A public utility intends to buy a turbine as part of an expansion plan and must now decide on the number of spare parts to order. One part, X135, can be purchased for $100 each. Holding and disposal costs are estimated to be 145 percent of the purchase price over tire life of the turbine. A stock-out would cost roughly $8,000 due to downtime, ordering, and ‘'special purchase” factors. Historical records based on the performance of similar equipment operating under similar conditions suggest that demand for the spare part will tend to approximate a Poisson distribution with a mean of 3.2 units for the useful life of tire turbine.
a. What is the optimal number of units of this spare part to order?
b. Carrying six spare parts would be the best strategy' for what range of shortage cost per unit?