1. Process and Capacity Analysis Capacity Analysis Tutorial
Problem Description
Solution
Developed by:
Alex J. Ruiz-Torres, Ph.D.

2. Problem Description Cut Sew Final Prep out
A highly specialized make to order clothing manufacturer is organized into three areas, cutting, sewing, and final prep.
65% of the products go to final prep.
There is one type of resource per step of the process.
Cut and final prep personnel work 150 hours per month.
Sew staff work 137 hours per month (union rules).
Sew
65%
Final Prep
out

3. Problem Description Current process information 14 11 4 7 8 12 5 10 6
Cut takes 6.8 min/unit
Final Prep takes 15 min/unit
The sew process has been recently changed due to new equipment.
24 observations (in minutes) of the new process have been collected – table below.
An allowance of 20% is used to determine standard times. 14 11 4 7 8 12 5 10 6 16 13 15

4. Problem Description. What must be answered.
How many resources are needed per step if the demand is 5,000 units per month?
What is the utilization of each resource?
What is the maximum output with the resulting resource plan?

5. Solving it. First step
First step is to have the standard time for all the activities. In this case two are provided.
Cut takes 6.8 min./unit
Final Prep takes 15 min/unit
Need to calculate the standard time for the sewing process.

6. Solving it. First step
To do this we determine the average of the values in the table.
The average = mins,
This is the normal time (nt). 14 11 4 7 8 12 5 10 6 16 13 15

7. Solving it. First step st (sew) = 13.3 mins.
To determine the standard time we need to include the allowance.
Standard time (st) = nt/(1 – allowance)
allowance = 20% (from the problem description)
st = /( 1 – 20%) =
We will round it to 13.3 minutes.
st (sew) = 13.3 mins.

8. Equations needed dp = Demand per product tp = Time per product
Rt = Total work time required to meet demand
=  for all p (dp × tp)
At = Time available per worker
x = ceiling function. For example 2.5 = 3
Nw = Number of workers = Rt/At
Op = Output if all available time is dedicated to product p
= (Nw  At) / tp
U = Utilization = Rt / (Nw  At)
Nw  At = total
available time

9. Solving it. Question 1.
How many resources are needed per step if the demand is 5,000 units per month?

10. Solving it. Question 1 We calculate the number of workers per area.
Step: cut
There is only one product, therefore d1 (cut) = 5,000.
We use the equations to calculate the Nw
t1 (cut) = 6.8 min/unit
Rt = 6.8 × 5,000 = 34,000min.
At = 150 hours. But need to convert to minutes
= 150 × 60 = 9,000 min.
Nw = 34,000/9,000 = 3.778 = 4 workers

11. Solving it. Question 1 We calculate the number of workers per area.
Step: sew
There is only one product, therefore d1 (sew) = 5,000.
We use the equations to calculate the Nw
t1 (cut) = 13.3 min/unit
Rt = × 5,000 = 66,500min.
At = 137 hours. But need to convert to minutes
= 137 × 60 = 8,220 min.
Nw = 66,500/8,220 = 8.09 = 9 workers

12. Solving it. Question 1 d1 (final prep) = 5,000  65% = 3,250.
We calculate the number of workers per area.
Step: final prep
The problem description indicates 65% of the units need this step.
d1 (final prep) = 5,000  65% = 3,250.
We use the equations to calculate the Nw
t1 (cut) = 15 min/unit
Rt = 15 × 3,250 = 48,750min.
At = 150 hours. But need to convert to minutes
= 150 × 60 = 9,000 min.
Nw = 48,750/9,000 = 5.41 = 6 workers

13. Solving it: Question 1
How many resources are needed per step if the demand is 5,000 units per month?
Resource capacity plan:
Step Nw (number of workers)
Cut 4
Sew 9
Final prep 6

14. Solving it: Question 2 What is the utilization of each resource? Step
U = Utilization = Rt / (Nw  At)
Step Nw Rt At U
Cut 4
34,000
9,000
94.4%
Sew 9
66,500
8,220
89.9%
Final Prep 6
48,750
90.3%
U = 34,000 / (4  9,000) = 34,000/ 36,000 = 94.4%
Results. All workers are busy, close to 90%.
The cut step workers have the highest utilization,
while the sew step workers have the lowest utilization.

15. Solving it: Question 3
What is the maximum output with the resulting resource plan?
Op = Output if all available time is dedicated to product p = (Nw  At) / tp
Step Nw tp At Op
Cut 4
6.8
9,000
5,294
Sew 9
13.3
8,220
5,562
Final Prep 6 15
3,600
O = (4  9,000)/ 6.8 = 36,000/ 6.8 = 5,294

16. Solving it: Question 3
Given the final prep processes 65% of the units that come in, the 3,600 must be divided by this percent.
3,600/65% = 5,538.
Maximum outputs
Cut: 5,294
Sew: 5,562
Final Prep: 5,538
The step with the smallest output capacity (cut) determines the maximum overall output. Therefore it would 5,294.
from prev. slide