You are the owner of ExoticCooking.com, an online retailer of hip, exotic, and hard-to-find spices. Consider your inventory of saffron, generally worth more by weight than gold. You order saffron from an overseas supplier with a shipping lead-time of four weeks and that you order weekly. Your 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 that there are 4.33 weeks per month.
a. If you wish to minimize inventory holding costs while maintaining 99.25% fill rate, then what should your order up-to level be?
b. If you wish to minimize inventory holding costs while maintaining 99.25% in-stock probability, then what should your order up-to level be?
c. If you wish to minimize inventory holding and backorder penalty costs, then what should your order up-to level be?
d. If you arbitrarily decide an order up-to level of 250, what fraction of the demand will not be met immediately? What is the expected on-hand inventory at the beginning of a period?