Determine the total annual cost of SoxyBack's current system if a series of promotions increases the standard deviation of demand for both the Dandy and Popinjay lines to 10. Assum... Determine the total annual cost of SoxyBack's current system if a series of promotions increases the standard deviation of demand for both the Dandy and Popinjay lines to 10. Assume that the mean weekly demand for both product lines remains the same.
Understand the Problem
The question asks us to determine the total annual cost of SoxyBack's current inventory system, given specific demand distribution (normal distribution with a mean of 3 and standard deviation of 10 for Dandy, and mean of 25 and standard deviation of 10 for Popinjay), costs, and service level requirements of 0.975 for each product. We need to consider holding costs, transportation costs from Oshkosh to each of the ten territories, and the cost of the products themselves to calculate the total annual cost.
Answer
\$6800
Answer for screen readers
$6800
Steps to Solve
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Calculate the safety stock for Dandy
We are given a service level of 0.975. This corresponds to a z-score. We need to find the z-score associated with 0.975. Using a z-table or calculator, we find that $z = 1.96$. Safety stock is $z * \sigma$, so for Dandy it is $1.96 * 10 = 19.6 \approx 20$ units considering only the demand variation.
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Calculate the safety stock for Popinjay
Using the same z-score of 1.96, the safety stock for Popinjay is $1.96 * 10 = 19.6 \approx 20$ units considering only the demand variation.
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Calculate the total inventory for Dandy
The average inventory is the average demand plus the safety stock. For Dandy, this is $3 + 20 = 23$ units.
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Calculate the total inventory for Popinjay
For Popinjay, the total inventory is $25 + 20 = 45$ units.
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Calculate the annual holding cost for Dandy
The holding cost is $1 per unit per year. The total holding cost for Dandy is then $23 \text{ units } * $1/\text{unit} = $23$ per territory. Since there are 10 territories, the total holding cost is $23 * 10 = $230$.
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Calculate the annual holding cost for Popinjay
The holding cost is $1 per unit per year. The total holding cost for Popinjay is then $45 \text{ units } * $1/\text{unit} = $45$ per territory. Since there are 10 territories, the total holding cost is $45 * 10 = $450$.
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Calculate the total annual holding cost
The total annual holding cost is the sum of holding costs for Dandy and Popinjay, so $$230 + $450 = $680$.
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Calculate the annual transportation cost for Dandy
The transportation cost is $3 per unit. The demand for Dandy is 3 units per territory and the safety stock is 20 units. So, $3+20 = 23$ units will be transported to each territory. For one territory, it costs $23 * $3 = $69$. So the transportation cost for all 10 territories is $$69 * 10 = $690$.
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Calculate the annual transportation cost for Popinjay
The transportation cost is $3 per unit. The demand for Popinjay is 25 units per territory and the safety stock is 20 units. So, $25+20 = 45$ units will be transported to each territory. For one territory it costs $45 * $3 = $135$. The transportation cost for all 10 territories is $$135 * 10 = $1350$.
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Calculate the total transportation cost
The total transportation cost is the sum of the transportation costs for Dandy and Popinjay, so $$690 + $1350 = $2040$.
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Calculate the cost of the products for Dandy
Dandy costs $6 per unit. So, it costs $23 * $6= $138$ for each territory. The total cost is $10 * $138 = $1380$.
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Calculate the cost of the products for Popinjay
Popinjay costs $6 per unit. So, it costs $45 * $6 = $270$ for each territory. The total cost is $10 * $270 = $2700$.
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Calculate the total product cost
The total product cost is the sum of the product costs for Dandy and Popinjay, so $$1380 + $2700 = $4080$.
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Calculate the total annual cost
The total annual cost is the sum of the holding cost, transportation cost, and product cost: $$680 + $2040 + $4080 = $6800$.
$6800
More Information
The total annual cost of SoxyBack's current inventory system is calculated by summing the holding costs, transportation costs, and the cost of the products themselves across all ten territories. This calculation takes into account the safety stock required to meet the desired service level of 0.975 for both Dandy and Popinjay products.
Tips
A common mistake is to forget to multiply the cost for a single territory by the number of territories (10). Another common mistake is failing to include the safety stock when calculating transportation and product costs. A third common mistake is using the wrong z-score.
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