Chicago’s Treadway Tires Dealer must order tires from its national warehouse. It costs $10,000 to place an order. Annual tire sales are normally distributed with mean 20,000 and standard deviation 5000. It costs $10 per year to hold a tire in inventory, and the lead time for delivery of an order is normally distributed with mean three weeks and standard deviation one week. Assume that all shortages are backlogged.

a. Find the (R,Q) policy the company should use to meet a service level where 96% of all demand is met with on-hand inventory.

b. Assume that the company could pay C dollars per year to decrease the variability in lead times to essentially 0. That is, the lead time would then be a certain three weeks. What is the most it would be willing to pay (and still meet the service level in part a)?