You are in charge of inventory control of a highly successful product retailed by your firm. Weekly demand for this item varies, with an average of 200 units and a standard deviation of 16 units. It is purchased from a wholesaler at a cost of $12.50 per unit. The supply lead lime is 4 weeks. Placing an order costs $50, and the inventory carrying rate per year is 20 percent of the item’s cost. Your firm operates 5 days per week, 50 weeks per year.
a. What is the optimal ordering quantity for this item?
b. How many units of the item should be maintained as safety stock for 99 percent protection against stock- outs during an order cycle?
c. If supply lead time can be reduced 102 weeks, what is the percent reduction in the number of units maintained as safety stock for the same 99 percent stock out protection?
d. If through appropriate sales promotions, the demand variability is reduced so that the standard deviation of weekly demand is 8 units Instead of 16, what is the percent reduction (compared to that In part (b) in the number of units maintained as safety stock for the same 99 percent stock out protection?