Operations Management and Quantitative Methods

Practice Exam 1

Section 1

You are in charge of a production process for a manufacturing company. For the questions below, assume that 50 parts were produced and 32 out of the 50 are good.

1. Let the random variable G = 1 if a part was good and zero, otherwise. What is the probability distribution of G?

2. There has been a recent concern of parts being recorded different than their actual outcome status (that is, good parts being recorded as bad parts and vice versa). Define the following random variables for i = 1, 2, . . . , 50 as:

• Ri = 1 if part i’s recorded label is different from its actual label • Ri = 0 if part i’s recorded label is the same as its actual label

It has been determined that parts are recorded correctly 52% of the time. What is the probability distribution of Ri?

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3. Suppose we want to ask how many times will a part’s label be incorrectly recorded? Define a new random variable T as:

T = R1 + R2 + . . . + R50

What is the probability distribution of T?

4. What is the expected value and variance of T?

5. Give an interval that is likely to contain 95% of the values of T.

6. What is the probability that more than 17 parts will be incorrectly recorded?

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Section 2

A manufacturing company has the process displayed below. The product only needs to go through one of the two drilling operations and one of the three assembly operations (the operations are “parallel” or “split”).

7. Assuming λ1 = µ1, what is the interarrival time (in minutes)?

8. Maintaining the above assumption, how fast does the current system actually produce another unit?

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9. What is the work in process buildup per hour between Sawing and Sanding?

10. What is the bottleneck stage in the process? What is the hourly capacity of the process?

11. If the firm operates on the standard production time-frame (8 hours per day, 22 days per month), what is the monthly capacity of the manufacturing process?

12. Suppose that a third drilling machine is added and it takes the same time as the original drilling machines. Does this affect the current system capacity? If so, what is the new system capacity and bottleneck stage?

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Section 3

Consider the production process for a product shown below.

13. How fast can the system produce another unit of output?

14. What is the capacity per hour?

15. Assume λ1 = µ1. What is the throughput time and queue time of the 50th unit? When will unit 50 be finished?

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