Homework 1 - Wine Ordering problem
Kramer is a catalog retailer that offers a large collection of wines to its customers, who receive a catalog every two months from the company. For the wines to be listed in a catalog, Kramer has to forecast the demand several months before publishing the catalog and then place orders to the growers. The purchase price Kramer pays a grower is 50% of the list price. The grower is responsible for the cost of shipping wines to 1Cramer's warehouse. For a wine that cannot be sold during the regular catalog season, it is discounted by 40% of its retail price in future catalogs and it takes on average an additional 8 months before the wine can be sold. The warehousing operating cost is 0.1 Euro per month per bottle. The cost of capital of the company is 20%. (If a wine is sold during the regular catalog season, the time it spends in warehousing is very short and can be assumed to be zero.) Regardless of whether a wine is sold during the regular catalog season or not, Kramer pays 1 Euro per bottle for shipping and handling to fulfill customer orders. When stock-out occurs, the unsatisfied demand will be lost because it is not possible for Kramer to re-order during the catalog season. Kramer is planning for the next catalog. After analyzing the past data, Kramer found that the mean and the standard deviation of the A/F ratios from the past are respectively 0.86 and 0.30. For the wine Chinon that will be listed in the next catalog, the forecast is 10.000 bottles and its list price is 10 Euro. Suppose Kramer would like to use a Normal distribution to approximate the demand uncertainty of Chinon.
a. What should be the mean and the standard deviation of Chinon's demand distribution?
b. How many bottles of Chinon should Kramer order from the grower?
Homework 2: Williantsport Hospital case
Read the Williamsport Hospital case and hand in answers to the following questions. Each group should submit only one write-up.
1. List the pros and cons of the proposed service line approach.
2. The number of patients within each service line on any day is a random variable. Assume that this random variable has a normal distribution with the standard deviation equal to the square root of the mean. For example, for the head injury service line, the mean is 9.07 and the standard deviation is √(9.07) = 3.01. According to Kramer's assumptions, each physical therapist can serve three patients per day. Thus three physical therapists in the head injury service line have the capacity to treat nine patients per day. Since the average number of patients is 9.07, with three physical therapists, the probability is about 0.5 that the demand for physical therapy will not be met. Suppose you assigned four physical therapists to the head injury line.
What is the probability that the demand for physical therapy will not be met on a particular day? Suppose the management would like to have a service level of at least 95%. That is, the probability that the demand for physical therapy will not be met on any given day should be less than 5%. How many physical therapists would you assign to the head injury service line?
3. How many physical therapists would you assign to each of the other four other service lines? What is the total number of physical therapists required under the service line organization? Compare that number to how many you would need if the physical therapists were organized in a single physical therapy department, as is currently the case, rather than in the proposed five service lines. Explain your results.
4. In what other ways could Kramer organize the physical therapists? What other options, if any, can you suggest to capture the benefits of the service lines while still maintaining a reasonable level of physical therapist utilization? Justify your suggestion.
Attachment:- Case.rar