1. Annual demand for number 2 pencils at the campus store is normally distributed with mean 1,000 and standard deviation 250. The store purchases the pencils for 6 cents each and sells them for 20 cents each. There is a two-month lead time from the initiation to the receipt of an order. The store accountant estimates that the cost in employee time for performing the necessary paperwork to initiate and receive an order is $20, and recommends a 22% annual interest rate for determining holding cost. The cost of a stockout is the cost of lost profit plus an additional 20 cents per pencil, which represents the cost of loss of goodwill.
a. Find the optimal values of the reorder point R assuming that the lot size used is the EOQ.
b. Find the simultaneous optimal values of Q and R.
c. Compare the average annual holding, setup, and stock-out costs of the policies determined in parts (a) and (b).
d. What is the safety stock for this item at the optimal solution?
2. Consider the problem of satisfying the demand for number 2 pencils faced by the campus store mentioned in problem number 1.
a. Re-solve the problem, substituing a Type 1 service level criterion of 95 percent for the stock-out cost.
b. Re-solve the problem, substituting a Type 2 service level criterion of 95 percent for the stock-out cost. Assume that Q is given by the EOQ.
c. Find the simultaneous optimal values of Q and R assuming a Type 2 service level of 95 percent.
PLEASE SHOW ALL WORK.