Cyber Chemicals uses liquid nitrogen on a regular basis. Average daily demand is 178 gallons with a standard deviation of 45. Due to a substantial ordering cost, which is estimated to be $58 per order (no matter the quantity in the order), Cyber currently orders from its supplier on a weekly basis. Cyber also incurs holding costs on its inventory. Cyber recognizes that its inventory is lowest at the end of the week but prefers a more realistic estimate of its average inventory. In particular, Cyber estimates its average inventory to be its average end-of-week inventory plus half of its average order quantity. The holding cost Cyber incurs on that average inventory is $0.08 per gallon per week. Cyber's supplier delivers in less than a day. Assume 52 weeks per year, five days per week.
a. Cyber wishes to maintain a 99.9 percent in-stock probability. If it does so, what is Cyber's annual inventory holding cost?
b. What is Cyber's annual ordering cost?
c. Should Cyber consider ordering every two weeks?