IENG 471 - Lecture 15
Layout Planning –
Systematic Layout Planning & Intro to
Mathematical Layout Improvement
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Warehousing Terms - Review
 SKU – Stock Keeping Unit
 Product in (packaged) form for warehouse operations.
 Value-Added
 A modification to the product to obtain business
(a product enhancement from the customer’s perspective or an
enhancement to the customer’s experience in getting the item).
 Cross-Docking
 Transforming incoming product to outgoing product without
moving the product to production or storage.
 Slotting
 Selecting the location of SKUs in the storage zones. Goal is to
optimize (reduce) pick times across all SKUs within a zone.
 Forward Pick Area
 An area housing fast-moving/frequently-picked items between
the shipping and storage areas for quick order fulfillment.
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Layout Alternatives - Strategies
 Fixed Position Layout
 (Difficult-to-move Products)
 Process Layout
 (Job Shop)
 Product Layout
 (Mass Production Line)
 Group Technology Layout
 (Product Family)
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Layout Alternatives: Fixed Pos.
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Layout Alternatives: Process
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Layout Alternatives: Product
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Layout Alternatives: GT / Family
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How to get from data to design?
 Product, Process &
Schedule Data:
 BOM
 Routing/Assembly Chrt
 Operations Process
Chart
 Precedence Diagram
 Scrap/Reject Rates
 Equipment Fractions
 Material Handling
 Unit Loads
 Storage Systems
Space Data:




Group Technology
From – To Chart
Relationship Chart
Dept Footprint & Aisle
Space
 Personnel Space
 Parking Lot
 Restroom/Locker room
 Food Prep/Cafeteria
 ADA Compliance
 Order Data Profile
 Efficiencies
 Transportation Systems
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 Flow, Activity &
 Multiple Analysis Profiles
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Muther: Systematic Layout Plan
 SLP
 Benefit is methodical
consideration of issues
 Can work the process
manually or with computer
aides
 “Roadmap” for the process is
good for communication
 Adds the following stages:
 Analysis
 Search
 Evaluation
 Engineering Design Process!
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Relationship Chart - Qualitative
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Converting Closeness to Affinity
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From – To Chart Example
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From – To Chart to Flow
 Review: flow volume in chart
 Above diagonal is forward flow
 Below diagonal is back-track flow
 Combine both flows to represent
volume of interactions, then Pareto!
 Qualitative Flow
 Quantitative Flow
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Converting Quantitative Flow to Affinity
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Converting Both to Final Affinity
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Review: Conversion Steps
 Convert Flows to Affinities
 Qualitative converts directly to A E I O U X
 Quantitative converts to A E I O U X via Pareto analysis of flow
volume
 Combine Flow Affinities Numerically
 A = 4, E = 3, I = 2, O = 1, U = 0, X = negative value
 Quantitative flow may be multiplied by a weighting factor
 Sum Quantitative & Qualitative
 Convert to Final Affinities
 Pareto analysis of numeric affinities to get A E I O U X
 Add: Check Final Affinities for Political Correctness
 Communication feedback to involved parties
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Converting Flow to Affinity
 Strength of
relationship is
shown graphically
 Number of lines
similar to rubber
bands holding depts
together
 Spring symbol to
push X relations
apart
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Converting Flow to Affinity
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Converting Flow to Affinity
Lay the
Affinity
Diagram
over a site
plan to get
better idea
of layout
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Improvement: Size of Departments
 Some experts suggest modification:
 Use circles instead of flow symbols
 Scale circles to equate with the estimated
size of the departments
 Use rectangular, sized blocks instead of
circles – improves input to computer layout
methods
 Computer packages are still being
developed …
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Layout Models –
Mathematical Objective Functions
 Mathematical models can be constructed to measure a design,
and help to quantify when it has been improved
 Like many mathematical
models of physical systems, part of the “art” is
knowing what assumptions are made in a model, and when these
assumptions are “reasonably met”
 The “best” models are not always the most complex – in fact many
“comprehensive” mathematical models become intractable or take too
long for computation when scaled up to a “realistically–sized” problem
 Frequently, meeting the data collection (and verification) requirements
for many mathematical problems is very difficult
 However, as the cost of automated data collection and storage drops,
and has computational power increases (hardware speeds and parallel
programming techniques improve), both mathematical models and
simulations become more attractive – more tools for the toolbox!
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Layout Models –
Mathematical Objective Functions
 Assume we have these variables defined for n departments:
 i is an index to the “FROM” department in a pair of departments
 j is an index to the “TO” department in a related pair
 Thus i and j could be the row/column indices for a From/To Chart
 fij is the unit load FLOW from the i
th
to the j th department
 Thus fij is the cell entry in the From/To Chart (matrix)
 cij is the COST to transport a unit load from the i
 dij is the travel DISTANCE from the i
 aij is the ADJACENCY of the i
th
th
th
to the j th dept
to the j th department
and j th department pair, which is
defined to be:
and j th departments share a common edge (border) – or
 0 if the departments have no common edge or only touch at a point
 1 if the i
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Layout Models –
Mathematical Objective Functions
 Minimize the transportation cost:
n
n
z   fij c ij dij
min
i1 j1
 Maximize the flow-weighted adjacency of departments:
n
n
y   fij aij
max
i1 j1
 Evaluate flow weighted layout efficiency (relative measure):
n
x
n
 f a
i1 j1
n
n
ij
 f
i 1 j1
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Example –
Mathematical Objective Function
 Assume the From/To matrix (below)
From\To
A
A
B
I
200
C
B
C
D
E
E
300
E
350
A
500
F
I
250
X
-20
U
10
I
175
O
100
D
E
F
 … and the department layout(s) (below):
A
A
A
C
C
A
A
A
C
C
B
B
F
F
C
B
B
F
F
C
B
B
D
D
E
B
B
D
D
E
E
E
E
E
E
E
E
E
A
A
A
C
C
A
A
A
C
C
B B B
B
F F D
F F D
C C E
B
B
D
D
E
B
E
E
E
E
B
E
E
E
E
A A B B
A A B B
A A D D
D D
F F F F
B
C
C
C
E
B
C
C
C
E
B
E
E
E
E
B
E
E
E
E
 then the Flow-Weighted Adjacency score(s) would be:
n
max
n
y   fij aij
i1 j1
200(1)+250(1)+300(1)+500(1)–20(1)+350(0)+10(1)+175(1)+100(0) = 1415
200(1)+250(1)+300(1)+500(1)–20(0)+350(0)+10(1)+175(1)+100(0) = 1435
200(1)+250(0)+300(1)+500(1)–20(0)+350(1)+10(0)+175(1)+100(1) = 1625
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Criticisms and Resources
 Frequently, improvements in the simpler mathematical objective
functions result in long, “snake-y” department shapes
 Not always physically possible
 Adjusting the objective function to penalize snake-y results in
more complex objective functions
 Data representations become more complex, too – and can
increase computation time disproportionately
 The simple, transportation cost function assumes we move
from/to the center “point” of the departments
 Isn’t really accurate for real departments (especially large sized)
 Becomes even less true when the departments get more snake-y
 Text Chapter 10 presents more mathematical models–try some!
 MIL Lab computers have some software available
 The software tends to be research prototypes, but can be fun to try!
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Questions & Issues
 Class time is for project (after Exam II)
 Review & HW solutions TODAY.
 Exam II scheduled for 07 NOV.
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