Facility Layout Two levels of layout problems: Machine : determine - - PowerPoint PPT Presentation

SLIDE 1

Facility Layout

• Two levels of layout problems:

– Machine: determine assignment of machines to (fixed) sites – Departmental: determine space requirements of each department (or room) and its shape and relation of other departments

102

SLIDE 2

Machine 1 Machine 2 Machine 3 Machine 4

Machine Layout

• A routing is the sequence of W/S (or M/C) that work visits

during its production

– Dedicated M/C ⇒ single routing ⇒ single flow of material ⇒ layout

• nly involves choice of straight-line or U-shaped layout

– Shared M/C ⇒ multiple routings ⇒ multiple flows of material ⇒ layout involves complex problem of finding assignment of M/C to Sites corresponding to the dominate flow

103

1 1 2 2 2 3 3 4 4

B C

4 1 2 3 4

A

1 2 3 4

A

SLIDE 3

Example: Kitchen Layout

104

SLIDE 4

Example: Kitchen Layout

105

SLIDE 5

From/To Chart

From\To

1 2 3 4 1 — 1+2+3 2 — 1+2 2+3 3 — 1+3 4 2+3 —

106

Machine 1 Machine 2 Machine 3 Machine 4

1 1 2 2 2 3 3 4 4

B C

4 1 2 3 4

A 1 trip/hr 2 trip/hr 3 trip/hr

From\To

1 2 3 4 1 — 6 2 — 3 5 3 — 4 4 5 —

SLIDE 6

Total Cost of Material Flow

107

1

( ) where moves between machines and for item equivalance factor for moves bet mach ween machines and for ite ine-to-machin m e

P ij ijk ijk k ijk ijk

w f h f i j k h i j k

=

= = =

∑

Equivalent Flow Volume : Total Cost of Materi

1 1

where machine assigned to site distance between sites and ( ) number of site si s and machines te-to-site

i j

M M MF a a ij i j i ij

TC w d a i d i j M

= =

= = = =

∑∑

al Flow :

SLIDE 7

Equivalent Factors

• Problem: Cost of move of item k from site i to j (hijk) usually

depends on layout

– equivalent factor used to represent likely “cost” differences due to, e.g., item volume

108

A B C A A B B B C C C C C C

6 3 5 All 1 4 5 1 2 3 1 2 2 3 1 3 2 3 3 2 1 10

ijk ij ijA ijB ijC ijA ijB ijC ij

h w f f f h h h w     = ⇒ =                         = = =                                     = = =             =     7 7 6 7            

Machine 1 Machine 2 Machine 3 Machine 4

1 1 2 2 2 3 3 4 4

B C

4 1 2 3 4

A 1 trip/hr 2 trip/hr 3 trip/hr

SLIDE 8

SDPI Heuristic

109

a

1

=[ 1234 ]: 3830 a

2

=[ 1243 ]: 3680 a

3

=[ 1342 ]: 5660 a

4

=[ 1324 ]: 5330 a

5

=[ 1423 ]: 4330 a

6

=[ 1432 ]: 4810 5490 :[ 2431 ]= a

7

5520 :[ 2413 ]= a

8

4820 :[ 2314 ]= a

9

4640 :[ 2341 ]= a

10

4020 :[ 2143 ]= a

11

4170 :[ 2134 ]= a

12

5350 :[ 3124 ]= a

13

5680 :[ 3142 ]= a

14

4320 :[ 3241 ]= a

15

4500 :[ 3214 ]= a

16

4180 :[ 3412 ]= a

17

3670 :[ 3421 ]= a

18

a

19

=[ 4321 ]: 3770 a

20

=[ 4312 ]: 4280 a

21

=[ 4213 ]: 5300 a

22

=[ 4231 ]: 5270 a

23

=[ 4132 ]: 4930 a

24

=[ 4123 ]: 4450

14 3 23 11 17 15 13 11 2 24 14 8 10 12 2 11 21 15

4020 36 1 2 3 4 3 1 4 2 5680 1 3 4 2 5660 4 1 3 2 4930 2 1 4 3 3 4 1 2 4180 3 2 4 1 4320 3 1 2 4 5350 2 1 4 3 4020 1 2 4 3 4 1 2 3 4450 3 1 4 2 5680 2 4 1 3 5520 2 3 4 1 4640 2 1 3 4 4170 1 2 4 3 3680 2 1 4 3 4020 4 2 1 3 5300 3 2 4 1 4320 80 TC a a a a a a a a a a a a a a a a a a

5 3 1

1 4 2 3 4330 1 3 2 2 5660 1 2 3 4 3830 a a a

Interchange

1 2 3 4 1,2 2 1 3 4 1,3 3 2 1 4 1,4 4 2 3 1 2,3 1 3 2 4 2,4 1 4 3 2 3,4 1 2 4 3

SLIDE 9

SDPI Heuristic

110

SLIDE 10

Layout Distances: Metric

111

(a) Open space.

2 4 1 3 5

(33,80) (45,76) (56,80) (52,90) (35,90) (x,y)

(b) Rectangular grid.

3 4 1 2 5

50 90 40 y x

SLIDE 11

Layout Distances: Network

112

(c) Circulating conveyor.

1 2 3 4 5 12 17 9 18 16

(d) General network.

1 5 4 3 2

40 55 54 52 25 30

SLIDE 12

Dijkstra Shortest Path Procedure

2 4 6 3 8 2 3 1 4 5 5 10 2 6 1

s t

∞ ∞ ∞ ∞ ∞ ∞

0,1 4,1 2,1 12,3 10,3 3,3 8,2 14,4 10,4 13,5

Path: 1 3 2 4 5 6: 13 ← ← ← ← ←

113

SLIDE 13

General Network Distances

114

118'-1 9/16" 7 5 '

• "

118'-11/16" 75'-0" 6'-7 11/16" 6'-7 11/16"

DAN 407

= Site Locations 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 = Intersection Nodes

15 14 7 10 9 9 7 9 5 9 9 7 15 20 7 6 9 15 18 13 15 6 13 13

SLIDE 14

General Network Distances

• Only need 10 × 10 distances between site locations, can throw

away distances between intersection nodes

115

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 13 26 33 29 27 31 40 43 55 7 13 22 31 40 15 24 39 2 13 13 46 28 26 35 44 54 44 6 12 21 30 39 28 37 26 3 26 13 53 26 29 38 47 57 31 19 15 24 33 42 35 44 13 4 33 46 53 37 25 16 7 10 40 40 38 30 21 25 18 9 50 5 29 28 26 37 12 21 30 40 31 22 16 7 16 25 36 28 13 6 27 26 29 25 12 9 28 35 38 20 14 5 14 23 25 16 25 7 31 35 38 16 21 9 23 26 47 29 23 14 23 32 16 7 34 8 40 44 47 7 30 28 23 17 38 38 32 23 14 23 25 16 43 9 43 54 57 10 40 35 26 17 30 48 42 33 24 15 28 19 48 10 55 44 31 40 31 38 47 38 30 48 42 33 24 15 58 49 18 11 7 6 19 40 22 20 29 38 48 48 6 15 24 33 22 31 32 12 13 12 15 38 16 14 23 32 42 42 6 9 18 27 20 29 28 13 22 21 24 30 7 5 14 23 33 33 15 9 9 18 29 21 20 14 31 30 33 21 16 14 23 14 24 24 24 18 9 9 38 30 29 15 40 39 42 25 25 23 32 23 15 15 33 27 18 9 43 34 33 16 15 28 35 18 36 25 16 25 28 58 22 20 29 38 43 9 48 17 24 37 44 9 28 16 7 16 19 49 31 29 21 30 34 9 41 18 39 26 13 50 13 25 34 43 48 18 32 28 20 29 33 48 41