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 servic... 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?
Understand the Problem
The question is about inventory management and determining the customer service level in a scenario where the Banana Stand loses all demand during a stockout, resulting in a loss of $2 profit per lost sale. We need to consider the weekly demand, standard deviation, lead time, order quantity, reorder point, cost per banana, and holding cost to calculate the customer service level.
Answer
$0.9950$
Answer for screen readers
- 9950
Steps to Solve
- Calculate the holding cost per banana per week
The holding cost is 40% of the cost of the banana, so we need to calculate 40% of $0.50. Holding cost per year = $0.40 \times $0.50 = $0.20$ per banana per year. Holding cost per week = $\frac{$0.20}{52} \approx $0.003846$ per banana per week
- Determine the stockout cost (Cs) and holding cost (Ch)
The problem states that each lost sale results in a loss of $2 profit, thus the stockout cost (Cs) = $2. We already calculated the holding cost per banana per week (Ch) in step 1, Ch ≈ $0.003846.
- Calculate the service level using the formula
The customer service level can be calculated using the formula: $Service\ Level = \frac{Cs}{Cs + Ch}$ Where: $Cs$ = Stockout cost per unit $Ch$ = Holding cost per unit
- Plug in the values and solve for service level
$Service\ Level = \frac{$2}{$2 + $0.003846} = \frac{2}{2.003846} \approx 0.998079$
- Round the service level to match the given options
The calculated service level is approximately 0.9981. Comparing this to the provided options, the closest value is 0.9950.
- 9950
More Information
The customer service level represents the probability of not stocking out during the lead time. In this scenario, it's approximately 99.50%, meaning the Banana Stand is expected to meet demand about 99.50% of the time.
Tips
A common mistake would be not converting the annual holding cost to the weekly holding cost. Alternatively, using the cost instead of profit for $C_s$ would produce the wrong result.
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