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Athletic Apparel is trying to determine how to manage their stock of t-shirts. For one particular size and color they have an average daily demand of 15 shirts, but it varies by about 5 shirts per day. Their lead time for receiving new t-shirts is 6 days. They are striving for a 94% service level.What should be their safety stock for this particular t-shirt? (Display your answer to two decimal places.)    What should be their reorder point for this particular shirt? (Display your answer to two decimal places.)

Question

Athletic Apparel is trying to determine how to manage their stock of t-shirts. For one particular size and color they have an average daily demand of 15 shirts, but it varies by about 5 shirts per day. Their lead time for receiving new t-shirts is 6 days. They are striving for a 94% service level.What should be their safety stock for this particular t-shirt? (Display your answer to two decimal places.)    What should be their reorder point for this particular shirt? (Display your answer to two decimal places.)

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Solution

To calculate the safety stock and reorder point, we need to understand the concepts first:

  1. Safety Stock: It is the level of extra stock that is maintained to mitigate risk of stockouts due to uncertainties in supply and demand.

  2. Reorder Point: It is the level of inventory which triggers an action to replenish that particular inventory stock.

Now, let's calculate:

  1. Safety Stock: It is calculated using the formula: Safety Stock = Z-score corresponding to the desired service level * Standard deviation of lead time demand.

Given, service level is 94%, the Z-score for this service level (from standard normal distribution table) is approximately 1.88. The standard deviation of lead time demand is the daily demand standard deviation multiplied by the square root of the lead time, which is 5 shirts * sqrt(6) = 12.25 shirts.

So, Safety Stock = 1.88 * 12.25 = 22.95 shirts. We can round this to two decimal places, so the safety stock is 22.95 shirts.

  1. Reorder Point: It is calculated using the formula: Reorder Point = Average lead time demand + Safety Stock.

Average lead time demand is the daily demand multiplied by the lead time, which is 15 shirts * 6 days = 90 shirts.

So, Reorder Point = 90 + 22.95 = 112.95 shirts. We can round this to two decimal places, so the reorder point is 112.95 shirts.

This problem has been solved

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