Incredible Machines is a company that sells machinery to 6 distinct geographic markets around the world. You are the inventory manager for the Super X milling machine. Weekly demand in each geographic market is normally distributed with mean 80 and standard deviation 20, and demands in each market are independent. The company fulfills all demand out of a single distribution center. Once an order is shipped from the supplier it takes four weeks to reach the distribution center. The company estimates the holding cost per unit inventory as $105 per week and also incurs a fixed cost of $60,000 per order. Assume you control the inventory in the distribution center with a continuous review (R,Q) policy. Lastly, assume that the company pays the supplier when its orders reach the distribution center and unsatisfied orders are backordered, i.e., the ownership of the in-transit (pipeline) inventory does not belong to Incredible Machines.
(a) The company operates with a target of fulfilling 97% of orders from on-hand inventory. What reorder point R and order quantity Q should be used? What is the average on-hand inventory for Super X?
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