PART A - Two-workstation line without variation

Consider the following two-workstation process:

WORKSTATION 1

Processing time = 1 minute

WORKSTATION 2

Processing time = 1 minute

In this scenario, there is no uncertainty about the processing time of the two workstations. That is, each workstation takes exactly one minute to perform its tasks before sending the unit on.

See below Image, and then use the Process Metrics data to answer questions 1, 2, and 3.

Work Station A Task Time = 1 Time Unit = Mins Utilization = 100%

Work Station B Task Time = 1 Time Unit = Mins Utilization = 100%

Process Metrics Avg. Throughput Time (Min) = 2 Cycle Time = 1 Min Output Rate Per Hour = 60 Utilization = 100%

1. What is the cycle time for this line?

Ans: Cycle Time = Output Time / Units

= 60 / (1 x 60 Min)

= 1 Minutes

Hence, the cycle time is 1 minute

2. What is the lines output during a 480-minute (8-hour) period?

Ans: Lines output = 8 hours x 60 Minutes

= 480 units

Hence, the lines output is 480 units

3. What is the utilization of each workstation during the 480-minute period?

Ans: The Processing time of both the workstation is 1 Min and the cycle time is 1 Minute. As the processing time of the workstation is equal to the cycle time, the utilization percentage of each workstation is 100%

PART B

Two-workstation line with variation

Work Station 1 Processing time = U(0.5,1.5)

Work Station 2 Processing time = U(0.5,1.5)

Now suppose the processing time for each workstation averages one minute, but varies along a uniform distribution ranging from 0.5 to 1.5 minutes (represented by U(0.5,1.5)).

Q4. Qualitatively, how do you expect your answers to the three previous questions to change for this process?

See the below table workstations with Random Variations & no buffers & watch closely to illustrate how the process changes for this uniform distribution. Then answer question

Workstation A Task Time: 1.00 +-0.50 Time Unit: Mins Utilization: 87%

Work Station B Task Time: 1.00 +-0.50 Time Unit: Mins Utilization: 85%

Process Metrics Avg. Throughput Time (Min) = 2.16 Cycle Time = 1.16 Output Rate per Hour = 51.52 Utilization = 86.02%

Q5. Why do the operating performance measures have the effect noted in Question 4?

PART C - The magnitude of variation

Now that you have some insight into how variability in processing time affects operational performance, lets see what happens when there is more or less variability. The following line has more variability, with the processing time for each workstation ranging from zero to two minutes on a uniform distribution (thus, average processing time for each workstation remains one minute).

See the below table workstations with Random Variations & no buffers and observe how the increase in variation affects operational performance.

Workstation A Task Time: 1.00 +-1.00 Time Unit: Mins Utilization: 73%

Work Station B Task Time: 1.00 +-1.00 Time Unit: Mins Utilization: 74%

Process Metrics Avg. Throughput Time (Min) = 2.32 Cycle Time = 1.33 Output Rate per Hour = 45.22 Utilization = 73.41%

The following line has less variability, with processing time ranging from 0.75 to 1.25 minutes on a uniform distribution (thus average processing time for each workstation remains one minute). Click start to play the video and observe how the decrease in variation affects operational performance.

Workstation A Task Time: 1.00 +-0.25 Time Unit: Mins Utilization: 92%

Work Station B Task Time: 1.00 +-0.25 Time Unit: Mins Utilization: 93%

Process Metrics Avg. Throughput Time (Min) = 2.08 Cycle Time = 1.08 Output Rate per Hour = 55.48 Utilization = 92.43%

Q6. Compared to the results in Part B, how do increases or decreases in variation affect the lines output and each workstations utilization? Why?

PART D - Four-workstation line with variation

Now that you have seen how variability affects a two-workstation line, lets see what happens in a more realistic line that has more processing steps. Consider a line that has four workstations with processing times ranging from 0.5 to 1.5 minutes on a uniform distribution (thus averaging one minute). Consider how you expect the line output and workstation utilization to differ relative to a two-workstation line with these workstations (the line in Part B) and why. After thinking about these questions, click start to play the video and observe how variability affects the line output and workstations utilization of this four-workstation line.

Work Station A Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 78%

Work Station B Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 81%

Work Station C Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 79%

Work Station D Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 79%

Process Metrics Avg. Throughput Time (Mins) = 4.60 Cycle Time in Mins = 1.26 Output Rate Per Hour = 47.48 Utilization = 79.35%

Q7. Compare the results for the two-workstation line from Part B to this four-workstation line. From the videos, note how they differ in terms of blocking and starving, as well as the resulting line output. Hypothesize how the number of workstations might moderate (a) the relationship between variability and workstations utilization, and (b) the relationship between variability and line output.

PART E - Buffers

To illustrate how buffers affect the operational performance of a process with variability, we return to the scenario from Part D: a four-workstation process where the processing time of each workstation varies along a uniform distribution from 0.5 to 1.5 minutes. In this instance, however, a buffer that can hold one unit of work-in-process inventory is placed between the four workstations. From your work in Part B, review the workstation utilization and line output for the 480-minute period. How do you anticipate the buffer will affect the utilization of each workstation and the line output? After thinking about these questions, click start to play the video and observe the line output and workstations utilization.

Work Station A Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 92%

Buffer 1 1

Work Station B Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 93%

Buffer 0 1

Work Station C Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 91%

Buffer 0 1

Work Station D Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 90%

Process Metrics Avg. Throughput Time (Mins) = 4.60 Cycle Time in Mins = 1.26 Output Rate Per Hour = 47.48 Utilization = 79.35%

Q8. Based on these results, how do line output, throughput time, and workstations utilization differ from those for the process in Part B (which is otherwise the same) when we add a one-unit buffer? Why?

The following two table Work station with Random Variable & Buffer depict this four-workstation process with a buffer with an increased capacity of two units, then four units.

See the simulation table. As you observe these lines, consider how increasing buffer capacity affects operational performance.

Work Station A Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 96%

Buffer 0 2

Work Station B Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 94%

Buffer 1 2

Work Station C Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 94%

Buffer 0 2

Work Station D Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 95%

Process Metrics Avg. Throughput Time (Mins) = 6.83 Cycle Time in Mins = 1.07 Output Rate Per Hour = 56.11 Utilization = 95.01%

Work Station A Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 97%

Buffer 3 4

Work Station B Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 96%

Buffer 1 4

Work Station C Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 96%

Buffer 0 4

Work Station D Task Time = 1.00 +-0.50 Time Unit = Mins Utilization = 95%

Process Metrics Avg. Throughput Time (Mins) = 8.72 Cycle Time in Mins = 1.05 Output Rate Per Hour = 57.37 Utilization = 96.07%

The following tables report the results for the four different lines with four workstations U(0.5,1.5) that you have observed. They differ only with respect to the presence of a buffer and the buffers capacity.

Four Workstations	No Buffers	One-Unit Buffer	Two-Unit Buffer	Four-Unit Buffer
Line Output for 480 Minutes	372	441	458	464
Average Throughput Time (in Minutes)	4.75	5.86	6.99	10.38
Cycle Time (in Minutes)	1.29	1.09	1.05	1.03
Output Rate in Capacity Units Per Hour	46.56	55.10	57.29	58.02
Utilization	75.24%	92.00%	94.83%	96.97%

Q9. Based on these results, how does buffer size affect line output and why?

Please help on Part B, Part C, Part D, & Part E Questions from 4 to 9

Part B:

Q4 Qualitatively, how do you expect your answers to the three previous questions to change for this process?

Q5. Why do the operating performance measures have the effect noted in Question 4?

Part C:

Q6. Compared to the results in Part B, how do increases or decreases in variation affect the lines output and each workstations utilization? Why?

Part D:

Q7. Compare the results for the two-workstation line from Part B to this four-workstation line. From the videos, note how they differ in terms of blocking and starving, as well as the resulting line output. Hypothesize how the number of workstations might moderate (a) the relationship between variability and workstations utilization

Part E:

Q8. Based on these results, how do line output, throughput time, and workstations utilization differ from those for the process in Part B (which is otherwise the same) when we add a one-unit buffer? Why?

Q9. Based on these results, how does buffer size affect line output and why?