The purchasing agent for a PC manufacturer is currently negotiating a purchase agreement for a particular electronic component with a given supplier. This component is produced in lots of 1000, and the cost of purchasing a lot is $30,000. Unfortunately, past experience indicates that this supplier has occasionally shipped defective components to its customers. Specifically, the proportion of defective components supplied by this supplier has the probability distribution given in the file P06_68.xlsx.
Although the PC manufacturer can repair a defective component at a cost of $20 each, the purchasing agent learns that this supplier will now assume the cost of replacing defective components in excess of the first 100 faulty items found in a given lot. This guarantee may be purchased by the PC manufacturer prior to the receipt of a given lot at a cost of $1000 per lot. The purchasing agent wants to determine whether it is worthwhile to purchase the supplier’s guarantee policy.
a. Create a cost table that specifies the PC manufacturer’s total cost (in dollars) of purchasing and repairing (if necessary) a complete lot of components for each possible decision and each outcome with respect to the proportion of defective items.
b. Use Precision Tree to identify the strategy that minimizes the expected total cost of achieving a complete lot of satisfactory microcomputer components.
c. Perform a sensitivity analysis on the optimal decision with respect to the number of components per lot and the three monetary inputs, and summarize your findings. In response to which of these inputs is the expected cost most sensitive?