You are the owner of Hotspices.com, an online retailer of hip, exotic, and hard-to-find spices. Consider your inventory of saffron, a spice (generally) worth more by weight than gold. You order saffron from an overseas supplier with a shipping lead time of four weeks and you order weekly. Average quarterly demand is normally distributed with a mean of 415 ounces and a standard deviation of 154 ounces. The holding cost per ounce per week is $0.75. You estimate that your back-order penalty cost is $50 per ounce. Assume there are 4.33 weeks per month.
a. If you wish to minimize inventory holding costs while maintaining a 99.25 percent in- stock probability, then what should your order-up-to level be?
b. If you wish to minimize holding and back-order penalty costs, then what should your order-up-to level be?
c. Now consider your inventory of pepperoncini (Italian hot red peppers). You can order this item daily and your local supplier delivers with a two-day lead time. While not your most popular item, you do have enough demand to sell the five-kilogram bag. Average demand per day has a Poisson distribution with mean 1.0. The holding cost per bag per day is $0.05 and the back-order penalty cost is about $5 per bag. What is your optimal order-up-to level?