Example 10 - D.R. Optical would like to determine an appropriate reorder point, and include some safety stock to deal with the variability in the demand for a particular popular eyeglass frame. Below is a table showing the probability distribution for the number of units D.R. Optical has experienced in demand during lead time. D.R. only orders from their supplier and only ships to their customers in multiples of ten. DEMAND DURING LEAD TIME (UNITS) 30 40 50 60 TOTAL: PROBABILITY 0.2 0.2 0.3 0.2 0.1 (a) What should Optical's reorder point without safety stock be? (b) The reorder point from part (a) does not account for the costs of stocking out in the event that actual demand exceeds average demand. Suppose the holding costs are $20 per frame per year, the stockout cost is $30 per frame, and Optical makes 6 orders per year. Determine an appropriate amount of safety stock for Optical, with the objective of keeping the expected sum of stockout costs plus additional holding costs at a minimum. With this safety stock, what is the probability of Optical experiencing a stockout? SAFETY STOCK ROP WITH SAFETY STOCK ADDITIONAL HOLDING COSTS ANNUAL STOCKOUT COSTS SUM OF EXPECTED ADDITIONAL HOLDING AND STOCKOUT COSTS