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The demand for suits from a local men's wear store is normally distributed. The manager has found that the store has an average weekly demand for 350 suits with a daily standard deviation of 25. The manager checks the inventory every 4 days. During a particular visit there were 55 suits left in stock. The lead-time to order replacement suits is 12 days. The store owner wants to maintain a service level of 98%. The store operates for 7 days a week.

What is the target level?

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Final answer:

To maintain a 98% service level over the 12-day lead-time, the local men's wear store should aim for a target inventory level of approximately 778 suits, based on the average weekly demand, daily standard deviation, lead-time, and desired service level.

Step-by-step explanation:

The target level for inventory is the stock level that a company must maintain to ensure a certain service level over a specified period. To calculate the target level for the local men's wear store, we need to use the normal distribution and the given data about the weekly demand, the standard deviation, and the lead-time for replacement suits. Since the store wants to maintain a 98% service level and the daily demand standard deviation is 25 suits, we calculate the z-score corresponding to the 98% service level and apply the formula for the target inventory level:

Target Level = (Average Daily Demand * Lead Time in Days) + (z-score * Standard Deviation * sqrt (Lead Time in Days))

The average daily demand is the average weekly demand divided by 7, which is 350 suits/7 days = 50 suits per day. The lead time is 12 days, we need to find the z-score for a 98% service level, which is typically around 2.05. We should multiply the z-score by the standard deviation, and by the square root of the lead time in days to account for the increased variability over time, and then add this to the product of average daily demand and the lead time.

Adjusting the formula with the given specifics, the calculation for the target level would be:

Target Level = (50 suits/day * 12 days) + (2.05 * 25 suits/day * sqrt (12 days)) = 600 + (2.05 * 25 * 3.46) = 600 + 177.62 ≈ 778 suits

Therefore, the store should maintain a target inventory level of approximately 778 suits to ensure the 98% service level over the 12-day lead-time period.

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