Process Capacity
A Process; Three Sequential Activities
Resource
Activity
Time
You
Operation A
Oven
Operation B
15 minutes
20
Friend
Operation C
5
3 sequential activities;
A (preparation), B (bake), and C (package and label).
3 resources; you, oven, and your friend.
To produce each batch of muffin, you prepare the material, then
put the batch in the oven (there is only a single oven and can bake
one batch at a time), then your friend take the batch out and does
packaging and labeling. The processing time at each operation is
given above. This system works for four hours. 4×60 = 240
(Estimating processing times is the subject of motion and time
studies.)
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
2
Resources, and Resource Units
Capital Resources – Fixed Assets such as land, buildings,
facilities, machinery, oven, etc.
Human Resources – People such as engineers, operators,
assemblers, chefs, customer-service representatives, you, your
friend, etc.
Each activity may require one or more resources and each
resource may be allocated to one or more activities. A resource, a
baker, may be used by several activities such as mixing, kneading
and forming dough. An activity like loading an oven, may require
multiple resources such as a baker and an oven.
Resource Unit – An individual resource (chef, mixer, oven), or a
combination of different individual resources (an operating
room).
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
3
Capacity of a Process with Sequential Activities
You
Operation A
Oven
Operation B
15 minutes
20
Friend
Operation C
5
Capacity (per hour)
= 60/15 = 4
= 60/20 = 3
= 60/5 = 12
Process Capacity = Min {4,3,12} = Capacity of the bottleneck = 3
Each hour we produce 3 units.
Starting from the second unit, every 60 mins a total of 3 units
may enter, pass, and leave the process.
60/3 = 20 interarrival time and interdeparture time (cycle Time).
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
4
Per Minute and Per Hour Reach the Same Results
You
Operation A
Oven
Operation B
Friend
Operation C
15 minutes
20
5
We computed capacity /hr, we could have computed the
capacity per min
Capacity (per min)
= 1/15
= 1/20
= 1/5
Process Capacity = Min{1/15. 1/20. 1/5}
Capacity of the bottleneck = 1/20 per min
Each min we produce 1/20 units. In 20 mins we can send out or
take in one product.
20 mins interarrival time and interdeparture time (Cycle Time).
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
5
Cycle Time
You
Operation A
Oven
Operation B
Friend
Operation C
15 minutes
20
5
a) How long does it take to produce a batch of muffin? In a
formal term, what is the flow time in this process?
Flow Time 15 + 20 + 5 = 40
b) How often a batch of muffin enter (exit) this process? In a
formal term, what is the Cycle time of this system?
You prepare a batch and pass it to the oven at min 15.
You then start the next batch and complete it at min 30.
Oven is still baking the first batch. It will be done at min 15+20 =
35.
You need to wait for 5 minutes to put the 2nd batch in the oven.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
6
Cycle Time
You
Operation A
Oven
Operation B
Friend
Operation C
15 minutes
20
5
Oven is the bottleneck. Batches exit the oven every 20 mins.
You also can put batches into the oven every 20 mins.
At min 35 your friend can take the first batch out of the oven, and
after 5 mins at min 40 he is done. First batch exits at min 40.
At min 35 you put the second batch in the oven.
Your friend takes it out of oven at min 35+20 = 55 and send it out
of the process at min 60.
That is 60-40=20 mins after the first batch.
Therefore the time between exit of two consecutive batches is?
Cycle time is 20 min. The oven is the bottleneck.
Cycle time = Max{15, 20, 5} = 20
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
7
Flow Time
You
Operation A
Oven
Operation B
15 minutes
20
Friend
Operation C
5
Operation A
Operation B
Operation C
CT
0
Capacity- Basics
Flow Time
40
CT
CT
60
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80
June-2013
100
8
Cycle Time; Starting from 0 vs. Continual
a) How many batches can you produce per day?
Case 1, Starting form 0. We have 4×60 minutes. It takes you 40
minutes to produce the first batch. In the remaining 240 - 40 =
200 mins, since cycle time is 20 mins, therefore, we produce 1
batch per 20 mins, that is 10 batches in 200 mins. We produce 1+10
= 11 per 4 hours.
We could have also said that in the first 40 minutes we produce 1
batch and in the next 200 minutes we produce 1/20 batch per min.
That is 1+200(1/20) = 11 per 4 hours.
Case 2, Continual. Suppose we are not producing muffins but
something else such that at the start of each day there are WIP of
the previous day in the system. For example suppose it is a
painting oven for a small part and you can make the part ready
and put it into the oven at the start of the next day.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
9
Utilization
What is the capacity (or maximum Throughput)?
The flow time is 40 mins. The cycle time is 20 mins. Therefore,
capacity is 1/20 per min. In 4 hours it is 240(1/20) = 12
By now we should know the followings
Flow time.
Cycle time.
Capacity.
What is Utilization of the oven?
Oven is always working. Every 20 minute 1 batch comes and 1
batch leaves. Utilization of the oven is 1 or 100%.
In each 20 minutes you only work 15 mins. Your utilization is
15/20 = 0.75 or 75%.
In each 20 minutes your friend only work 5 mins. Your friend’s
utilization is 5/20 = 0.25 or 25%.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
10
Utilization
We can compute Utilization in an alternative way.
Oven
You
Friend
Operation B
Operation C
Operation A
Activity Time 15 minutes
20
= 60/15 = 4
Capacity
Process Capacity = min{4,3,12}
Utilization
= 3/4 = 0.75
Capacity- Basics
5
= 60/20 = 3
=3
= 3/3 = 1
Ardavan Asef-Vaziri
June-2013
= 60/5 = 12
= 3/12 = 0.25
11
Parallel Activities, Resource Pool
Resource Pool – A collection of
interchangeable resource units
that can perform an identical set
of activities.
Processing time = Tp = 20 minutes
Oven
Operation B
Operation B
20
Resource Pool contains 2 Resource units. c =2
Capacity of a resource unit = 1/20 per min
Capacity of a resource pool = 2(1/20) = 1/10 per min
After how many minutes a product exist this system
Every one minute 0.1 product. After how many minutes 1
product?
1/0.1 = 10 Cycle time is 10 minutes.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
12
Network of Activities
Now suppose there are two ovens. Compute flow time. Capacity
or maximum accessible throughput, cycle time, and utilization of
each resource unit and resource pool.
Oven
Friend
You
Operation B
Operation C
Operation A
Operation B
15 minutes
5
Capacity of
20
Resource Unit
= 1/5
= 1/15
= 1/20
batch/min
Capacity of
= (1/15)(1) =1/15= (1/20)(2) = 1/10
Resource Pool
batch/min
= (1/5)(1)=1/5
Process Capacity = Capacity of the bottleneck = 1/15 per min
You are the bottleneck.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
13
Network of Activities
You
Operation A
Oven
Operation B
Operation B
20
Capacity of
Resource Pool (1/15)(1) =1/15 (1/20)(2) = 1/10
Friend
Operation C
15 minutes
5
(1/5)(1)=1/5
batch/min
Process Capacity = 1/15 per min
Each min the system produces 1/15 units. In 15 mins we can
send out or take in one product.
Interarrival time and interdeparture time (cycle Time) = 15 min.
U = (1/15)/(1/15)=1 = (1/15)/(1/10) = 0.67 = (1/15)(1/5)=0.33
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
14
Per Minute and Per Hour Reach the Same Results
Oven
Operation B
You
Operation A
Operation B
20
(60/20)(2) = 6
15 minutes
Capacity of
(60/15)(1) =4
Resource Pool
batch/hr
Friend
Operation C
5
(60/5)(1)=12
Process Capacity = 4 per hour
Each hr the system produces 4 units. In 15 mins we can send
out or take in one product.
Interarrival time and interdeparture time (cycle Time) = 15 min.
U=
Capacity- Basics
4/4=1
4/6 = 0.67
Ardavan Asef-Vaziri
June-2013
4/12=0.33
15
Two Ovens Plus Cross Functional Workers
Human
Operation A
15 mins
Resource
Time
Capacity
Human
5+15
2*60/20 =6
Oven
Operation B
Human
Operation C
Operation B
20
5
Oven
20
2*60/20 =6
Cross functional workers and resource pooling are great
operational strategies.
However, in this specific example we need to be careful.
We did not increase throughput. Furthermore, U of all resources
is now 100%. Very risky, a small variation can reduce the capacity.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
16
Resources, Resource Pools and Resource Pooling
Resource Pooling – Combining separate resource pools into a
single more flexible pool that is able to perform several
activities. Transforming specialized resources into general
purpose resources. Cross-trained workers. General purpose
machines.
It is a powerful operational concept that can significantly affect
not only process flow rate and capacity but also flow time.
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
17
Christine, Roommate, Mixer, and Oven
Christine, Roommate, Mixer, and One Oven
Resource
Christine
Roommate Mixer
Time
8
3
6
Capacity/hr 60/8 =7.5
60/3=20
60/6=10
Oven
10
60/10 = 6
Christine, Roommate, Mixer, and Two Ovens
Resource
Christine
Roommate Mixer
Time
8
3
6
Capacity
60/8 = 7.5
60/3=20
60/6=10
Oven
10
120/10 =12
One Oven and Cross Functional Workers
Resource
Human
Mixer
Time
8+3
6
Capacity
120/11 =10.9
60/6 = 10
Capacity- Basics
Ardavan Asef-Vaziri
June-2013
Oven
10
120/10 =12
18
Christine, Roommate, Mixer, and Oven
Christine, Roommate, Mixer, and One Oven
Resource
Christine
Roommate Mixer
Time
8
3
6
Capacity
1/8
1/3
1/6
Oven
10
1/10
Christine, Roommate, Mixer, and Two Ovens
Resource
Christine
Roommate Mixer
Time
8
3
6
Capacity
1/8
1/3
1/6
Oven
10
2(1/10) =1/5
Cross Functional Workers and Two Ovens
Resource
Human
Mixer
Time
8+3
6
Capacity
2(1/11) =2/11
1/6
Capacity- Basics
Ardavan Asef-Vaziri
Oven
10
2(1/10) = 1/5
June-2013
19
Network of Activities
The following graph shows a production process for two
products AA and BC. Station D and E are flexible and can
handle either product. No matter the type of the product, station
D can finish 100 units per day and station E can finish 90 units
per day. Station A works only for Product AA and have a
capacity of 60 units per day. Station B and C are only for
Product BC and have capacity of 80 and 45 units per day,
respectively. The demands for each product is 50 units per day.
Which station is the bottleneck?
A) Stations A and C
B) Station B and C
C) Stations C and D
D) Stations D and E
E) Station C and E
Capacity- Basics
A:
60
B:
80
Ardavan Asef-Vaziri
D:
100
E:
90
C:
45
June-2013
20
Network of Activities
Which of the following is NOT correct?
A) The utilization rate of station A is at least 75%
B) The utilization rate of station B at least 50%
C) The utilization rate of station B is at most 56.25%
D) The utilization rate of station D is 90%
E) None of the above.
E  We can produce at most 90 AA and BC.
C  We can produce at most 45 BC
We may produce all combinations from 50AA and 40 BC to
45AA and 45 BC
A:
Station A- At least 45/60 = 75%
Station D : 90/100 = 90%
B:
Station B - At least 40/80 = 50%
Station B – At most 45/80 = 0.5625 80
Capacity- Basics
D:
100
60
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E:
90
C:
45
June-2013
21
Flow Time; Parallel Tasks
M1
A
H1
B
H2
C
2
2
4
M2
D
Flow Time = 2+2+4+1 = 9
1
Capacity /hr M1 =30, H1=30, H2=15, M2=60
Capacity = 15 per hour
Capacity /min M1 =1/2, 1/2, 1/4, 1/1
H1
B
M1
A
2 H2
C
M2
D
2
4
1
Path 1 = 2+2+1 = 5
Path 2 = 2+4+1 = 7
Flow Time = 7
Capacity- Basics
Capacity M1 =30, H1=30, H2=15, M2=60
Ardavan Asef-Vaziri
June-2013
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Parallel Operations – Resource Pooling & Splitting
Activities
H
B
2 H
C
M1
A
M2
D
4
2
1
T = Max{5,7} = 7
Capacity M1 =30, H=10*2=20, M2=60
H
H
C2
B
M1
A
2
2
T = Max{6,6} = 6
Capacity- Basics
H
C1
3
1
M2
D
1
Capacity M1 =30, H=10*2=20, M2=60
Ardavan Asef-Vaziri
June-2013
23