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8/24/04

Paul A. Jensen

Operations Research Models and MethodsCopyright 2004 - All rights reserved

Material Movement

The movement of material through theproduction facility is a waste because

material movement does not add valueto the product.

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The amount of movement

depends on: the set of products manufactured,

the sequence of operations (process) identified foreach product,

the assignment of machines to the operations of theprocesses,

and the layout of the machines in the manufacturingfacility.

Here we assume that the first two are fixedand we concentrate on the latter two.

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The several generic types of

layout

M1 M2

M3

M5

M4

M7

M6

Offices

The Job shop

M1

M2

M3

M5

M4

M7

M6

Offices

The assembly line or

flow shop

Offices

M3

M2

M1

M4

M7

M1

M5

M6M2

M7

M2

M3

M4

M6

Group technology

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Example Orders for products arrive as Poisson processes.

Processing begins when an order arrives.

Operations are performed in a numerical sequence. There are no losses in the operations.

Operation Times (hours/unit)

PRODUCTS

Operation A B C D E F G H I J K L

1 Mould 0.1 0.1 0.2 0.2 0.3 0.1 0.4 0.6 0.7 0.4 0.1 0.1

2 De-fraze 0.3 0.5 0.2 0.1 0.23 Barrel Polish 0.3 0.6 0.2 0.2

4 Test 0.4 0.1 0.3

5 Machine 0.4 0.2 0.2 0.3 0.4

6 Paint 0.2 0.2 0.2 0.2 0.2 0.2 0.6

7 Sub-assemble 0.1 0.3 0.2 0.3 0.1 0.1

8 Chemical Test 0.2

9 Dimensional insp. 0.1 0.3 0.1 0.2 0.5 0.4 0.2 0.2

10 Final insp. 0.4 0.4 0.2 0.3 0.3 0.2 0.2 0.4 0.1 0.2 0.3 0.3

Weekly Demand 100 200 50 300 80 40 120 200 250 100 120 180

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Machine information Each operation requires a unique machine.

All machines operate 40 hours per week.

Assume operation times have an exponentialprobability distribution.

Provide enough machines so that all

workstations are to have no more than 80%utilization.

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Space and Economic

Information

WIP requires 0.4 sq. m. floor space per unit.

Provide sufficient space at each station toaccommodate WIP 90% of the time.

Transportation cost is $0.10/unit-meter Use a plant with length twice as great as width.

The cost of the plant is $20 per week per squaremeter.

Operation 1 2 3 4 5 6 7 8 9 10

Machine Size (sq.m.) 2 3 4 5 4 3 2 3 4 1

Machine cost ($/w eek) 50 30 40 30 100 80 60 20 70 40

Value Added ($) 10 1 2 1 3 1 2 2 1 1

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Design a plant that uses a job

shop (or functional) layout

M1 M2

M3

M5

M4

M7

M6

Offices

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Step 1: Queuing Analysis Do a Queuing Analysis for each

machine type

Machine 1 2 3 4 5 6 7 8 9 10

Arrival Rate

Service Rate

Number of Mach.Spaces for WIP

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Queuing Analysis

Machine 1 2 3 4 5 6 7 8 9 10

Arrival Rate 1740 850 520 440 540 1270 760 200 1120 1740Service Rate 129 158 125 114 129 156 197 200 187 142

Number of Mach. 17 7 6 5 6 11 5 2 8 16

Spaces for WIP 4 5 3 6 3 3 6 1 4 3

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Step 2: Space Analysis Find the space requirements of each

machine type.

Find the space required for WIP.

Machine 1 2 3 4 5 6 7 8 9 10

Number

Space

Space for WIP

Total Space

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Space analysis

Machine 1 2 3 4 5 6 7 8 9 10

Number 17 7 6 5 6 11 5 2 8 16

Space for Mach. 34 21 24 25 24 33 10 6 32 16

Space for WIP 2 2 2 3 2 2 3 1 2 2

Total Space 36 23 26 28 26 35 13 7 34 18

Space for Plant 246 Sq. M.

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Step 3: Flow Analysis Construct the from-to chart for weekly

flowsMachine 1 2 3 4 5 6 7 8 9 10

1

2

3

4

56

7

8

9

10

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Step 4: Construct a Layout Use a plant dimension of 12x24 with

area 288 sq. m.1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

1

2

3

4

5

6

78

9

10

11

12

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Step 5: Economic Analysis Plant cost:

Machine cost:

Transportation Cost Cost of WIP

Total Cost:

How will these costs change with larger

lot sizes?

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Design a plant that uses a

flow shop layout We assume that each product visits each station but

receives no processing at some stations.

What do you think changes with respect to thefunctional layout?

M1

M2

M3

M5

M4

M7

M6

Offices

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Queuing and space analyses

Machine 1 2 3 4 5 6 7 8 9 10

Arrival Rate

Service Rate

Number of Mach.

Spaces for WIP

Machine 1 2 3 4 5 6 7 8 9 10

Number

Space

Space for WIP

Total Space

Queuing analysis

Space analysis

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Flow Analysis Construct the from-to chart for weekly

flowsMachine 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

8

9

10

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Economic analysis Plant cost:

Machine cost:

Cost of WIP at machines:

Cost of WIP in material movement:

Total Cost:

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Design a plant that uses a

separate line for each product Let moulding and final inspection be

separate departments

What will be different in this type oflayout?

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Queuing and space analyses

for each productProduct A

Machine 1 2 3 4 5 6 7 8 9 10

Arrival Rate

Service Rate

Number of Mach.

Spaces for WIP

Total Space

Product B

Machine 1 2 3 4 5 6 7 8 9 10Arrival Rate

Service Rate

Number of Mach.

Spaces for WIP

Total Space

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Economic Analysis Plant cost:

Cost of WIP at machines:

Cost of WIP in material movement:

Total Cost:

How does this cost relate to the cost ofa functional layout?

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Design a plant that uses group

technology Let moulding and final inspection be separate departments

Offices

M3M2

M1

M4

M7M1

M5

M6M2

M7

M2

M3

M4

M6

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Queuing

and spaceanalysis foreach family

Family 1

Machine 1-2 1-6 1-8 1-9

Arrival Rate

Service Rate

Number of Mach.

Spaces for WIPTotal Space

Family 2

Machine 2-5 2-6 2-7

Arrival Rate

Service RateNumber of Mach.

Spaces for WIP

Total Space

Family 3

Machine 3-3 3-4 3-5 3-6 3-7 3-9

Arrival Rate

Service Rate

Number of Mach.

Spaces for WIP

Total Space

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Flow AnalysisMachine 1 1-2 1-6 1-8 1-9 2-5 2-6 2-7 3-3 3-4 3-5 3-6 3-7 3-9 10

1

1-2

1-6

1-8

1-9

2-5

2-6

2-7

3-33-4

3-5

3-6

3-7

3-9

10

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Economic Analysis Plant cost:

Cost of WIP at machines:

Cost of WIP in material movement:

Total Cost: