True Colors Co. purchases a number of chemical additives for its line of colors and dyes.

After a recent classification of stock, the inventory manager has to decide the purchase criteria for the B items. Consider the pigment Red-105: demand forecast for the next 12 months of 200 gallons, with a standard deviation of 50 gallons. They cost $25/gallon at the supplier’s plant, in addition to $30 per order for shipping and handling; expected lead time is 45 days. It is believed that each day costs the firm $5 per gallon short. Inventory carrying charge is 0.18 $/$/year.

a. What (s, Q) policy should be adopted for this product. What is the implicit TBS?

b. Looking through some of the recent orders, the manager observed that, in fact, 90%

of the shipments arrived in 30 days, the remainder in 75 days (the later arrivals due to unpredictable losses at the supplier). Should the inventory policy be adjusted to account for this lead time uncertainty? Discuss.