Quick Print Inc. uses plain and three-hole-punched paper for copying needs. Demand for each type of paper is highly variable. Weekly demand for the plain paper is estimated to be normally distributed with mean 100 and standard deviation 65 (measure in boxes). Each week a replenishment order is placed to the paper factory and the order arrives five weeks later. All copying orders that cannot be satisfied immediately due to lack of paper are back ordered. The inventory holding cost is about $1 per box per year.
a. Suppose that Quick Print decides to establish an order-up-to level of 700 for plain paper. At the start of the week, there are 523 boxes in inventory and 180 boxes on order. How many boxes will Quick Print order this week?
b. Again, suppose that Quick Print uses an order-up-to level of 700 for plain paper. What is Quick print’s fill rate?
c. What is Quick Print’s optimal order-up-to level for plain paper if it operates with 99% instock probability?
d. What is Quick Print’s optimal order-up-to level for plain paper if it operates with 99% fill rate?