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).