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Chapter 6 Layout Planning Models and Design

Algorithms

- Dr. Chen
- chenc_at_fiu.edu

Introduction

- Generating layout alternatives is a critical step
- Comprehensive and creative
- Layouts
- Block relative locations and sizes of planning

departments - Detailed exact location of all equipment,

benches, storage areas within each department - Our focus will be on Block Layout

Introduction

- Chapter 1
- Facilities planning and its relationship with

manufacturing, distribution and marketing - Chapter 2
- Process, product and schedule design
- Chapter 3
- Flow, activity and space relationships

Introduction

- Which comes first?
- Facility layout or Material handling
- Many appear to believe that it should be facility

layout - Material handling affects
- Centralized vs. decentralized storage of WIP,

tooling, supplies - Fixed path vs. variable path handling
- Unit load
- Degree of automation used in handling
- Type of level of inventory control, physical

control and computer control of materials - Each of the above affects requirements for space,

equipment and personnel, as well as the proximity

required between functions

Introduction

- Facility layout is considered first over

emphasis on mfg - If parts move from department A to B
- It is logical to have department B next to A
- Handling is minimized
- If parts cannot move from department A to B

directly - WIP storage is necessary
- Parts move from A to Storage and then to B
- In such a case, A and B need not be close to each

other - Both facility layout and material handling should

be designed simultaneously

Basic Layout Types

Basic Layout Types continued

Basic Layout Types continued

Basic Layout Types continued

Layout Procedures

- Many procedures are available
- Broadly classified
- Construction type layout methods
- Layout from scratch
- Improvement type layout methods
- Alternatives based on existing layout

Apples Plant Layout Procedure

- Procure the basic data
- Analyze the basic data
- Design the productive process
- Plan the material flow pattern
- Consider the general material handling plan
- Calculate equipment requirements
- Plan individual workstations
- Select specific material handing equipment
- Coordinate groups of related operations
- Design activity interrelationships

Apples Plant Layout Procedure continued

- Determine storage requirements
- Plan service and auxiliary activities
- Determine space requirements
- Allocate activities to total space
- Consider building types
- Construct master layout
- Evaluate, adjust, and check the layout with the

appropriate persons - Obtain approvals
- Install the layout
- Follow up on implementation of the layout

Reeds Plant Layout Procedure

- Analyze the product or products to be produced
- Determine the process required to manufacture the

product - Prepare layout planning charts
- Determine workstations
- Analyze storage area requirements
- Establish minimum aisle widths
- Establish office requirements
- Consider personnel facilities and services
- Survey plant services
- Provide for future expansion

Reeds Plant Layout Procedure continued

- Most important
- Prepare layout planning charts
- Layout planning chart incorporates the following
- Flow process, including operations,

transportation, storage, and inspections - Standard times for each operation
- Machine selection and balance
- Manpower selection and balance
- Material handling requirements

Layout Planning Chart

Muthers Systematic Layout Planning Procedure

Activity Relationship Chart

Relationship Diagram

RD positions activities spatially Proximities

are typically used to reflect the relationship

between pairs of activities

Space Requirement

Read section 3.7 from the textbook

Space Relationship Diagram

Alternative Block Layouts

Algorithmic Approaches

- Relative placement of departments based on
- Closeness ratings
- Material flow intensities
- SLP and other approaches discussed earlier are

not formal approaches - The algorithmic approach can be computerized
- Easy to conduct what-if analysis
- Solve large layout problems rapidly
- However, cannot replace human designers

Algorithmic Classification

- Input to the algorithms
- Only qualitative data (relationship diagram)
- Need input from several individuals
- Possible inconsistencies should be resolved
- Not practical for problems with 20 or more

departments - Only quantitative data (from-to chart)
- Predominantly used in practice
- Requires more time and effort to prepare the

from-to chart - Both qualitative and quantitative data
- BLOCPLAN

Algorithmic Classification continued

- Objectives
- Minimize the sum of flow distances
- From-to matrix
- Maximize an adjacency score
- Relationship chart

Flow Distance Objective

Note cij independent of the material handling

equipment used

Adjacency Score Objective

Normalized adjacency ratio is 0,1 When it is

1, it means that all the departments with a

positive flow are adjacent to each other

Adjacency Score Objective continued

- Some times it is unimportant (relationship is

represented as X) to have departments i and j

adjacent to each other - A negative fij is used to avoid i and j adjacent

to each other - F represent the set of departments with positive

flow values - Adjacency objective do not account for the

distance between departments - Consequently, two layouts with same score can

result in different total distance between

departments

Discrete vs. Continuous Layout

Choosing an appropriate grid size is

important If the grid size is smaller there

are larger number of grids- computationally

burden

Discrete vs. Continuous Layout

- Discrete Layout
- Easy to implement in a computer
- Selecting appropriate grid size is important
- Smaller grids computationally burdensome

- Continuous Layout
- Hard to implement in a computer
- Highly flexible
- Representing L-shaped, U-shaped departments is

not straightforward

Discrete vs. Continuous

- For a rectangular department with known area
- If you know the x,y coordinates of centroid of

the department and its length along the

north-south direction, it is easy to represent

its exact location and shape - For a T-shaped department with known area, this

is not possible - If a department is too large, it may be

represented as two departments - But the two departments cannot be split in the

final layout

Split Departments

Different Layout Methods

- Pairwise Exchange Method
- Graph-based Method
- CRAFT
- BLOCPLAN
- MIP
- LOGIC
- MULTIPLE

Pairwise Exchange Method

- Improvement type layout algorithm
- Current layout has to be changed
- New machine is included
- Space required for storage has to be altered
- Existing layout is poor
- Can be used for both adjacency based or distance

based objective

Pairwise Exchange Method continued

Assume all the departments are of equal size, for

simplicity

TC1234 10x1 15x2 20x3 10x1 5x2 5x1

125

Pairwise Exchange Method continued

- In each iteration
- Consider all possible pairwise exchanges
- The pair which results in the largest reduction

in TC is selected (steepest descent approach) - The procedure is terminated when the objective

does not improve - For the example problem, all pairwise exchanges

are feasible as all the departments are of equal

size

Pairwise Exchange Method continued

- Initial solution

TC1234 125 - TC2134(1-2) 10x1 15x1 20x2 10x2 5x3

5x1 105

Distance matrix for 2-1-3-4

Pairwise Exchange Method continued

Iteration 0

Pairwise Exchange Method continued

Iteration 1

Pairwise Exchange Method continued

Iteration 2

STOP

Graph-Based Layout Planning

- Construction type algorithm
- Adjacency based objective

Graph-Based Layout Planning continued

Graph-Based Layout Planning continued

Graph-Based Layout Planning continued

- Some observations
- Adjacency score does not account for distance,

nor does it account for relationships other than

those between adjacent departments - Dimensional specifications of departments are not

considered - Planar graph arcs do not intersect (adjacency

graph). Non-planar graph relationship diagram. - Score is very sensitive to the assignment of

numerical weights in relationship chart

Graph-Based Layout Planning continued

- Maximize weighted planar adjacency graph
- Approach 1
- Start with the relationship diagram
- Prune arcs while making sure the final graph is

planar - Approach 2
- Iteratively construct an adjacency graph via a

node insertion algorithm while retaining

planarity at all times

Graph-Based Layout Planning continued

- Node insertion heuristic
- Step 1 from the relationship chart, select the

department pair with the largest weight. Break

ties arbitrarily.

Choose departments 3 and 4

Graph-Based Layout Planning continued

- Node insertion heuristic continued
- Step 2 select the third department to enter.

Third department is chosen based on the sum of

the weights w.r.t departments 3 and 4.

Yet to be chosen

Graph-Based Layout Planning continued

- Node insertion heuristic continued
- Step 3 fourth department is chosen by evaluating

the value of adding one of the unassigned

departments represented by a node on a face of

the graph - A face of a graph is a bounded region of a graph

Recall we are trying to build a planar graph.

Graph-Based Layout Planning continued

- Node insertion heuristic continued
- Step 4 evaluate inserting department 5 in

different faces, namely 1-2-3, 1-2-4, 1-3-4, and

2-3-4.

Graph-Based Layout Planning continued

- Step 5 using the adjacency graph, draw the block

layout.

CRAFT

- Computerized Relative Allocation of Facilities

Technique - From-to-chart is the input
- Distance based objective
- Departments are not restricted to rectangular

shapes - Discrete layout
- Improvement algorithm
- Centroids for each department is calculated
- Rectilinear distance between departments using

centroids - All possible two-way (pairwise) or thee-way

department exchanges are considered - Departments with equal area
- Departments which are adjacent to each other

CRAFT continued

- Steepest descent procedure
- May stop at local optima
- Initial solution matters

CRAFT Example

Each grid is 20 x 20 sq. ft

Total area required (70,000 sq. ft) is more than

available (72,000 sq. ft) The extra space is

modeled as a department

CRAFT Example continued

Distance between A and B is 6 grids Flow between

A and B is 45 units A and B 6 x 45 270 Total

z 2974 grids

Note The location of department A (receiving)

and G (shipping) is fixed. They cannot be

considered for two-way exchanges

CRAFT Example continued

Departments E and F are adjacent Area required

for E and F are different

First draw a single box around E and F Choose

the bigger department Start from left or right

column to fill Label first 20 grids of

department F as department E

CRAFT Example continued

Exchange departments B (8000 sq. ft) and C (6000

sq. ft)

No improvements achieved with other two-way or

three-way exchanges. STOP

CRAFT Example continued

CRAFT continued

Exchanging departments 2 and 4 will lead to

splitting department 2 not acceptable

CRAFT continued

- Three-way exchange
- The departments should be adjacent or of equal

area - Complicated to implement

MCRAFT

- Micro CRAFT
- Input
- Building length
- Building width
- Number of bands
- Initial layout vector
- The program calculates appropriate grid size, the

number of rows columns

MCRAFT

Length 360 ft, Width 200 ft, number of bands

3 Initial layout vector 1-7-5-3-2-4-8-6

MCRAFT

6 rows / band

Initial layout vector 1-7-5-3-2-4-8-6

MCRAFT

BLOCPLAN

- Similar to MCRAFT
- Inputs
- From-to chart
- Relationship chart
- The number of bands is determined by the program
- Number of bands limited to two or three
- Band widths may vary
- Construction and improvement algorithm

MIP

- Mixed integer program
- Construction algorithm
- If interested, read pages 333-339 from the

textbook

LOGIC

- Layout Optimization with Guillotine Induced Cuts
- Input from-to chart
- Construction and improvement algorithm
- Horizontal and vertical cuts are added
- With each cut, appropriate departments are

assigned to - East or West of a vertical cut
- North or South of a horizontal cut

LOGIC Example

None of the departments are fixed Length 360

ft Width 200 ft

First Vertical cut Area of D,F,G 36,000 Width

200 Length 36000/200 180

LOGIC Example

Horizontal cut AB total area 20000 Length

180 Width 20000/180 111.11

Horizontal cut DF total area 24000 Length

180 Width 24000/180 133.34

LOGIC Example

LOGIC Example

East or right side of a vertical cut

South or bottom of a horizontal cut

LOGIC Example

- LOGIC can also be used as an improvement

algorithm - Suppose we consider a pair-wise exchange (D and

E) - Swap D and E in the tree shown in the previous

slide - Recalculate the x y coordinates

LOGIC Example

CORELAP

- Computerized Relationship Layout Planning
- Input relationship chart
- Total Closeness Rating (TCR)
- Sum of closeness relationship between a

department and all other departments - A 6 E 5 I 4 O 3 U 2 X 1
- Department with highest TCR is placed in the

center of the layout - Break ties using the following rules
- Department having the largest area
- Department with the lowest department number

CORELAP continued

- Next, scan the relationship chart
- If a department is found with a relationship of

A with the selected department - It is brought into the layout
- Else
- The relationship chart is scanned for E

relationship, then I and so on - If two or more departments are found having same

relationship with the selected department - Ties are broken using
- TCR
- Area of the department
- Department number

CORELAP continued

- Selecting third department to enter the layout
- Unassigned department with A relationship with

the first selected department - If tie exists, same tie breaking rule
- If no unassigned department with A relationship

with second department - The procedure is repeated for E then I and so

on - Same procedure for all the other departments to

enter the layout

CORELAP continued

- Once a department is chosen to enter the layout,

a placement decision is made - Placing rating sum of weighted closeness

ratings between the department to enter the

layout and its neighbors

CORELAP continued

Relationships 2 and 1 is A (64) 2 and 7 is E (16)

Break placing rating ties by looking at boundary

lengths of the tied locations number of unit

square sides that the department to enter the

layout has in common with its neighbors

CORELAP continued

- Layout score sum for all departments

numerical closeness rating x length of the

shortest path - Rectilinear path between departments (not

centroids of dept.) - Irregular shaped departments
- Rectilinear path distance may not be a realistic

measure

CORELAP Example

CORELAP Example continued

A 6 E 5 I 4 O 3 U 2 X 1

CORELAP Example continued

CORELAP Example continued

CORELAP Example continued

ALDEP

- Automated Layout Design Program
- Input relationship chart
- Basic idea similar to CORELAP
- Difference
- CORELAP first department to enter using TCR
- aims to produce one best layout
- ALDEP first department is chosen randomly
- many layouts, rates each layout, and leaves

the - evaluation of the layouts to layout designer

ALDEP

- Choose the first department randomly
- Scan the relationship chart for departments with

A relationship with the first selected

department - If one exists, it is selected to enter the layout
- If more than one exists, one is randomly selected

to enter the layout - If no departments have a relationship at least

equal to the minimum acceptable closeness rating

specified by the user, the second department is

selected randomly - Repeat the process until all the departments are

selected

ALDEP

- Placement routine with in ALDEP
- Places the first department in the upper left

corner of the layout and extends it downward - Width of the downward extension is specified by

sweep width - Each additional department added begins where the

previous department ends and continue to follow

the serpentine path - A 64 E 16 I 4 O 1 U 0 X -1024

ALDEP

- The scores added only for adjacent departments
- Several iterations of the procedure is repeated

ALDEP

ALDEP Example

ALDEP Example

Suppose the minimum acceptable level of

importance is E and dept 4 is selected first to

enter the layout 4-2-1-6 (randomly chosen)-5-7

(randomly chosen) -3

ALDEP Example

ALDEP Example

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