The Jessica Co. has been searching for more formal ways to analyze its alternative courses of action. The expected value decision model was among those considered. In order to test the effectiveness of the expected value model, a l-year trial in a small department was authorized.

This department buys and resells a perishable product. A large purchase at the beginning of each month provides a lower cost than more frequent purchases and also assures that Jessica Co.

can buy all of the item it wants. Unfortunately, if too much is purchased the product unsold at the end of the month is worthless and must be discarded.

If an inadequate quantity is purchased, additional quantities probably cannot be purchased. If any should be available, they would probably be of poor quality and be overpriced. Jessica chooses to lose the potential sales rather than furnish a poor quality product. The standard purchase arrangement is $50,000 plus $0.50 for each unit purchased for orders of 100,000 units or more.

Jessica is paid $1.25 per unit by its customers.

The needs of Jessica’s customers limit the possible sales volumes to only four quantities per month—100,000, 120,000, 140,000, or 180,000 units. However, the total quantity needed for a given month cannot be determined prior to the date Jessica must make its purchases. The sales managers are willing to place a probability estimate on each of the four possible sales volumes each month. They noted that the probabilities for the four sales volumes change from month to month because of the seasonal nature of their customers’ businesses. Their probability estimates for December 19X8 sales units are 10% for 100,000, 30% for 120,000, 40% for 140,000, and 20% for 180,000. klp856 The following schedule shows the quantity purchased each month based upon the expected value decision model. The actual units sold and product discarded or sales lost are shown also.

Transcribed Image Text:

QUANTITY (IN UNITS) Sales units Purchased Sold Discarded lost January 100,000 100,000 0 20,000 February 120,000 100,000 20,000 0 March 180,000 140,000 40,000 0 April 100,000 100,000 0 80,000 May June 100,000 100.000 0 140,000 140.000 0 July 140.000 100,000 40,000 August 140.000 120,000 20,000 0 September 120,000 100,000 20,000 0 October 120.000 120,000 0 20,000 November 180,000 140,000 40,000 0 Required: a What quantity should be ordered for December 19X8 if the expected value decision model is used? b Suppose Jessica could ascertain its customers' needs prior to placing its purchase order rather than relying on the expected value decision model. What is the maximum amount it would be willing to pay to obtain this information for December? c The model did not result in purchases equal to potential sales except during 2 months. Is the model unsuitable in this case or is this a characteristic of the model? Explain your answer. (CMA Adapted.)