Facility Layout 2

Basic Data and Layout Evaluation

The objective is to design a block layout.

4b

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Block Layout

Show the general placement, dimensions and relative position of departments

Next, how do we evaluate the block layout.

• Flow Patterns – qualitatively

• Qualitatively generated reward matrix– REL chart– Maximize A-based measure

• Quantitatively generated reward matrix– Flow x Distance x Cost– Minimize this D-based objective

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100 100100

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Flow patterns – qualitative measure

An example

ABC Widgets Inc. is trying to create a layout for a new facility. The lot of terrain available is a square, 300 ft. by 300 ft.

The company is organized in four departments, with the following dimensions:

Dept 1: 100’ x 300’Dept 2: 100’ x 200’Dept 3: 100’ x 200’Dept 4: 100’ x 200’

First, try to build a couple of feasible layouts in the next page

300 x 300300 x 300 300 x 300300 x 300 300 x 300300 x 300

Let’s play with layouts

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2

4

3

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4

1

2

Now, let’s explore the relationships between the departments

It is absolutely necessary that depts. 1 and 2 are close, and it is especially important that 1 and 4 are close.

It is also important that 3 and 4 are somehow close and it’s OK if departments 2 and 4 are close to each other.

Other than that, all other relationships are unimportant.

REL 1 2 3 4

1 - A U E

2 - - U O

3 - - - I

4 - - - -

Rating Definition

A Absolutely Necessary

E Especially Important

I Important

O Ordinary Closeness OK

U Unimportant

X Undesirable

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Layout 1 Layout 2

100 100 100 200100

200

100 100

100

100

REL 1 2 3 4

1 - A U E

2 - - U O

3 - - - I

4 - - - -

In this example, we will calculate an Adjacency Based and a Distance Based Score for two layouts

Step 1: Convert REL data to a Reward Matrix

REL 1 2 3 4

1 - A U E

2 - - U O

3 - - - I

4 - - - -

A = 8 E = 4 I = 2 O = 1 U = 0(X = -8)

REL 1 2 3 4

1 - 8 0 4

2 - - 0 1

3 - - - 2

4 - - - -

Scores are usually powers of a base number

fij

Step 2: Find the Adjacency-Based score

m

i

m

jijij xfZSBA

1 1

...

xij = 1 if the departments are adjacent = 0 if the departments are not adjacent

• Adjacency means that they share a border, not corners• Layouts with same adjacency score may have different travel

distances

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Layout 1

100 100100

200

100

1

2

4

3

Layout 2

100 200

100

100

100

Here is the data we need

REL 1 2 3 4

1 - 8 0 4

2 - - 0 1

3 - - - 2

4 - - - -

fij

ABS1 = 11

ABS2 = 15

151 1

m

i

m

jijf

Step 3: Find the Relative Efficiency for both layouts

m

i

m

jij

m

i

m

jijij

f

xf

z

1 1

1 1

ABS1Rel. Efficiency1 = = 73%

m

i

m

jijf

1 1

ABS2Rel. Efficiency2 = = 100%

m

i

m

jijf

1 1

Back to the company

Now we will obtain some data related to the production processes that take place on ABC Widgets

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200 units a day

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Size of the unit load

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200

Flow 1 2 3 4

1 - 8 0 4

2 - - 0 1

3 - - - 2

4 - - - -

fij

Step 1: Find the flow data

In this example, we will use the number of daily trips between departments

m

i

m

jijijij dcfZDBS

1 1

f flow between dept i and j

c cost of moving the load (independent of MHE)

d distance from dept i to j (Centroid-to-Centroid and Rectilinear)

Flow 1 2 3 4

1 - 8 0 4

2 - - 0 1

3 - - - 2

4 - - - -

fij

How do we calculate Rectilinear Distances?

Rectilinear Distance means that we move horizontally and vertically, not diagonally

Does this make sense? When or where?

y1

y2

x1 x2

dx

dy

Rect. Dist. = dx + dy

Rect. Dist. = |x1-x2| + |y1-y2|

Step 2: Let’s find the the distances between departments

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100 100100

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100

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100 200

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1 2 3 4

x 50 200 150 250

y 150 250 100 100

1 2 3 4

x 50 200 200 200

y 150 250 50 150

CentroidsRectilinear Distances

d 1 2 3 4

1 - 250 150 250

2 - - 200 200

3 - - - 100

4 - - - -

d 1 2 3 4

1 - 250 250 150

2 - - 200 100

3 - - - 100

4 - - - -

Step 3: Find the Distance Based score

d 1 2 3 4

1 - 250 150 250

2 - - 200 200

3 - - - 100

4 - - - -

d 1 2 3 4

1 - 250 250 150

2 - - 200 100

3 - - - 100

4 - - - -

Flow 1 2 3 4

1 - 8 0 4

2 - - 0 1

3 - - - 2

4 - - - -

fij

DBS1 = 3400

DBS2 = 2900

Next few classes will we discuss FLP algorithms.

• Methods to generate layouts from scratch or just generating improvements to layouts.

• Once we have a layout, we use our D-based and A-based measures to compare the layouts and select the best alternative.

4b

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