Part 1 – Fundamental Concepts
Chapter 1
INTRODUCTION TO MANUFACTURING SYSTEM
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Contents:
1.1 Manufacturing industries.
1.2 Types of production.
1.3 Function in manufacturing.
1.4 Organization and information processing
1.5 Automation strategies
1.6 Advanced manufacturing charactreistics
1.7
Production concepts and mathematical models
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1.1 Manufacturing industries
Basis industries in general: Manufacturing or Service?
Advertising
Aerospace
Auto-motive (cars, trucks, buses)
Beverages
Building materials
Cement
Chemicals
Clothing
Drugs, soaps, cosmetics
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1.1 Manufacturing industries
Basis industries in general: Manufacturing or Service?
Equipment/machinery
Financial (Banks, investment companies, loans)
Foods
Health care service
Hotels / restaurants
Insurance
Transportation (railroad, Airline, trucking,...)
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59
1.1 Manufacturing industries
Manufacturing industry vs Process industry
Industries Representative companies
Aerospace
Car
Beverage
Building materials
Cement
Chemicals
Soaps, cosmetic,...
Clothing
Boeing,…
General Motors, Toyota, Mitsubishi…
Coca-Cola, Pepsi-cola, Tribeco,…
US. Gypsum, Southern steel,…
Sao mai, Hà tiên,..
EI. Du pont, Nippon,
Hanes-Corp., V. Thắng, Thắng lợi,…
Proctor&Gambles, Unilever, Kao,…
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1.1 Manufacturing industries
Classification: Manufacturing industries:
Produce discrete items: cars, mobile, TV, clothes,...
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1.1 Manufacturing industries
Classification: Manufacturing industries:
Produce discrete items: cars, mobile, TV, clothes,...
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1.1 Manufacturing industries
Classification: Process industries:
Produce continuous items: liquid, pure water,
beverage, beer, milk
Petro processing Paint processing
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59
1.1 Manufacturing industries
Classification: Process industries:
Produce continuous items: liquid, pure water,
beverages, beer, milk
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1.1 Manufacturing industries
Three classifications in manufacturing industries:
a. Basic producer: transforms natural resources into raw
materials (for others industrial firms)
b.
Converter: intermediate link in the chain (semi-
products or components).
c. Fabricator: final products assembly to market.
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59
1.1 Manufacturing industries
Garment Co.: fabricator
Input: clothing, button,
thread,...
Output: shirts, clothes
Textile Co.: converter
Input: thread,...
Output: clothing,
Yarn Co.: basis producer
Input: silk-worm,...
Output: thread,...
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1.1 Manufacturing industries
Honda Co.: fabricator
Input: moto-bike
components,...
Output: Airblade, Wave,
Vision, Future,...
Plastic Co.: converter
Input: raw materials,...
Output: plastic components,
Tires M. Co.: converter
Input: rubber,...
Output: inner tubes & tires,...
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1.2 Types of production
1. Jobbing / Project Production: very small volume
2.
Batch Production: small volume
3.
Mass Production: large volume
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59
1.2 Types of production
1. Jobbing / Project Production: very small volume
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1.2 Types of production
1. Jobbing / Project Production: very small volume
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1.2 Types of production
1. Jobbing / Project Production: very small volume
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1.2 Types of production
1. Jobbing / Project Production: very small volume
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1.2 Types of production
2. Batch Production: small volume
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1.2 Types of production
2. Batch Production: small volume
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1.2 Types of production
3. Mass Production: large volume
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1.2 Types of production
3. Mass Production: large volume
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1.2 Types of production
Mass production
Batch production
Jobbing
Volume/quantity
Production rate
Worker skills level
Multi-functional Equipment single-functional
Special tools
Process focus Plant Layout Product focus
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1.3 Functions in manufacturing
Raw
materials
1. Processing
2. Assembly
3. Materials handling
4. Inspection and test
Items
5. Process control
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1.3 Functions in manufacturing
1. Processing
a. basic processes: raw material to initial form make
initial sharp of product
b.
secondary processes: initial form to final desired
geometry final sharp
c. Operations to enhance physical properties:
improved all product functions
value added.
d. finishing operations: final process performed
smooth, attractive to customers
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1.3 Functions in manufacturing
2. Assembly operations: assembly/joining process
make/combine all components to final products.
3. Material handling: moving & storing materials,
components for next processing and assembly
operations
materials/components available to
production planning
.
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59
1.3 Functions in manufacturing
4. Inspection and test: generally considered part of
quality control
to test/confirm for items’
qualification to customers
5. Control process: both regulations for individual jobs
& assembly operations, and the management of
plant-level activities
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1.4 Organization & Information processing
1. Business functions:
Customer negotiation:
a/. Make to order contracts (
specific orders);
b/. Meet customers’ demand from stock (
make to
stock contracts
);
c/. Forecasting demand contracts (
based on forecast
information/data
).
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59
1.4 Organization & Information processing
2. Product/item design:
Including some documents as follows:
- Specific product design drawings,
- Product characteristics and materials requirement
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59
1.4 Organization & Information processing
3. Production planning:
Production planning and implementation based on:
+ final design of item,
+ technology process/facilities requirements,
+ and production/implementation,…
4. Production control:
Inspection and test/monitoring (product, job,
process, machines,…).
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1.5 Automation strategies (10)
1. Specialization of operations.
2. Combined operations.
3. Simultaneous operations.
4. Integration operations.
5. Increased flexibility.
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59
1.5 Automation strategies (10)
6. Improved material handling and storage.
7. Online inspection.
8. Process control and optimization.
9. Plant operations control.
10. Computer integrated manufacturing - CIM.
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59
1.6 Advanced manufactuirng characteristics (9)
1. Top managers pay more attention to their
production.
2. Quality problems consideration.
3.
Human resources consideration.
4.
Cost factors consideration.
5.
Specialization consideration.
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59
1.6 Advanced manufactuirng characteristics (9)
6. Old/disadvantage mass production tools are
troublesome to develop.
7. Mechanization consideration.
8. Application of
Computer and software in
production and operations management.
9. Application of useful theories.
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59
1.7 Production concepts & mathematical model
1. Manufacturing Lead Time - MLT
MLT includes all processing time at each machine/work station
where: i: machine order in process
m: number of machines that products will be processed
Q: product volume/batch; T
s
: set up time/machine
T
n
: none-operating time; T
p
: unit processing/service time
1
( ) (1)
m
MLT s p n i
i
T T QT T
=
= + +
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1.7 Production concepts & mathematical model
If total times spending at each Work station (WS) are equivalent, then
T
MLT
= n (T
s
+ QT
p
+ T
n
) (2)
+ For jobbing case (Q=1)
T
MLT
= n (T
s
+ T
p
+ T
n
) (3)
+ For mass production (with one machine case) Q is very high.
T
MLT
= QT
p
or T
MLT
= T
p
(1 item) (4)
+ For flow line (including n machines)
T
MLT
= Q(T
t
+ max[T
p
])
i
(5)
Or T
MLT
= (T
t
+ max[T
p
])
i
(1 item) (5’)
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1.7 Production concepts & mathematical model
Example: one order includes 50 items to produce over
8 work stations in a factory. The set-up time (everage)
for each WS is
3 hours, the processing time (everage)
is
6 munites / 1 item / 1 WS. The none-productive
time (everage) is
7 hours / 1 WS.
Determine the completion time of this order (days),
given that working time is one shift (
7 hours) per day.
Hint: manufacturing lead time is calculated as
formula (2)
T
MLT
= 8x(3 + 50x0.1 + 7) = 120 (hours)
Required days: 120 / 7 = 17.14 (days)
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1.7 Production concepts & mathematical model
2. Production rate R
p
Production rate of a production line/machine is
product quantity produced per hour (
hourly rate)
+ For batch production, processing time at k
th
WS:
(T
b
)
k
= (T
s
+ QT
p
)
k
(6)
If the processing time at each WS is equivalent, then
processing time is calculated as follow:
(T
b
)
m
= (T
s
+ QT
p
)
m
(7)
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1.7 Production concepts & mathematical model
2. Production rate R
p
If defective rate is q then required volume is Q/(1–q)
The average processing time per unit as follow:
(T
p
) = (T
b
)
m
/Q (8)
So production rate of certain WS as follow:
R
p
= 1/(T
p
) = Q/(T
b
)
m
(9)
(T
b
)
m
= (T
s
+ QT
p
/[1-q])
m
(7’)
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1.7 Production concepts & mathematical model
2. Production rate R
p
For jobbing, Q = 1, manufacturing lead time: (T
s
+T
p
)
R
p
= 1/(T
s
+ T
p
)
m
(9’)
For mass production, processing time: (T
MLT
= T
p
)
R
p
= 1/(T
p
) (9’’)
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1.7 Production concepts & mathematical model
3. Capacity C
a
Capacity
C
a
is total quantity of items
produced in a consideration time
week/month !
Capacity and productivity are the same
dimensions (unit of product/certain period).
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1.7 Production concepts & mathematical model
3. Capacity C
a
Capacity vs Productivity
Weekly/monthly Hourly
Units Units
Total items in factory Total items in machine
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1.7 Production concepts & mathematical model
3. Capacity C
a
Denoted that:
+ W: number of WS (No. of machines) in factory;
+ R
p
: productivity (in consideration time – hour)
+ H: time per shift (in hours)
+ S: No. of shifts (in consideration time – week/month)
C
a
= W x SxH x R
p
(10)
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1.7 Production concepts & mathematical model
Example: a factory has 6 machines (lathe) that can
produce a certain item, production manager said that
this factory runs
10 shifts each week, with realistics
operating time is
6,4 hours per shift, and equipment
productivity is
17 items per hour. Determine the
weekly capacity of this factory?
C
a
= 6 x 10x6,4 x 17 = 6528 (items/week)
3. Capacity C
a
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1.7 Production concepts & mathematical model
3. Capacity C
a
If products required N machines ( production line
includes
N machines) to finish N jobs (work
elements), then
C
a
can be calculated as follows:
C
a
= (W x SxH x R
p
)/N (11)
So the (W/N) is number of lines in factory
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59
1.7 Production concepts & mathematical model
3. Capacity C
a
If factory can produce some types of product, then
we denoted i as products kinds.
C
a
can be calculated each type of product separately
as follows :
C
a
i
= (W/N)
i
x SxH x R
p
i
(11’)
So the (W/N)
i
is number of lines produce item i.
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59
1.7 Production concepts & mathematical model
3. Capacity C
a
If we replace (weekly) capacity by (weekly) demand
then we have an other formula to control demand
satisfation as follow:
WxSxH = DxN/R
p
(12)
Three factors affect the factory capacity that
satisfies weekly
demand.
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59
1.7 Production concepts & mathematical model
3. Capacity C
a
WxSxH = DxN/R
p
(12)
With multi-product cases, right hand size (RHS) is
total demand.
With a certain product i, RHS is demand of i product
and formula can be rewritten as follow:
W
i
xSxH = D
i
xN
i
/R
pi
(12’)
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59
1.7 Production concepts & mathematical model
3. Capacity C
a
Example: 3 types of items are produced at some
similar WS, the information (
past data) is given in the
below table:
Item Weekly demand Productivity (item/hour)
1
2
3
600
1000
2200
10
20
40
Determine number of similar WS to meet all the
above demand, given that this factory runs
10 shifts
per week, and the operating time is
6,5 hours / shift,
No. of machine in each WS is N =
1.
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59
1.7 Production concepts & mathematical model
3. Capacity C
a
Hint:
item 1: D
1
/R
P1
= 600/10 = 60 hours,
item 2: D
2
/R
P2
= 1000/20 = 50 hours,
item 3: D
3
/R
P3
= 2200/40 = 55 hours,
Total required time: (60+50+55) =
165 hours,
Total required time for each WS: 10
x6.5 = 65 hours,
Min. No. of WS: 165/65 =
2.54 Work stations,
The minimum No. of WS is 3 to meet all product demand.
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59
1.7 Production concepts & mathematical model
4. Utilization U
U is resource using ratio (equipment, lines,
machines,...
+ relative to
using planning/production planning;
+ [operating time] / [available time]
+ [realistic volume] / [capacity]
50/
59
1.7 Production concepts & mathematical model
4. Utilization U
Example: a production line can run 65 hours/week,
and this line can make
20 units/hour.
This week this production line only produces 1000
units, and the rest time is idle time.
1. Determine the capacity of this line,
2. Determine the last week utilization (U) of this line.
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59
1.7 Production concepts & mathematical model
4. Utilization U
Hint:
Capacity of this line: C
a
= 65x20 = 1300 units/week,
Utilization of this line: U = 1000/1300 = 76.92%
Real operating time of last week:
T
R
= 1000/20 = 50 hours
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1.7 Production concepts & mathematical model
4. Utilization U
+ related to machine operating time (running time of
machine
), it is considered as a very useful factor to
control and measure the equipment (such as
reliability of equipment), this parameter indicates
the
availability of machines/equipment.
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59
1.7 Production concepts & mathematical model
4. Utilization U
Denoted: MTBF the average time between 2
consecutive failure (
Mean Time Between Failures)
MTTR the average repair time (Mean Time To
Repair)
So, the availability parameter is calculated by formula:
A = (MTBF MTTR) / MTBF (%) (13)
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59
1.7 Production concepts & mathematical model
5.
Work-in-process WIP
WIP = (C
a
x U) x (T
MLT
) / (S x H) (11)
where:
C
a
: factory capacity in consideration time,
U: utilization of factory equipment,
T
MLT
: processing time/manufacturing lead time,
S: number of shifts in consideration time,
H: number of hours for real operating in shift,
55/
59
1.7 Production concepts & mathematical model
5.
Work-in-process WIP
WIP: number of work in process items/un-finished
items in production line (factory),
WIP = (C
a
x U) x (T
MLT
) / (S x H) (11)
WIP is the ratio of processing time on available time
in factory.
The total none-operating time (95%) O. time (5%)
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59
1.7 Production concepts & mathematical model
5. Work-in-process WIP
Number of machine in real operating in factory:
N
m
= WxU x QT
p
/[T
s
+ QT
p
] (12)
where:
W: number of machines in factory,
U: utilization
Q: averagre lot size
T
s
: the set up time of machine,
T
p
: the processing time of machine,
57/
59
1.7 Production concepts & mathematical model
5. Work-in-process WIP
WIP ratio in processing is the ratio of WIP and real
operating machines in factory, can be calcultaed as
follow:
WIP
R
= WIP / N
m
(13)
Ideal WIP
R
is 1:1 each machine makes one WIP at
a period.
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59
1.7 Production concepts & mathematical model
5.
Work-in-process WIP
WIP in time ratio is called TIP ratio, can be calculated
as follow:
TIP
R
= T
MLT
/ (N x T
p
) (14)
Ideal ratio is 1:1 difficult.
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Preview text:

Contents: 1.1 Manufacturing industries.
Part 1 – Fundamental Concepts 1.2 Types of production. Chapter 1 1.3 Function in manufacturing.
1.4 Organization and information processing
INTRODUCTION TO MANUFACTURING SYSTEM 1.5 Automation strategies
1.6 Advanced manufacturing charactreistics
1.7 Production concepts and mathematical models 1/59 2/59 1.1 Manufacturing industries 1.1 Manufacturing industries
Basis industries in general: Manufacturing or Service?
Basis industries in general: Manufacturing or Service? Advertising Aerospace Equipment/machinery
Auto-motive (cars, trucks, buses)
Financial (Banks, investment companies, loans) Beverages Building materials Foods Cement Health care service Chemicals Hotels / restaurants Clothing Insurance Drugs, soaps, cosmetics
Transportation (railroad, Airline, trucking,...) 3/59 4/59 1.1 Manufacturing industries 1.1 Manufacturing industries
Manufacturing industry vs Process industry
Classification: Manufacturing industries:
Produce discrete items: cars, mobile, TV, clothes,... Industries
Representative companies Aerospace Boeing,… Car
General Motors, Toyota, Mitsubishi… Beverage
Coca-Cola, Pepsi-cola, Tribeco,… Building materials US. Gypsum, Southern steel,… Cement Sao mai, Hà tiên,.. Chemicals EI. Du pont, Nippon, Clothing
Hanes-Corp., V. Thắng, Thắng lợi,… Soaps, cosmetic,...
Proctor&Gambles, Unilever, Kao,… 5/59 6/59 1.1 Manufacturing industries 1.1 Manufacturing industries
Classification: Manufacturing industries:
Classification: Process industries:
Produce discrete items: cars, mobile, TV, clothes,...
Produce continuous items: liquid, pure water, beverage, beer, milk Petro processing Paint processing 7/59 8/59 1.1 Manufacturing industries 1.1 Manufacturing industries
Classification: Process industries:
Three classifications in manufacturing industries:
Produce continuous items: liquid, pure water, beverages, beer, milk
a. Basic producer: transforms natural resources into raw
materials (for others industrial firms)
b. Converter: intermediate link in the chain (semi- products or components).
c. Fabricator: final products assembly to market. 9/59 10/59 1.1 Manufacturing industries 1.1 Manufacturing industries Yarn Co.: basis producer Tires M. Co.: converter Input: silk-worm,... Input: rubber,... Output: thread,...
Output: inner tubes & tires,... Textile Co.: converter Plastic Co.: converter Input: thread,... Input: raw materials,... Output: clothing, Output: plastic components, Garment Co.: fabricator Honda Co.: fabricator Input: clothing, button, Input: moto-bike thread,... components,... Output: shirts, clothes Output: Airblade, Wave, Vision, Future,... 11/59 12/59 1.2 Types of production 1.2 Types of production
1. Jobbing / Project Production: very small volume
1. Jobbing / Project Production: very small volume
2. Batch Production: small volume
3. Mass Production: large volume 13/59 14/59 1.2 Types of production 1.2 Types of production
1. Jobbing / Project Production: very small volume
1. Jobbing / Project Production: very small volume 15/59 16/59 1.2 Types of production 1.2 Types of production
1. Jobbing / Project Production: very small volume
2. Batch Production: small volume 17/59 18/59 1.2 Types of production 1.2 Types of production
2. Batch Production: small volume
3. Mass Production: large volume 19/59 20/59 1.2 Types of production 1.2 Types of production
3. Mass Production: large volume Mass production Batch production Jobbing Volume/quantity Production rate Worker skills level Multi-functional Equipment single-functional Special tools Process focus Plant Layout Product focus 21/59 22/59 1.3 Functions in manufacturing 1.3 Functions in manufacturing 1. Processing 1. Processing
a. basic processes: raw material to initial form  make Raw 2. Assembly Items initial sharp of product materials 3. Materials handling 4. Inspection and test
b. secondary processes: initial form to final desired geometry  final sharp 5. Process control
c. Operations to enhance physical properties:
improved all product functions  value added.
d. finishing operations: final process performed 
smooth, attractive to customers 23/59 24/59 1.3 Functions in manufacturing 1.3 Functions in manufacturing
4. Inspection and test: generally considered part of
2. Assembly operations: assembly/joining process 
quality control  to test/confirm for items’
make/combine all components to final products. qualification to customers
3. Material handling: moving & storing materials,
components for next processing and assembly
5. Control process: both regulations for individual jobs
operations  materials/components available to
& assembly operations, and the management of production planning. plant-level activities 25/59 26/59
1.4 Organization & Information processing
1.4 Organization & Information processing 1. Business functions: 2. Product/item design: Customer negotiation:
Including some documents as follows:
a/. Make to order contracts (specific orders);
- Specific product design drawings,
b/. Meet customers’ demand from stock (make to
- Product characteristics and materials requirement stock contracts);
c/. Forecasting demand contracts (based on forecast information/data). 27/59 28/59
1.4 Organization & Information processing 1.5 Automation strategies (10) 3. Production planning:
1. Specialization of operations.
Production planning and implementation based on: 2. Combined operations. + final design of item,
+ technology process/facilities requirements, 3. Simultaneous operations.
+ and production/implementation,… 4. Integration operations. 4. Production control: 5. Increased flexibility.
Inspection and test/monitoring (product, job, process, machines,…). 29/59 30/59 1.5 Automation strategies (10)
1.6 Advanced manufactuirng characteristics (9)
1. Top managers pay more attention to their
6. Improved material handling and storage. production. 7. Online inspection.
2. Quality problems consideration.
8. Process control and optimization.
3. Human resources consideration. 9. Plant operations control.
10. Computer integrated manufacturing - CIM. 4. Cost factors consideration.
5. Specialization consideration. 31/59 32/59
1.6 Advanced manufactuirng characteristics (9)
1.7 Production concepts & mathematical model
6. Old/disadvantage mass production tools are 1.
Manufacturing Lead Time - MLT troublesome to develop.
MLT includes all processing time at each machine/work station
7. Mechanization consideration. m T
=  (T + QT + T ) (1) MLT s p n i i 1 =
8. Application of Computer and software in
production and operations management.
where: i: machine order in process
m: number of machines that products will be processed
9. Application of useful theories.
Q: product volume/batch; T : set up time/machine s
T : none-operating time;
T : unit processing/service time n p 33/59 34/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model
Example: one order includes 50 items to produce over
If total times spending at each Work station (WS) are equivalent, then
8 work stations in a factory. The set-up time (everage) T
= n (T + QT + T ) (2)
for each WS is 3 hours, the processing time (everage) MLT s p n
is 6 munites / 1 item / 1 WS. The none-productive
+ For jobbing case (Q=1)
time (everage) is 7 hours / 1 WS. T = n (T + T + T ) (3) MLT s p n
Determine the completion time of this order (days),
+ For mass production (with one machine case)  Q is very high.
given that working time is one shift (7 hours) per day. T = QT or T = T (1 item) (4) MLT p MLT p Hint: manufacturing lead time is calculated as
+ For flow line (including n machines) formula (2) T = Q(T + max[T ]) (5) MLT t p i T
= 8x(3 + 50x0.1 + 7) = 120 (hours) MLT Or T = (T + max[T ]) (1 item) (5’) MLT t p i Required days: 120 / 7 = 17.14 (days) 35/59 36/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model
2. Production rate – R
2. Production rate – R p p
Production rate of a production line/machine is
If defective rate is q then required volume is Q/(1–q)
product quantity produced per hour (hourly rate) (T ) = (T + QT /[1-q]) (7’) b m s p m
The average processing time per unit as follow:
+ For batch production, processing time at kth WS: (T ) = (T + QT ) (6) (T ) = (T ) /Q (8) b k s p k p b m
If the processing time at each WS is equivalent, then
So production rate of certain WS as follow:
processing time is calculated as follow:
R = 1/(T ) = Q/(T ) (9) (T ) = (T + QT ) (7) p p b m b m s p m 37/59 38/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model
2. Production rate – R 3. Capacity – C p a
For jobbing, Q = 1, manufacturing lead time: (T +T ) s p
Capacity – Ca is total quantity of items R = 1/(T + T ) (9’) p s p m
produced in a consideration time  week/month !
For mass production, processing time: (T = T ) MLT p R = 1/(T ) (9’’)
Capacity and productivity are the same p p
dimensions (unit of product/certain period). 39/59 40/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 3. Capacity – C 3. Capacity – C a a Capacity vs Productivity Denoted that: Weekly/monthly Hourly
+ W: number of WS (No. of machines) in factory; Units Units
+ R : productivity (in consideration time – hour) p Total items in factory Total items in machine
+ H: time per shift (in hours)
+ S: No. of shifts (in consideration time – week/month) C
= W x SxH x R (10) a p 41/59 42/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 3. Capacity – C 3. Capacity – C a a
Example: a factory has 6 machines (lathe) that can
If products required N machines ( production line
produce a certain item, production manager said that
includes N machines) to finish N jobs (work
elements), then C can be calculated as follows:
this factory runs 10 shifts each week, with realistics a
operating time is 6,4 hours per shift, and equipment C
= (W x SxH x R )/N (11)
productivity is 17 items per hour. Determine the a p
weekly capacity of this factory?
So the (W/N) is number of lines in factory
C = 6 x 10x6,4 x 17 = 6528 (items/week) a 43/59 44/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 3. Capacity – C 3. Capacity – C a a
If factory can produce some types of product, then
If we replace (weekly) capacity by (weekly) demand
we denoted i as product’s kinds.
then we have an other formula to control demand
C can be calculated each type of product separately a as follows : satisfation as follow:
WxSxH = DxN/R ( p 12) C
= (W/N) x SxH x R (11’) ai i pi
 Three factors affect the factory capacity that
So the (W/N) is number of lines produce item i. satisfies weekly demand. i 45/59 46/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 3. Capacity – C 3. Capacity – C a a
Example: 3 types of items are produced at some
WxSxH = DxN/R ( p 12)
similar WS, the information (past data) is given in the below table:
With multi-product cases, right hand size (RHS) is total demand. Item Weekly demand Productivity (item/hour) 1 600 10
With a certain product i, RHS is demand of i product 2 1000 20
and formula can be rewritten as follow: 3 2200 40
Determine number of similar WS to meet all the
W xSxH = D xN /R ( i i i pi 12’)
above demand, given that this factory runs 10 shifts
per week, and the operating time is 6,5 hours / shift,
No. of machine in each WS is N = 1. 47/59 48/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 3. Capacity – C 4. Utilization – U a Hint: U is resource using ratio (equipment, lines, item 1: D /R = 600/10 = 60 hours, 1 P1 machines,... item 2: D /R = 1000/20 = 50 hours, 2 P2 item 3:
+ relative to using planning/production planning; D /R = 2200/40 = 55 hours, 3 P3
Total required time: (60+50+55) = 165 hours,
+ [operating time] / [available time]
Total required time for each WS: 10x6.5 = 65 hours,
+ [realistic volume] / [capacity]
Min. No. of WS: 165/65 = 2.54 Work stations,
 The minimum No. of WS is 3 to meet all product demand. 49/59 50/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 4. Utilization – U 4. Utilization – U
Example: a production line can run 65 hours/week, Hint:
and this line can make 20 units/hour.
Capacity of this line: C = 65x20 = 1300 units/week, a
This week this production line only produces 1000
Utilization of this line: U = 1000/1300 = 76.92%
units, and the rest time is idle time.
Real operating time of last week:
1. Determine the capacity of this line, T = 1000/20 = 50 hours R
2. Determine the last week utilization (U) of this line. 51/59 52/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model 4. Utilization – U 4. Utilization – U
+ related to machine operating time (running time of Denoted:
MTBF the average time between 2
machine), it is considered as a very useful factor to
consecutive failure (Mean Time Between Failures) control and measure the equipment (such as
MTTR the average repair time (Mean Time To
reliability of equipment), this parameter indicates Repair)
the availability of machines/equipment.
So, the availability parameter is calculated by formula:
A = (MTBF – MTTR) / MTBF (%) (13) 53/59 54/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model
5. Work-in-process – WIP
5. Work-in-process – WIP
WIP = (C x U) x (T ) / (S x H) (11) a MLT
WIP: number of work in process items/un-finished where:
items in production line (factory),
C : factory capacity in consideration time, a
U: utilization of factory equipment,
WIP = (C x U) x (T ) / (S x H) (11) a MLT T
: processing time/manufacturing lead time, MLT
WIP is the ratio of processing time on available time
S: number of shifts in consideration time, in factory.
H: number of hours for real operating in shift,
The total none-operating time (95%) O. time (5%) 55/59 56/59
1.7 Production concepts & mathematical model
1.7 Production concepts & mathematical model
5. Work-in-process – WIP
5. Work-in-process – WIP
 Number of machine in real operating in factory:
WIP ratio in processing is the ratio of WIP and real N
= WxU x QT /[T + QT ] (12)
operating machines in factory, can be calcultaed as m p s p where: follow:
W: number of machines in factory, WIPR = WIP / N (13) m U: utilization Q: averagre lot size
Ideal WIPR is 1:1  each machine makes one WIP at
T : the set up time of machine, a period. s
T : the processing time of machine, p 57/59 58/59
1.7 Production concepts & mathematical model
5. Work-in-process – WIP
WIP in time ratio is called TIP ratio, can be calculated as follow: TIPR = T / (N x T ) (14) MLT p
Ideal ratio is 1:1  difficult. 59/59