Firebird Packaging Operations manufactures small plastic cups used in a popular single cup brewing systems for coffee, tea, and hot chocolate. The cups are thermoformed with several different plastic resins including High Impact Polystyrene (HIPS). Firebird stores this material in a bulk storage silo that holds 100,000 kg of material. Firebird would like to determine the optimal reorder point and order quantity for their HIPS inventory. Firebird's goal is to always have sufficient levels of HIPS on hand to satisfy the manufacturing process's daily requirement. At the same time, Firebird would like to avoid any penalties charged by the bulk carrier arising from Firebird not having enough space in the silos to unload a scheduled delivery. Firebird's supplier of HIPS only delivers in full truckload amounts of 21,500 kg. Firebird's purchasing department currently places an order for a truckload of HIPS when its inventory position falls to 35,000 kg. The lead time for receiving an order is 2, 3, or 4 days with probabilities of 0.45, 0.35, and 0.2, respectively. Daily demand for HIPS varies from 5,000 kg to 11,000 kg with a most likely value of 7,500 kg.

a. Modify the spreadsheet for the Millennium Computer example in this chapter to address Firebird's inventory problem. Assume the beginning balance of HIPS is 45,400 kg. What is the probability that Firebird will be unable to satisfy its need of HIPS?

b. Assume Firebird wants to maintain a 100% service level while minimizing its average inventory level of HIPS and avoiding any penalties associated with having a bulk delivery that exceeds the available capacity in the storage silo. What reorder point should Firebird use?