Capacity Management with Set-Ups – Focused on Set-Up Time
Set-up times
dominate
Compute
Capacity as
function of
batch size
Compute cycle
time (CT) of the
rest of the
process
Compute
set-up costs &
inventory costs
Use EOQ
model or one
of its variants
Solve for
batch size:
Cap(B)=1/CT
Analyze
Set-up times &
Set-up Costs
Set-up costs
dominate
Reduce the need
for batches
• Set-up time reduction, SMED
• Process lay-out
•10-minute rule
• Externalize internal set-ups
Figure 7.11.: Summary of batching
Batching Under Set-Up Times
Capacity Management with Set-Ups – Focused on Set-Up Time
Set-up times
dominate
Compute
Capacity as
function of
batch size
Compute cycle
time (CT) of the
rest of the
process
Compute
set-up costs &
inventory costs
Use EOQ
model or one
of its variants
Solve for
batch size:
Cap(B)=1/CT
Analyze
Set-up times &
Set-up Costs
Set-up costs
dominate
Reduce the need
for batches
• Set-up time reduction, SMED
• Process lay-out
•10-minute rule
• Externalize internal set-ups
Figure 7.11.: Summary of batching
An Example Application
Single bottleneck recourse – a milling machine – which produces two
components (one steer support and two ribs) for manufacturing a
single scooter
A steer support requires 1 minute per unit, & A rib requires 0.5 minutes per unit
Other remaining step in the process is an assembly operation which
does not require any setup and the per unit time for this process is 3
minutes/unit
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part x 2 parts = 1min
Step 2
3 min/unit
Set-Up Times
To switchover from one product to another on the milling
machine requires a 60 minute delay for resource set up.
60 min
1 min/unit
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part x 2 parts = 1min
60 min
2x(.5 min/unit)
Step 2
3 min/part
No setup
If there were no set up, then given batch size Q and
the total time to produce one unit would be equal
to p, the total capacity of the bottleneck resource
would be = [Q/(p*Q)] = 1/p (capacity/unit time)
Capacity WO Set-up=
Batch Size
Batch-size*Time per unit
=
1
Time per unit
Thus, in this case, the batch size Q does not matter.
No setup (example)
In fact, the time per unit for our example
application would be p=1+(2*.5)=2 minutes per unit
and with zero setup times, the capacity would be
0.5 units/minutes (since 1/p=1/2=0.5)
Activity Time
60/2 = 30 unit/hr
60/3 = 20 unit/hr
Step 1
Step 2
one Steer support: 1 min/part
Two Rib: 0.5 min/part
Total processing 1 x 1min + 2 x 0.5 min
= 2 min/unit
3 min/part
Setup
Set-up time + Batch-size*Time per unit
1-unit
122 min/unit
60 min
1 min/unit
1/122 = 0.00819 unit/min
Step 1
Activity Time
Batch Size
Capacity given Batch Size=
one Steer support: 1 min/part
Two Rib: 0.5 min/part
60 min
2x(.5 min/unit)
1/3 = .333 unit/min
Step 2
3 min/part
Setup
Set-up time + Batch-size*Time per unit
12-unit
144 min/12unit
60 min
(1 min/unit)x12
1/144 x 12 = 0.0833 unit/min
Step 1
Activity Time
Batch Size
Capacity given Batch Size=
one Steer support: 1 min/part
Two Rib: 0.5 min/part
60 min
[2x(.5 min/unit)]x12
1/3 = .333 unit/min
Step 2
3 min/part
Setup
Set-up time + Batch-size*Time per unit
24-unit
168 min/24unit
60 min
(1 min/unit)x24
1/168 x 24 = 0.1428 unit/min
Step 1
Activity Time
Batch Size
Capacity given Batch Size=
one Steer support: 1 min/part
Two Rib: 0.5 min/part
60 min
[2x(.5 min/unit)]x24
1/3 = .333 unit/min
Step 2
3 min/part
Setup
Capacity given Batch Size=
Set-up time + Batch-size*Time per unit
48-unit
216 min/48unit
1/216 x 48 = 0.2222 unit/min
Step 1
Activity Time
Batch Size
one Steer support: 1 min/part
Two Rib: 0.5 min/part
1/3 = .333 unit/min
Step 2
3 min/part
Setup
Capacity given Batch Size=
Batch Size
Set-up time + Batch-size*Time per unit
92-unit
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part
Step 2
3 min/part
Capacity as a function of Batch Size
Capacity given Batch Size=
Batch Size
Batch Size
Set-up time + Batch-size*Time per unit
Supports
Ribs
Total
Capacity
Set-Up
Prododuction Time Set-Up Prododuction Time Time
per minute
1
60
1
60
1
122
0.01
12
60
12
60
12
144
0.08
24
60
24
60
24
168
0.14
36
60
36
60
36
192
0.19
48
60
48
60
48
216
0.22
60
60
60
60
60
240
0.25
120
60
120
60
120
360
0.33
240
60
240
60
240
600
0.40
360
60
360
60
360
840
0.43
720
60
720
60
720
1560
0.46
1440
60
1440
60
1440
3000
0.48
2880
60
2880
60
2880
5880
0.49
Process Analysis with Batching
 Note: Capacity increases with batch size:
0.5
Capacity
1/p
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
650
610
570
530
490
450
410
370
330
290
250
210
170
130
90
50
10
Batch Size
 So why not choose a large batch size to increase capacity?
Larger Batch Leads to a Lot of Inventory(either in process or in storage)
Production with large batches
Cycle
Inventory
Production with small batches
Cycle
Inventory
Produce Sedan
Produce Station wagon
Beginning of
Month
End of
Month
Example: 2 car models. Average demand is 400 per day.
Beginning of
Month
End of
Month
Choosing a “Good” Batch Size
Requires balance of capacity and inventory since
both increase with increases in batch size.
General principals
Capacity at a bottleneck is extremely valuable;
If setup occurs at a bottleneck, increase batch size.
If setup occurs at non-bottleneck, decrease batch size
Capacity as a function of Batch Size (60)
Batch Size
Supports
Ribs
Total
Capacity
Set-Up
Prododuction Time Set-Up Prododuction Time Time
per minute
1
60
1
60
1
122
0.01
12
60
12
60
12
144
0.08
24
60
24
60
24
168
0.14
36
60
36
60
36
192
0.19
48
60
48
60
48
216
0.22
60
60
60
60
60
240
0.25
120
60
120
60
120
360
0.33
240
60
240
60
240
600
0.40
360
60
360
60
360
840
0.43
720
60
720
60
720
1560
0.46
1440
60 x 60 = 0.25 unit/min
1440
60
1440 1/3 = 3000
(1/240)
.333 unit/min 0.48
2880
60
2880
60
2880
5880
0.49
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part
Step 2
3 min/part
Capacity as a function of Batch Size (240)
Batch Size
Supports
Ribs
Total
Capacity
Set-Up
Prododuction Time Set-Up Prododuction Time Time
per minute
1
60
1
60
1
122
0.01
12
60
12
60
12
144
0.08
24
60
24
60
24
168
0.14
36
60
36
60
36
192
0.19
48
60
48
60
48
216
0.22
60
60
60
60
60
240
0.25
120
60
120
60
120
360
0.33
240
60
240
60
240
600
0.40
360
60
360
60
360
840
0.43
720
60
720
60
720
1560
0.46
1440
60 x240 = 0.4 unit/min
1440
60
1440 1/3 = 3000
(1/600)
.333 unit/min 0.48
2880
60
2880
60
2880
5880
0.49
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part
Step 2
3 min/part
Capacity as a function of Batch Size (120)
Batch Size
Supports
Ribs
Total
Capacity
Set-Up
Prododuction Time Set-Up Prododuction Time Time
per minute
1
60
1
60
1
122
0.01
12
60
12
60
12
144
0.08
24
60
24
60
24
168
0.14
36
60
36
60
36
192
0.19
48
60
48
60
48
216
0.22
60
60
60
60
60
240
0.25
120
60
120
60
120
360
0.33
240
60
240
60
240
600
0.40
360
60
360
60
360
840
0.43
720
60
720
60
720
1560
0.46
1440
60 x120 = 0.333 unit/min
1440
60
1440 1/3 = 3000
(1/360)
.333 unit/min 0.48
2880
60
2880
60
2880
5880
0.49
Step 1
Activity Time
one Steer support: 1 min/part
Two Rib: 0.5 min/part
Step 2
3 min/part
Batch size for our example
For our example, the milling machine is the bottleneck
(p=2 min/unit) plus a setup time of 120 minutes, as
compared to the assembly process of 3 minutes/unit.
To find the recommended batch size we need to have a
target CT. The CT is variable for the bottleneck
depending on the batch size because of setup.
Therefore, we will use the CT for smallest capacity of
the non-bottleneck steps.
Step 1
Activity Time
Setup time:
one Steer support: 1 min/part
Two Rib: 0.5 min/part
60 minutes x 2 = 120 minutes
Step 2
3 min/part
Batch size for our example
Capacity given Batch Size
=
Batch Size
Set-up time + Batch-size*Time per unit
And we will set Capacity = Capacity for the slowest non-bottleneck
SO:
Batch Size
Cap for the slowest non-bottleneck =
Batch Size
0 + Batch-size*3
=
Set-up time + Batch-size*Time per unit
Batch Size
120 + Batch-size*2
Therefore we can solve for recommended batch size:
B = 120
0 + Batch-size*3
= 120 + Batch-size*2
Choosing a “Good” Batch Size
0.5
Capacity
1/p
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
0
Batch<120 no products in non-bottleneck
Batch>120 piles up inventory
650
610
570
530
490
450
410
370
330
290
250
210
170
130
90
50
10
Batch Size
Example (Batch sizes are 50, 249, and 251)
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Q=50
Processing time for
one batch
Step 1
Step 2
What is a bottleneck?
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch size is 50 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 50 = 25
60/25 = 2.4
2.4*50 = 120
Step 2
40 + 0.1 x 50 = 45
60/45 = 1.33
1.33*50 = 66.66
Example (Batch sizes are 50, 249, and 251)
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Q=100
Processing time for
one batch
Step 1
Step 2
What is a bottleneck?
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch size is 100 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 100= 35
60/35 = 1.714
1.714*100 = 171.4
Step 2
40 + 0.1 x 100= 50
60/50 = 1.2
1.2*100 = 120
Example (Batch sizes are 50, 249, and 251)
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Q=249
Processing time for
one batch
Step 1
Step 2
What is a bottleneck?
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch size is 249 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 249= 64.8
60/64.8 = 0.9259
0.9259 x 249 = 230.549
Step 2
40 + 0.1 x 249= 64.9
60/64.9 = 0.9244
0.9244 x 249 = 230.176
Example (Batch sizes are 50, 249, and 251)
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Q=251
Processing time for
one batch
Step 1
Step 2
What is a bottleneck?
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch size is 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 251= 65.2
60/65.2 = 0.9202
0.9202 x 251 = 230.97
Step 2
40 + 0.1 x 251= 65.1
60/65.1 = 0.9217
0.9217 x 251 = 231.34
Example (Batch sizes are 50, 249, and 251)
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch sizes are 50, 249 or 251 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Q=300
Processing time for
one batch
Step 1
Step 2
What is a bottleneck?
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Compute the capacity of the system when the batch size is 300 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 300= 75
60/75 = 0.8
0.8 x 300 = 240
Step 2
40 + 0.10 x 300 = 70
60/70 = 0.857
0.857 x 300 = 257.1
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
For what maximum value of batch size does step 2 become a bottleneck in the system?
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.10 min/part
Setup Time
15min
40 min
For what maximum value of batch size does step 2 become a bottleneck in the system?
Compare the processing times (including setup) of two steps.
If processing time at Step 1 is greater than at Step 2, Step 1 becomes a bottleneck.
Processing time @step 1 >= Processing time @step 2
Set up (@ step 1) + B x processing time (@ step 1) >=
Set up (@ step 2) + B x processing time (@ step 2)
15 min + 0.2 x B >=40 min + 0.1 B  0.1B >=25  B >=250
Answer: If batch size is less than 250, Step 2 is a bottleneck.
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 1 part.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Step 1
Step 2
Step 3
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 1 part.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Step 1
15 + 0.2 x 1= 15.2
60/15.2
Step 2
20 + 0.2 x 1 = 20.2
60/20.2
Step 3
40 + 0.10 x 1 = 40.1
60/40.1
Capacity
(# of units per hour)
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 50 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 50= 25
60/25 = 2.4
2.4*50 = 120
Step 2
20 + 0.2 x 50 = 30
60/30 = 2.0
2 * 50 = 100.0
Step 3
40 + 0.10 x 50 = 45
60/45 = 1.33
1.33*50 = 66.66
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 199 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 199= 54.8
60/54.8 = 1.095
1.095*199 = 217.88
Step 2
20 + 0.2 x 199 = 59.8 60/59.8 = 1.003
1.003 *199 = 199.67
Step 3
40 + 0.10x199 = 59.9 60/59.9 = 1.0016
1.0016 * 199 = 199.33
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 200 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 200= 55
60/55 = 1.09
1.09*200 = 218.18
Step 2
20 + 0.2 x 200 = 60
60/60 = 1.0
1 * 200 = 200.0
Step 3
40 + 0.10 x 200 = 60
60/60 = 1.0
1 * 200 = 200.0
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 201 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1
15 + 0.2 x 201= 55.2
60/55.2 = 1.087
1.087*201 = 218.487
Step 2
20 + 0.2 x 201 = 60.2
60/60.2 = 0.9967
0.9967 * 201 = 200.337
Step 3
40 + 0.10 x 201 = 60.1
60/60.1 = 0.9983
0.9983 * 201 = 200.6583
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Compute the capacity of the system when the batch size is 500 parts.
What is the bottleneck?
Processing time for one batch = Setup Time + Batch size * runtime (min)
Processing time for
one batch
Capacity
(# of batches per hour)
Capacity
(# of units per hour)
Step 1 15 + 0.2 x 500= 115
60/115
(60/115) x 500
Step 2 20 + 0.2 x 500 = 120
60/120
(60/120) x 500
Step 3 40 + 0.10 x 500 = 90
60/90
(60/90) x 500
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
For what maximum value of batch size is step 3 bottleneck in the system?
Example
Step 1
Step 2
Activity Time
0.2 min/part
0.2 min/part
Setup Time
15min
20 min
Step 3
0.10 min/part
40 min
For what maximum value of batch size is step 3 bottleneck in the system?
Set up (@ step 3) + B x processing time (@ step 3)
= Set up (@ step 2) + B x processing time (@ step 2)
40 + B x 0.1 = 20 + B x 0.2  20 = 0.1 B  B = 200
Example
Step 1
Step 2
Activity Time
0.15 min/part
0.2 min/part
Setup Time
30 min
20 min
Step 3
0.10 min/part
40 min
Practice Problem
Q5.5 (JCL Inc.) (a)
Practice Problem
Q5.5 (JCL Inc.) (b)
Practice Problem
Q5.5 (JCL Inc.) (c)
Observations
Setups have an impact on process capacity so it is important to
integrate them when choosing batch size:
Use either setup time or setup cost to determine batch size
If we adopt a process flow perspective, then setup TIMEs
should be used to determine batch size
If we are incurring out-of-pocket cost and the focus is on a
single resource, then use setup COSTS to determine batch
sizes.
If we encounter both, then compute the Q based on both and
choose one for implementation