Movement 2
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Transcript of Movement 2
8/24/04
Paul A. JensenOperations Research Models and Methods
Copyright 2004 - All rights reserved
Material Movement
The movement of material through the production facility is a waste because
material movement does not add value to the product.
2
The amount of movement depends on: the set of products manufactured, the sequence of operations (process) identified for
each product, the assignment of machines to the operations of the
processes, and the layout of the machines in the manufacturing
facility.
Here we assume that the first two are fixed and we concentrate on the latter two.
3
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
M7M1
M5
M6M2
M7
M2
M3
M4
M6
Group technology
4
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 0.2
3 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
5
Machine information Each operation requires a unique machine. All machines operate 40 hours per week. Assume operation times have an exponential
probability distribution. Provide enough machines so that all
workstations are to have no more than 80% utilization.
6
Space and Economic Information
WIP requires 0.4 sq. m. floor space per unit. Provide sufficient space at each station to
accommodate 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 $20 per week per square
meter.
Operation 1 2 3 4 5 6 7 8 9 10
Machine Size (sq.m.) 2 3 4 5 4 3 2 3 4 1
Machine cost ($/week) 50 30 40 30 100 80 60 20 70 40
Value Added ($) 10 1 2 1 3 1 2 2 1 1
7
Design a plant that uses a job shop (or functional) layout
M1M2
M3
M5
M4
M7
M6
Offices
8
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
9
Queuing Analysis
Machine 1 2 3 4 5 6 7 8 9 10
Arrival Rate 1740 850 520 440 540 1270 760 200 1120 1740
Service 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
10
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
11
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.
12
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
5
6
7
8
9
10
13
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
7
8
9
10
11
12
14
Step 5: Economic Analysis Plant cost: Machine cost: Transportation Cost Cost of WIP Total Cost:
How will these costs change with larger lot sizes?
15
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 the
functional layout?
M1
M2
M3
M5
M4
M7
M6
Offices
16
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
17
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
18
Economic analysis Plant cost: Machine cost: Cost of WIP at machines: Cost of WIP in material movement: Total Cost:
19
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 of
layout?
20
Queuing and space analyses for each product
Product 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 10
Arrival Rate
Service Rate
Number of Mach.
Spaces for WIP
Total Space
21
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 of a functional layout?
22
Design a plant that uses group technology Let moulding and final inspection be separate departments
Offices
M3
M2
M1
M4
M7M1
M5
M6M2
M7
M2
M3
M4
M6
23
Grouped operations and families of products
PRODUCTS GROUP
Operation A B C D E F G H I J K L 1 2 3
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 x x x
2 De-fraze 0.3 0.5 0.2 0.1 0.2 x
3 Barrel Polish 0.3 0.6 0.2 0.2 x
4 Test 0.4 0.1 0.3 x
5 Machine 0.4 0.2 0.2 0.3 0.4 x x
6 Paint 0.2 0.2 0.2 0.2 0.2 0.2 0.6 x x x
7 Sub-assemble 0.1 0.3 0.2 0.3 0.1 0.1 x x
8 Chemical Test 0.2 x
9 Dimensional insp. 0.1 0.3 0.1 0.2 0.5 0.4 0.2 0.2 x x
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 x x x
Weekly Demand 100 200 50 300 80 40 120 200 250 100 120 180
Family 1 x x x x
Family 2 x x x x
Family 3 x x x x
24
Queuing and space analysis for each family
Family 1
Machine 1-2 1-6 1-8 1-9
Arrival Rate
Service Rate
Number of Mach.
Spaces for WIP
Total Space
Family 2
Machine 2-5 2-6 2-7
Arrival Rate
Service Rate
Number 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
25
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
3-3
3-4
3-5
3-6
3-7
3-9
10
26
Economic Analysis Plant cost: Cost of WIP at machines: Cost of WIP in material movement: Total Cost: