sweep pattern. Texas A&M
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ALDEP • Sweep Pattern
– Can accommodate a variety of building shapes and irregularities.
• Scoring Mechanism: Adjacency Score – ALDEP rates the layouts by determining an adjacency score by assigning values to the relationships among adjacent departments. » A = 64, E = 16, I = 4, O = 1, U = 0, X = -1024 Texas A&M
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ALDEP Example • Layout Construction 4 4 4 4 4 4 4 4 4 4
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2 2 2 2 2 4 4 4 4 4
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ALDEP Example • Scoring Procedure Adjacent Departments 4-2 and 2-4 4-1 and 1-4 2-1 and 1-2 1-6 and 6-1 6-5 and 5-6 6-7 and 7-6 5-7 and 7-5 7-3 and 3-7
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Relationship E I E U A E I U
Value 16 4 16 0 64 16 4 0 Total
Rating 32 8 32 0 128 32 8 0 240
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Spiral • Graph based algorithm which attempts to create a structured adjacency graph. – The objective is to maximize the adjacency score. – The selection and location decisions are made simultaneously, using a greedy approach on a hexagonal grid.
• Procedure – – – –
Convert the flow matrix to a symmetric matrix. Sort the pairwise relationships by decreasing value. Place the first two departments in the layout. Add the departments by order in the list from step 2, such that the adjacency with already placed departments is maximized. Use a random tie breaker.
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Spiral Example • Input Data – Asymmetrical Flow Matrix Dept 1 2 3 4 5 6 7
1 -
2 3 4 5 6 7 45 15 25 10 5 30 25 15 5 10 20 - 35 - 65 35 5 25 - 65 -
– Symmetrical Flow Matrix Dept 1 2 3 4 5 6 7
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1 -
2 3 4 5 6 7 45 15 25 10 5 50 25 20 5 10 - 35 - 90 35 - 65 -
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Spiral Example • Sorted Flow List Dept 5 6 2 1 4 5 1 2 2 1 1 3 1 3
Dept 6 7 4 2 5 7 4 5 6 3 5 6 6 5
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Flow 90 65 50 45 35 35 25 25 20 15 10 10 5 5
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Spiral Example • Graph Construction 2 5
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Spiral Example • Graph Evaluation – Adjacency Matrix * Symmetrical Flow Matrix Dept 1 2 3 4 5 6 7
1 -
2 1 -
3 1 0 -
4 1 1 1 -
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6 0 0 0 0 1 -
7 0 1 0 0 1 1 -
Dept 1 2 3 4 5 6 7
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2 3 4 5 6 7 45 15 25 10 5 50 25 20 5 10 - 35 - 90 35 - 65 -
– Score is 385 – Maximum score is 435 – Efficiency is 385/435 = 88% Texas A&M
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Spiral Example • Alternative Adjacency Graph 7 5 4
6 2
1
3
– Score is 405 – Efficiency is 93%
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Spiral • Creating a Layout – Can use a sweep pattern similar to ALDEP to sweep through the adjacency graph and create a block layout 7 5 4
6 2
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3
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Excel Layout Tool • Uses CRAFT-type flow*distance objective • Layout is specified by a department sequence – User-specified and random sequences can be used
• ALDEP placement procedure based on a vertical sweep pattern is used to place departments in layout – Sweep width parameter can be changed – Grid size and facility shape can also be adjusted
• Pairwise exchange is performed on the sequence position of departments – Not restricted to adjacent or equal size departments » Due to using the sweep method to create a layout
• Additional add-ins to generate and improve sequences are available • Software also solves “traditional CRAFT”
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M-Craft • Layout is specified by a sequence of departments • Horizontal sweep patterns are used to place departments in layout – Number of bays controls sweep width
• Pairwise exchange is performed on the sequence position of departments – Not restricted to adjacent or equal size departments » Due to using the sweep method to create a layout
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MULTIPLE / LayOpt • Layout is specified by a sequence of departments • Sweep patterns are used to place departments in layout – Sweep pattern is based on space filling curve (SFC) concept – Many alternative SFCs can be created
• Pairwise exchange is performed on the sequence position of departments – Not restricted to adjacent or equal size departments » Due to using the sweep method to create a layout
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Factory CAD/Flow/Plan • AutoCAD based add-on • Has multiple applications – CAD: drawing templates – FLOW: evaluation of material flow; manual SLPtype manipulation – PLAN: layout alternative generation
• FactoryPLAN – Uses Spiral-type algorithm to generate alternative layout options
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Computerized Layout Planning Conclusion • Does not provide an absolute best model for finding the optimal layout. • Does provide algorithms for evaluating a large number of alternative layouts. • It is important to understand the underlying assumptions and scoring models of each procedure in order to correctly interpret the results.
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