Principles of Inventory Management ,John A. Muckstadt Amar Sapra

A manufacturer of a part, purchased by Llenroc Electronics (LE) for its airline customers, has just informed LE that it is going to terminate production of the part type. The manufacturer has informed LE that it has one last opportunity to obtain the part at the normal production rate price. The manufacturer is willing to sell units to LE for $2,000 at this point in time. However, if LE wishes to procure the part type at a later point in time the unit price will likely increase to $25,000. Another factor that LE faces is the remaining length of time the airlines might use the part. Suppose the remaining life is gamma distributed with a mean of 5 years and a standard deviation of 1.25 years. The demand for the part is Poisson distributed with a rate of 2 units per year. There is no residual value for these parts if they are not used. What quantity of this part would you recommend LE to purchase from the manufacturer? Assume LE has no stock on hand or on order.