Question: A very large mining operation has decided to control the inventory of high-pressure piping by a "periodic review, order up to M" policy, where M is a target level. The annual demand for this piping is normally distributed, with mean 600 and variance 800. This demand occurs fairly uniformly over the year. The lead time for resupply is Erlang distributed of order k = 2 with its mean at 2 months. The cost of each unit is $400. The inventory carrying charge, as a proportion of item cost on an annual basis, is expected to fluctuate normally about the mean 0.25 (simple interest), with a standard deviation of 0.01. The cost of making a review and placing an order is $200, and the cost of a backorder is estimated to be $100 per unit backordered. Suppose that the inventory level is reviewed every 2 months, and let M = 337.
(a) Make five independent replications, each of run length 100 months, to estimate long-run mean monthly cost by means of a 90% confidence interval:
(b) Investigate the effects of initial conditions. Calculate an appropriate number of monthly observations to delete to reduce initialization bias to a negligible level.