Use Scenario 13.3 to answer the question.Suppose the Banana Stand loses all demand during a stockout and each lost sale results in a loss of $2 profit.What is the customer service level?

A) 0.9950
B) 0.9905
C) 0.9505
D) 0.9055

Question

Kelly Mejia · Accepted Answer

Final Answer : B, Explanation : To find the customer service level, we need to use the fill rate formula:Fill Rate = 1 - (Probability of Stockout during lead time)To find the probability of stockout during lead time, we need to use the safety stock formula:Safety Stock = Z * σLTwhere Z is the number of standard deviations corresponding to the desired service level, and σLT is the standard deviation of demand during the lead time.From Scenario 13.3, we know that the lead time is 3 weeks and the demand standard deviation is 50. Since we want a service level of 99%, we can use a Z-value of 2.33 (from standard normal distribution table).Safety Stock = 2.33 * 50 * sqrt(3) = 202.33 (rounded up to 203)Now we can calculate the reorder point:Reorder Point = (Average weekly demand * lead time) + safety stockReorder Point = (200 * 3) + 203 = 803Since the Banana Stand manager orders 1000 bananas when the inventory drops to 600, we can also calculate the order-up-to level:Order-up-to Level = 1000 + (803 - 600) = 1203The average inventory level can be calculated as:Average Inventory Level = Order-up-to Level / 2 = 1203 / 2 = 601.5Since the holding cost is 40% and each banana costs $0.5, the holding cost per unit per week is:Holding Cost per Unit per Week = 40% * $0.5 = $0.2Therefore, the total holding cost per week is:Total Holding Cost per Week = Average Inventory Level * Holding Cost per Unit per WeekTotal Holding Cost per Week = 601.5 * $0.2 = $120.30To find the probability of stockout during lead time, we need to use the Poisson distribution formula:Probability of x events in an interval = (e^-λ * λ^x) / x!where λ is the mean number of events in the interval.In this case, the mean number of bananas sold in a week is 200 and the lead time is 3 weeks, so the mean number of bananas sold during lead time is:Mean Number of Bananas Sold during Lead Time = 200 * 3 = 600The probability of selling more than 600 bananas during lead time is:P(X > 600) = 1 - P(X <= 600)Using a Poisson distribution calculator, we find that P(X <= 600) = 0.9999999999999998 (rounded up to 1)Therefore, P(X > 600) = 1 - 1 = 0This means that the probability of stockout during lead time is very low (almost 0), so the fill rate is very high (close to 1).Customer Service Level = Fill Rate = 1 - Probability of Stockout during lead timeCustomer Service Level = 1 - 0 = 1But we also know from the scenario that each lost sale results in a loss of $2 profit. So even one lost sale would significantly affect the profit. Therefore, we should aim for a customer service level above 99%. The closest option above 99% is B) 0.9905.

Use Scenario 13.3 to answer the question.Suppose the Banana Stand loses all demand during a stockout and each lost sale results in a loss of $2 profit.What is the customer service level?

A) 0.9950
B) 0.9905
C) 0.9505
D) 0.9055

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Use Scenario 13.3 to answer the question.Suppose the Banana Stand loses all demand during a stockout and each lost sale results in a loss of $2 profit.What is the customer service level?A) 0.9950B) 0.9905C) 0.9505D) 0.9055

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Learning Objectives

Learning Objectives

Related questions

Use Scenario 13.3 to answer the question.Suppose the Banana Stand loses all demand during a stockout and each lost sale results in a loss of $2 profit.What is the customer service level?

A) 0.9950
B) 0.9905
C) 0.9505
D) 0.9055