A particular stock keeping unit (SKU) has demand that averages 14 units per year and is Poisson distributed. That is, the time between demands is exponentially distributed with a mean of 1/14 years. Assume that 1 year = 360 days. The inventory is managed according to a (r, Q) inventory control policy with r = 3 and Q = 4. The SKU costs $150. An inventory carrying charge of 0.20 is used and the annual holding cost for each unit has been set at 0.2 * $150 = $30 per unit per year. The SKU is purchased from an outside supplier and it is estimated that the cost of time and materials required to place a purchase order is about $15. It takes 45 days to receive a replenishment order. The cost of backordering is very difficult to estimate, but a guess has been made that the annualized cost of a backorder is about $25 per unit per year.

(a) Using the analytical results for the (r, Q) inventory model, compute the total cost of the current policy.

(b) Using Arena™, simulate the performance of this system using Q = 4 and r = 3.

Report the average inventory on hand, the cost for operating the policy, the average number of backorders, and the probability of a stock out for your model.

(c) Now suppose that the lead-time is stochastic and governed by a lognormal distribution with a mean of 45 days and a standard deviation of 7 days. What assumptions do you have to make to simulate this situation? Simulate this situation and compare/contrast the results with parts (a) and (b).