Applying the Stochstic Inventory Control to caculate $($Q$,$ R$)$ model question$2.$

The central warehouse of a large manufacturer of heavy machinery and engines stocks three different engine oil

products. The central warehouse orders these three products from the company's manufacturing operations

division and stocks them to meet demands of the company's dealers, which serve customer demand for these

engine oil products. The lead time and fixed order costs are about the same for each order, regardless of the

quantity or product type ordered; it is safe to assume that lead time is about one month and fixed order costs

are $$7,500$ per order.

The following table includes information on various costs and demand for each of the products.

If the central warehouse does not have the item in stock when a dealer puts in an order, the order is recorded

and is delivered to the retailer as soon as the next shipment arrives from the manufacturing division. The

warehouse estimates the stock$-$out cost to be equal to the same$-$day shipping costs that they incur as a result of

the stock$-$out incident $($given in the table above$).$

Questions:

EOQ Model: The company management has indicated a desire to adopt a very simple inventory control

policy for the three engine oil products. In particular, they have heard that the economic order quantity

model is easy to understand due to the constant and known demand assumption. Determine the EOQ and

reorder level for each of the three engine oil products and calculate the inventory costs $($fixed order, and

holding costs$)$ under this constant demand scenario.

$($Q$,$R$)$ Model: A new member of the management team, Alex Hamm, has an MBA and is eager to see how

much of an impact modeling uncertainty may have on the inventory control policy used. In particular, he

would like to see the stockout costs factored into the calculation of the inventory control policy since he

feels that the estimated stockout costs are not negligible, especially in comparison to the estimated holding

costs. Now determine the optimal order quantity and reorder level using a $(Q,R)$ policy designed to consider

the stochasticity of demand explicitly. First check that all of the $(Q,R)$ policy assumptions are met in this

case.