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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

Efficiencies Transportation Systems

Flow, Activity & Space Data: Group Technology From – To Chart Relationship Chart Dept Footprint & Aisle

Space Personnel Space

Parking LotRestroom/Locker roomFood Prep/CafeteriaADA Compliance

Order Data Profile 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 chartAbove diagonal is forward flowBelow 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 graphicallyNumber 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 symbolsScale circles to equate with the estimated

size of the departmentsUse 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 th to the j th dept

dij is the travel DISTANCE from the i th to the j th department

aij is the ADJACENCY of the i th and j th department pair, which is defined to be:

1 if the i th and j th departments share a common edge (border) – or 0 if the departments have no common edge or only touch at a point

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Layout Models – Mathematical Objective Functions

Minimize the transportation cost:

Maximize the flow-weighted adjacency of departments:

Evaluate flow weighted layout efficiency (relative measure):

n

1i

n

1jijijij dcfzmin

n

1i

n

1jijijafymax

n

1i

n

1jij

n

1i

n

1jijij

f

af

x

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Example – Mathematical Objective Function

Assume the From/To matrix (below)

… and the department layout(s) (below):

then the Flow-Weighted Adjacency score(s) would be:

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

From\To A B C D E F A

I 200

I 250

B

E 300

A 500

X -20

C

E 350

U 10

D

I 175

E

O 100

F

A A B B B BA A B B B B E EA A F F D D E EC C F F D D E EC C C C E E E E

A A B B B B B BA A B B E EA A F F D D E EC C F F D D E EC C C C E E E E

A A B B B B B BA A B B C C E EA A D D C C E E

D D C C E EF F F F E E E E

n

1i

n

1jijijafymax

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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.