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Lara is the office administrator for the Department of Management at your University. The faculty uses a lot of printer paper and Lara is constantly reordering and frequently runs out of stock. She orders the paper from the university central stores and several faculty have determined that the lead-time to receive an order is normally distributed, with a mean of 2 weeks and a standard deviation of 0.5 weeks. The faculty have also determined that weekly demand for the paper is also normally distributed, with a mean of 20 packages and a standard deviation of 2 packages. The cost of carrying one paper package in inventory is 25% per year, and each time Lara places an order it costs 10€. The cost of a paper package is 5€, and each time printer paper runs out of stock a stock out cost of 3€ must be considered. Lara wants to guarantee an in stock probability of 90%.
1. Help Lara designing a reorder point control system for this item, given the assigned in stock probability. How would you state the inventory control policy?
2. Determine the relevant costs (procurement, carrying, and stock out costs) of this inventory policy and determine the average inventory level.
3. What service level (fill rate) do Lara actually achieve with this policy?
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