ANALYSIS FOR PRODUCTION MANAGEMENT
1. Magnum Products packages lawn fertilizer for sale to local garden stores. Each bag is labeled as containing 20 pounds. In order to ensure that no customers are shorted, the firm requires that each bag contains at least 20 lbs., with a target of 20.1 lbs. and an upper limit of 20.2 lbs. The firm operates two packaging machines, and wishes to check whether they are performing satisfactorily. A sample from each is taken, with the following results:
Machine A Machine B
1 bag contained 20.01 2 bags contained 20.03
3 bags contained 20.02 7 bags contained 20.05
5 bags contained 20.06 9 bags contained 20.10
6 bags contained 20.10 2 bags contained 20.12
4 bags contained 20.12
1 bag contained 20.18
a. After looking at the 2 samples above, one employee concluded that both machines are operating satisfactorily, since none of the sampled bags were out of tolerance. Explain why this is not a satisfactory criterion for quality control purposes.
b. (5) Find the mean and sample standard deviation of each sample. What are the lightest and heaviest bags that are expected to occur for each machine, assuming a normal distribution?
Is each machine operating satisfactorily at present?
c. (3) Find the capability index for each machine. Is the packaging process capable of being controlled for Machine A? For machine B? What type of action, if any, should the firm take?
2. Sappora Office Supply is considering whether to purchase flood insurance for its headquarters building in North Natomas, CA. The firm expects that in each year, there is a 2% chance of a major flood causing $1,000,000 in damage, and a 4% chance of a minor flood causing $100,000 in damage. The firm is considering 3 options:
Policy A costs $21,000/year. It has a deductible of $30,000, then pays for 80% of any damages above that amount.
Policy B costs $25,000/year. It has a $10,000 deductible, and pays all damages above that amount.
Self-insure. The firm pays for all its own damages should they occur.
(a) Develop a decision matrix that shows the actual dollar outcomes that can occur for each of the three options above, and their expected values. Also calculate the standard deviation for each option. If the firm is risk-neutral, which option should it choose?
(b) Now suppose the firm is risk-averse. (i) Which strategy should be chosen, if the firm follows a maxi-min policy? (ii) What should the firm choose, if it selects the policy with the best expected value, subject to a loss limit of no more than $300,000? (ii) If the firm considers both expected value and standard deviation, can any strategies be rejected as dominated? Explain.
3. Judith operates a machine that cuts steel pipe. The machine has performed satisfactorily up till now. Over the past several months, she has taken a sample of 4 pipes each hour and carefully measured them, to be sure that the machine continues to perform properly. She maintains a mean control chart based on these samples.
Based on thousands of units that have previously been sampled from this machine, the mean of her hourly samples (Xbarbar) has been 120 inches. The population standard deviation is= .1 inch.
a.What are the upper and lower mean control limits for this process, if the firm uses a 3-sigma mean control chart?
b. (6) Suppose the next 5 hourly samples Judith takes are as shown below:
1 2 3 4 5
119.9 119.8 120 119.8 120.0
119.9 119.9 120 120.1 120.1
120.0 119.9 120.1 120.2 120.2
120.2 120.0 120.1 120.2 120.2
Draw a 3 sigma mean control chart and plot these 5 samples on it. Is the mean in control? Show how you know.
c. (1) Would your answer differ, if the firm used 2-sigma control charts instead of 3-sigma? Explain.
4. In class, we discussed two criteria that are often used to evaluate the effectiveness of a firm's mission statement.
a. What were the two criteria?
b. Find an example of a mission statement that you feel is a good example of an effective statement. (You can copy it by hand, or print it out, as you prefer) Explain how it fits the criteria above. Don't use firms whose mission statements were used as examples in class.
c. Find an example of a mission statement that you feel is a poor or ineffective example, and explain why you dislike it. Again, don't use the firms we discussed as examples in class.
Hint: these statements may also be called Statement of Values or something similar, and are often located on a firm's web page, under the heading Investor Relations.