Flow Time Problems
Set 2
This is indeed Christine Cookies modified in MBPF 2nd Edition
4.2 - Kristen and her roommate are in the business of baking custom cookies. As soon as
she receives an order by phone, Kristen washes the bowl and mixes dough according to
the customer's order - activities that take a total of 6 minutes. She then spoons the dough
onto a tray that holds one dozen cookies (2 minutes). Her roommate then takes 1 minute
to set the oven and place the tray in it. Cookies are baked in the oven for 9 minutes and
allowed to cool outside for 5 minutes. The roommate then boxes the cookies (2 minutes)
and collects payment from the customer (1 minute)
a. Draw a flowchart for the process described here and determine theoretical flow time
from the time of order until the time of payment collection. Assume no waiting over the
course of the process
b. suppose that each other consists of two dozen cookies. Assume that although the mixing
bowl can accommodate dough for two dozen cookies at a time, the oven can accommodate
only one tray of one dozen cookies at a time. As before, spooning each tray takes 2 minutes,
and both trays must be cooled prior to boxing the cookies for customer pickup. Draw a
modified flowchart and determine theoretical flow time. Consider the effect on flow time of
the following possible alternatives to the system:
1. Buying a second oven that can bake one tray of one dozen cookies
2. Buying a second oven that can hold two trays of one dozen cookies each
3. Buying a faster convection oven that can bake one dozen cookies in 6 minutes instead of
9 minutes.
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
2
Problem 5.2: Flow unit = 1 order of 1 dozen.
Take
wash
order
mix
spoon
load
bake
unload
& set
cool
pack
get
pay
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
3
Problem 4.2
a)
Take
Take
order
order
wash
wash
mix
mix
6/1-2 doz
spoon
spoon
2
6/1-2 doz
2
load
load
& set
& set
1
1
bake
bake
9
unlounload
ad
cool
cool
pack
pack
5
2
9
5
2
get
get
pay
pay
1/order
1/order
TFT = 6+2+1+9+5+2+1 = 26
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
4
Part (a): Gant Chart and the theoretical flow time for 1 doz orders
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
u
s
l
pack
g
p
bake
cool
1
25
2
26
3
4
5
6
7
Throughput Problems – Set2
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9
10
11
12
13
14
15
16
Ardavan Asef-Vaziri
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Nov-2011
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20
21
22
23
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5
Part (b): general explanations; mix can handle 2 doz, oven 1 doz
Take
wash
spoon
load
bake
unlo-
cool
pack
get
order
ad
pay
Flow
unit =mix
1 order of 2 dozen. & set
6/1-2 doz
5
2
1/order
Certain activities
can be2 performed1 in parallel. 9
For example, while the oven is baking the first dozen, You can spoon the dough for the
second dozen into another tray. Therefore, the flow time of such an order is not simply the
sum of the activity times.
A useful tool is a Gantt chart that shows the times during which different resources of
interest are occupied for various activities.
The dough for the 2 dozen cookies is mixed by You in 6 minutes and subsequently you
spoon dough for 1 dozen in 2 minutes.
Therefore in the 8th minute, the RM is ready to load the oven and set timer, which takes 1
minute. The oven starts baking the first dozen at the 9th minute and completes baking at
the 18th minute. Meanwhile, You spoon the second dozen into another tray.
At the 18th minute, the RM unloads the first tray from the oven and loads the second tray
into the oven and sets the timer. So the second dozen starts baking at the 19th minute.
While the second dozen bakes, the first dozen cookies cool and RM packs them into a bag,
which takes a total of 7 minutes.
At the 28th minute the second dozen finishes baking at which time the RM unloads the
tray.
After cooling for 5 minutes, the RM packs the second dozen in 2 minutes by the 35th
minute.
Finally, payment for the order and delivery to customer takes place in the 36th minute.
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
6
Part (b): Gant Chart and the theoretical flow time for 2 doz orders
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
u l
s
l s
bake
pack
u
l
bake
cool
cool
1
25
2
26
3
27
4
28
5
29
30
6
7
Throughput Problems – Set2
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9
10
11
12
13
14
15
16
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20
21
22
23
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Part (b): Gant Chart and the theoretical flow time for 2 doz orders (cont.)
Take
wash
order
mix
spoon
load
bake
& set
6/1-2 doz
2
1
unlo-
cool
pack
ad
9
get
pay
5
2
1/order
2
pack
g
p
cool
31
32
33
34
35
36
37
Throughput Problems – Set2
38
39
40
Ardavan Asef-Vaziri
Nov-2011
8
Part (b): CPM
Take
wash
order
mix
spoon
6/1-2 doz
2
spoon
load
bake
& set
2
unlo-
cool
pack
ad
1
9
5
2
get
pay
1/order
load
bake
& set
1
unlo-
cool
pack
ad
9
Throughput Problems – Set2
5
2
Ardavan Asef-Vaziri
Nov-2011
9
Part (b): CPM
0
0 0
Take
order
6
wash
6
spoon
8
mix
6/1-2 doz
8
spoon
2
1018
load
10
18
2
1 1
9 9 bake
2 2
8 8
& set
unlo-
2 2
8 8 cool
3 3
3 3pack
3
5
ad
1
9
5
2
3
25 5
3
5
get
3
6
pay
1/order
8
load
99
18 18
bake
& set
1
unlo-
18 1
8
2323
cool
25
pack
ad
9
Throughput Problems – Set2
5
2
Ardavan Asef-Vaziri
Nov-2011
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Forward Path
Max = 30
10
35
35
30
20
35
5
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
11
Part (b): CPM
0
0
0 0
Take
order
8
8
0
spoon
1
6
6
2
load
6/1-2 doz
6
6
2
8
8
18
10 load
10
18
1
8
99
bake
181
1
unlo- 8
8
1818
1
9
bake
1
9
1 1
8 8
Throughput Problems – Set2
1 2
8 8
1 1
9 9
9
2323
cool
5
unlo-
2 2
8 8 cool
3 3
3 3pack
3
5
3 3
3 3
3
5 3
25 5
ad
2 2
8 8
2 2
8 8
5
2
25
3
5
3
5
get
pay
1/order
3
6
3
6
pack
ad
9 9
2 2
8 8
& set
1
8
& set
1
spoon
mix
0
8
6
wash
3 3
3 3
2
3
5
Ardavan Asef-Vaziri
Nov-2011
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Backward Path
30
Min = 35
30
35
30
30
45
5
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
13
Part (b1): theoretical flow time when buying a second oven with 1 doz
capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
l
u
u
s
s
l
l
pack
g
p
bake
bake
cool
1
25
2
26
3
27
4
28
5
29
6
7
Throughput Problems – Set2
8
9
10
11
12
13
14
15
cool
16
Ardavan Asef-Vaziri
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20
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22
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Part (b1): CPM
spoon
load
bake
& set
2
1
unlo-
cool
pack
ad
9
5
2
get
Take
wash
order
mix
6/1-2 doz
spoon
pay
1/order
2
load
bake
& set
1
Throughput Problems – Set2
unlo-
cool
pack
ad
9
Ardavan Asef-Vaziri
5
Nov-2011
2
15
Part (b2): theoretical flow time when buying a large oven with 2 doz
capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
u
s
l
pack
g
p
bake
cool
1
25
2
26
3
27
4
28
5
29
6
30
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
We do not need CPM since activities are sequential
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
16
Part (b3): theoretical flow time when buying a fast oven with 1 doz
capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
u l
s
l s
pack
u
l
bake
2
26
3
27
4
28
5
29
30
6
7
8
g
p
bake
cool
1
25
pack
9
10
11
12
13
cool
14
15
16
17
18
19
20
21
22
23
24
CPM is the same as the CPM for original case, just bake time is 6 min instead o
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
17
Trade-off Analysis
No Investment
Second Oven
Large Oven
Fast Ovens
36
28
30
30
The second oven
(a)leads to the shortest flow time
(b)Perhaps is cheaper than a large oven or 2 fast ovens
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
18
Problem 4.2 Version2 - Both Boxed together: Part (a)
Take
wash
order
mix
6/1-2 doz
spoon
load
bake
& set
2
1
unlo-
cool
box
ad
9
get
paid
5
2
1/order
TFT = 6+2+1+9+5+2+1 = 26
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
19
Part (a): Gant Chart and the theoretical flow time for 1
doz orders
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
cool
box
get
ad
1
paid
9
5
2
1/order
spoon
mix
l
u
s
l
box
g
p
bake
cool
1
25
2
26
3
4
5
6
7
Throughput Problems – Set2
8
9
10
11
12
13
14
15
16
Ardavan Asef-Vaziri
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Nov-2011
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20
21
22
23
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Part (b): general explanations; mix can handle 2 doz,
oven 1 doz
Take
wash
spoon
load
bake
unlo-
cool
box
get
order
ad
paid
Flow
unit =mix
1 order of 2 dozen. & set
6/1-2 doz
5
2
1/order
Certain activities
can be2 performed1 in parallel. 9
For example, while the oven is baking the first dozen, You can spoon the dough for the
second dozen into another tray. Therefore, the flow time of such an order is not simply the
sum of the activity times.
A useful tool is a Gantt chart that shows the times during which different resources of
interest are occupied for various activities.
The dough for the 2 dozen cookies is mixed by You in 6 minutes and subsequently you
spoon dough for 1 dozen in 2 minutes.
Therefore in the 8th minute, the RM is ready to load the oven and set timer, which takes 1
minute. The oven starts baking the first dozen at the 9th minute and completes baking at
the 18th minute. Meanwhile, You spoon the second dozen into another tray.
At the 18th minute, the RM unloads the first tray from the oven and loads the second tray
into the oven and sets the timer. So the second dozen starts baking at the 19th minute.
While the second dozen bakes, the first dozen cookies cool and RM packs them into a bag,
which takes a total of 7 minutes.
At the 28th minute the second dozen finishes baking at which time the RM unloads the
tray.
After cooling for 5 minutes, the RM packs the second dozen in 2 minutes by the 35th
minute.
Finally, payment for the order and delivery to customer takes place in the 36th minute.
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
21
Part (b): Gant Chart and the theoretical flow time for 2
doz orders
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
box
get
ad
1
paid
9
5
2
1/order
spoon
mix
l
u l
u
s
l s
l
bake
bake
cool
cool
1
25
2
26
3
27
4
28
5
29
30
6
7
Throughput Problems – Set2
8
9
10
11
12
13
14
15
16
Ardavan Asef-Vaziri
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Nov-2011
19
20
21
22
23
24
22
Part (b): Gant Chart and the theoretical flow time for 2
doz orders (cont.)
Take
wash
order
mix
spoon
load
bake
& set
6/1-2 doz
2
1
unlo-
cool
box
ad
9
get
paid
5
2
1/order
2
box
g
p
cool
31
32
33
34
35
36
37
Throughput Problems – Set2
38
39
40
Ardavan Asef-Vaziri
Nov-2011
23
Part (b): CPM
Take
wash
order
mix
spoon
6/1-2 doz
2
spoon
load
bake
& set
2
load
1
bake
& set
1
unlo-
unlo-
cool
box
5
2
ad
9
get
paid
1/order
cool
ad
9
Throughput Problems – Set2
5
Ardavan Asef-Vaziri
Nov-2011
24
Part (b): CPM
0
0 0
Take
order
6
wash
6
spoon
8
mix
6/1-2 doz
8
spoon
2
1018
load
10
18
2
8
load
& set
99
18 18
bake
unlo-
18 1
8
2 2
8 8
unlo-
2 2
8 8 cool
ad
1
& set
1
1 1
9 9 bake
9
5
3 3
3 3box
23
3
5
3
5
get
3
6
paid
2
1/order
23
cool
ad
9
Throughput Problems – Set2
5
Ardavan Asef-Vaziri
Nov-2011
25
Forward Path
Max = 30
10
35
35
30
20
35
5
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
26
Part (b): CPM
0
0
0 0
Take
order
8
8
0
spoon
1
6
6
2
load
6/1-2 doz
6
6
2
8
8
18
10 load
10
18
1
8
99
bake
181
1
unlo- 8
8
1818
1
9
bake
2 2
8 8
& set
1
8
& set
1
spoon
mix
0
8
6
wash
1
unlo-
2 2
8 8 cool
3 3
3 3box
ad
1 1
9 9
9
2 2
8 8
2 2
8 8
5
3 3
3 3
2
3
5
3
5
3
5
get
3
6
paid
3
5
1/order
3
6
23
cool
ad
9 9
9
1 1
8 8
Throughput Problems – Set2
1 2
8 8
5
3
3
Ardavan Asef-Vaziri
Nov-2011
27
Backward Path
30
Min = 35
30
35
3
0
30
45
5
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
28
Part (b1): theoretical flow time when buying a second
oven with 1 doz capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
pack
get
ad
1
pay
9
5
2
1/order
spoon
mix
l
l
u
u
s
s
l
l
box
g
p
bake
bake
cool
1
25
2
26
3
27
4
28
5
29
6
7
Throughput Problems – Set2
8
9
10
11
12
13
14
15
cool
16
Ardavan Asef-Vaziri
17
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Nov-2011
19
20
21
22
23
24
29
Part (b1): CPM
spoon
load
bake
& set
2
1
unlo-
cool
ad
9
5
box
Take
wash
order
mix
6/1-2 doz
spoon
get
paid
2
1/order
2
load
bake
& set
1
Throughput Problems – Set2
unlo-
cool
ad
9
Ardavan Asef-Vaziri
5
Nov-2011
30
Part (b2): theoretical flow time when buying a large
oven with 2 doz capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
box
get
ad
1
paid
9
5
2
1/order
spoon
mix
l
u
s
l
box
g
p
bake
cool
1
25
2
26
3
27
4
28
5
29
6
30
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
We do not need CPM since activities are sequential
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
31
Part (b3): theoretical flow time when buying a fast
oven with 1 doz capacity
Take
wash
order
mix
spoon
load
bake
unlo-
& set
6/1-2 doz
2
wash
spoon
cool
box
get
ad
1
paid
9
5
2
1/order
spoon
mix
l
u l
u
s
l s
l
bake
2
26
3
27
4
28
5
29
30
6
7
8
g
p
bake
cool
1
25
box
9
10
11
12
13
cool
14
15
16
17
18
19
20
21
22
23
24
CPM is the same as the CPM for original case, just bake time is 6 min instead o
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
32
Trade-off Analysis
No Investment
Second Oven
Large Oven
Fast Ovens
28
30
36
28
The second oven
(a)leads to the shortest flow time
(b)Perhaps is cheaper than a large oven or 2 fast ovens
Throughput Problems – Set2
Ardavan Asef-Vaziri
Nov-2011
33