1. Assignment Capacity The recorded solution to the first problem is available at

2. Key Problem 2
MamossaAssaf Inc. fabricates garage doors. Roofs are punched in a roof punching press (15 minutes per roof) and then formed in a roof forming press (8 minutes per roof). Bases are punched in a base punching press (3 minutes per base) and then formed in a base forming press (10 minutes per base), and the formed base is welded in a base welding machine (12 minutes per base). The base sub-assembly and the roof then go to final assembly where they are welded together (10 minutes per garage) on an assembly welding machine to complete the garage. Assume one operator at each station. 8 R -
Form 10 B 15
Punch 12
Weld
Assembly 3
Roof
Base
Door

3. Key Problem 2: Flow Time 8 R -
Form 10 B 15
Punch 12
Weld
Assembly 3
Roof
Base
Door
What is the Theoretical Flow Time? (The minimum time required to produce a garage from start to finish.)
Flow Time 
Theoretical Flow Time 
Roof Path: 15+8 = 23
Base Path: = 25
Max = = 35
Critical Path = Max(33,35) = 35
Theoretical Flow Time = 35

4. Key Problem 2: Capacity Process Capacity is 4 per hour
(b) What is the capacity of the system in terms of garages per hour? 8 R -
Form 10 B 15
Punch 12
Weld
Assembly 3
Roof
Base
Door
R-Punch:1/15 per min. or 4 per hr.
R-Form:1/8 per min. or 7.5 per hr.
B-Punch:1/3 per min. or 20 per hr.
B-Form:1/10 per min. or 6 per hr.
Welding: 1/12 per min. or 5 per hr.
Assembly: 1/10 per min. or 6 per hr.
Process Capacity is 4 per hour
(c) If you want to increase the process capacity, what is the activity process that you would put some additional resource?
R-Punch

5. Key Problem 2: Capacity
(d) Compute utilization of all the resources at the full process capacity. In other words, assume that the throughput is equal to process capacity. Throughput = 4
In reality, utilization of all the resources will be less than what we have computed.
This process can never produce 4 flow units per hour continually.
R-Punch Utilization = 4/4 = 100%.
R-Form Utilization = 4/7.5 = 53.33%.
B-Punch Utilization = 4/20 = 20%.
B-Form Utilization = 4/ 6 = 66.67%.
Welding Utilization = 4/5 = 80%.
Assembly Utilization = 4/6 = 66.67%
No Process can work at 100% capacity. Impossible.

6. Key Problem 2: Bottleneck Shift
(e) Suppose we double the capacity of the bottleneck by adding the same capital and human resources. What is the new capacity of the system. 8 R -
Form 10 B 15
Punch 12
Weld
Assembly 3
Roof
Base
Door
R-Punch: 2/15 per min. or 8 per hr.
R-Form:1/8 per min. or 7.5 per hr.
B-Punch:1/3 per min. or 20 per hr.
B-Form:1/10 per min. or 6 per hr.
Welding: 1/12 per min. or 5 per hr.
Assembly: 1/10 per min. or 6 per hr.
Process Capacity is 5 per hour

7. Key Problem 2: Diminishing Marginal Return
(f) We doubled the capacity of the bottleneck but the capacity of the system increased by only 25%. This situation is an example of what managerial experiment?
Bottleneck shifts from R-Punch to Welding
Diminishing Marginal Return
g) Now suppose we return back to the original situation where we have a single machine and a single operator at each operation. However, also suppose that we pool R-Punch and B-Punch machines and we cross-train their operations and form a new resource pool named Punch where both R-Punch and B-Punch operations can be done in this resource pool. What is the new capacity of the system?

8. Key Problem 2: Pooling and Cross Training
R-Form 8
B-Form 10
R-Punch 15
Punch
B-Punch 3
R-Punch 15
B-Punch 3
Weld 10
Assembly
Assembly 12
You may imagine activities R-Punch Activity and B-Punch Activity on the two Punch Resources in the Punch Resources Pool as follows
Punch Resource Pool

9. Key Problem 2: Pooling and Cross Training
R-Form 8
B-Form 10 12
Weld
Assembly
R-Punch&B-Punch
Punch
15,3
Punch: 2/18 per min. or 6.67 per hr.
R-Form:1/8 per min. or 7.5 per hr.
B-Form:1/10 per min. or 6 per hr.
Welding: 1/12 per min. or 5 per hr.
Assembly: 1/10 per min. or 6 per hr.
Process Capacity is 5 per hour

10. Key Problem 2: Productivity Improvement -Method, Training, Technology, Management
h) This situation is an example of what managerial experiment?
Cross training and pooling can increase the capacity
Usually cost of cross training and pooling is lower than the cost of adding the second resource unit.
k) Compute utilization of all the resources if the throughput is equal to 4 units per hour. What is the utilization of the bottleneck.

11. Key Problem 2: Productivity Improvement -Method, Training, Technology, Management
i) Now suppose by investing in improved jigs and fixtures (technology), and also by implementing a better method of doing the job, and also training, we can reduce the welding time from 12 minutes to 10 minutes. What is the new capacity of the system ?
R-Form 8
B-Form 10
Process Capacity is 6 per hour
R-Punch&B-Punch
Punch
15,3
Weld 10
Assembly
Assembly 10

12. Key Problem 2: More Than One Bottleneck
R-Form 8
B-Form 10
R-Punch&B-Punch
Punch
15,3
Weld 10
Assembly
Assembly 10
j) Why it is impossible to work at 100% of capacity?
There are 3 bottlenecks. This is a risky situation. Any of the bottlenecks could cause the throughput of the system to fall below 6 per hour.
The more bottlenecks in the system, the higher the probability of not meeting the capacity.
Suppose punch fail to provide input to B-Form for 1 hour, or B-Form fails to provide Weld, or Weld fails to provide Assembly- That hour of capacity perishes. Input material may also occur.

13. Key Problem 2: Critical Chain
R-Form 8
B-Form 10
R-Punch&B-Punch
Punch
15,3
Weld
Assembly 10 10
Not only the system has two bottlenecks, but one bottleneck feeds the second. Furthermore. Both paths to the last bottleneck are critical. They can both increase the flow time. 23
Path 2
Path 1
Assembly
Assembly 10

14. Lessons Learned
A process cannot have a throughput greater than or equal to its capacity.
Capacity is perishable- it is lost if input is not ready. The more the bottleneck recourses the lower the utilization.
Flow Time increases with utilization and does so sharply as utilization approaches 100%.
When we relax a Bottleneck Resource, the Bottleneck shifts to another resource
By doubling the bottleneck resource, the capacity usually does not double. This could be interpreted as diminishing marginal return situation.
One other way to increase capacity is cross training (for human resources ) and pooling (for Capital Resources).

15. Lessons Learned
Usually cost of cross training and pooling is lower than the cost of adding the second resource unit.
One other way to increase capacity in to reduce unit load. This is done by better management, (a) better methods, (b) training, (c) replacing human resources by capital resources (more advanced technology), and (d) better management.
Convergence points are important in managing the flow time. The more convergence points the high the probability of the flow time exceed the average flow time.
Over the long term, in a stable process, RT=I
At a single station with no limit on the capacity of the waiting line, Flow Time = V×U×T, where U is a measure of Utilization, V is a measure of Variability, and T is a measure of the Activity Time (or unit-load).