Chapter 6: Layout Planning Models and Design Algorithms

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Chapter 6 Layout Planning Models and Design
Algorithms

• Dr. Chen
• chenc_at_fiu.edu

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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

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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

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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

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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

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Basic Layout Types
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Basic Layout Types continued
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Basic Layout Types continued
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Basic Layout Types continued
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Layout Procedures

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

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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

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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

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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

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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

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Layout Planning Chart
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Muthers Systematic Layout Planning Procedure
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Activity Relationship Chart
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Relationship Diagram
RD positions activities spatially Proximities
are typically used to reflect the relationship
between pairs of activities
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Space Requirement
Read section 3.7 from the textbook
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Space Relationship Diagram
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Alternative Block Layouts
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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

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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

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Algorithmic Classification continued

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

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Flow Distance Objective
Note cij independent of the material handling
equipment used
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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
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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

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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
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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

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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

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Split Departments
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Different Layout Methods

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

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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

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Pairwise Exchange Method continued
Assume all the departments are of equal size, for
simplicity
TC1234 10x1 15x2 20x3 10x1 5x2 5x1
125
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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

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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
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Pairwise Exchange Method continued
Iteration 0
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Pairwise Exchange Method continued
Iteration 1
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Pairwise Exchange Method continued
Iteration 2
STOP
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Graph-Based Layout Planning

• Construction type algorithm
• Adjacency based objective

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Graph-Based Layout Planning continued
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Graph-Based Layout Planning continued
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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

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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

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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
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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
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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.
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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.

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Graph-Based Layout Planning continued

• Step 5 using the adjacency graph, draw the block
  layout.

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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

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CRAFT continued

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

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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
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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
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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
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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
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CRAFT Example continued
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CRAFT continued
Exchanging departments 2 and 4 will lead to
splitting department 2 not acceptable
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CRAFT continued

• Three-way exchange
• The departments should be adjacent or of equal
  area
• Complicated to implement

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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

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MCRAFT
Length 360 ft, Width 200 ft, number of bands
3 Initial layout vector 1-7-5-3-2-4-8-6
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MCRAFT
6 rows / band
Initial layout vector 1-7-5-3-2-4-8-6
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MCRAFT
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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

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MIP

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

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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

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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
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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
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LOGIC Example
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LOGIC Example
East or right side of a vertical cut
South or bottom of a horizontal cut
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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

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LOGIC Example
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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

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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

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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

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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

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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
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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

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

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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

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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

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ALDEP

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

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ALDEP
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ALDEP Example
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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
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ALDEP Example
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ALDEP Example