Use Scenario 14.2 to determine the total annual cost of Option A for SoxyBack's distribution system.
Understand the Problem
The question asks to calculate the total annual cost of Option A for SoxyBack's distribution system, given information about their inventory management, demand, costs, and shipping options for two product categories: Dandy and Popinjay. Option A involves keeping the current structure but replenishing inventory once a week instead of every five weeks.
Answer
$486.16
Answer for screen readers
$486.16
Steps to Solve
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Calculate safety stock for Dandy products
With weekly replenishment, the lead time demand is for one week. Service level CSL = 0.975, so z = 1.96 (from z-table). Safety stock for Dandy = $z \times \sigma_H = 1.96 \times 6 = 11.76$ units.
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Calculate safety stock for Popinjay products
With weekly replenishment, the lead time demand is for one week. Service level CSL = 0.975, so z = 1.96. Safety stock for Popinjay = $z \times \sigma_L = 1.96 \times 6 = 11.76$ units.
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Calculate average inventory for Dandy products
Average inventory = Weekly demand / 2 + Safety Stock Average inventory for Dandy = $3/2 + 11.76 = 1.5 + 11.76 = 13.26$ units
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Calculate average inventory for Popinjay products
Average inventory = Weekly demand / 2 + Safety Stock Average inventory for Popinjay = $25/2 + 11.76 = 12.5 + 11.76 = 24.26$ units
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Calculate holding cost for Dandy products
Holding cost per unit per year = Product cost $\times$ Annual holding cost percentage = $35 \times 0.30 = $10.50 Annual holding cost for Dandy = Average inventory $\times$ Holding cost per unit per year = $13.26 \times 10.50 = $139.23$
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Calculate holding cost for Popinjay products
Holding cost per unit per year = Product cost $\times$ Annual holding cost percentage = $35 \times 0.30 = $10.50 Annual holding cost for Popinjay = Average inventory $\times$ Holding cost per unit per year = $24.26 \times 10.50 = $254.73$
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Calculate total holding cost per territory
Total holding cost = Holding cost for Dandy + Holding cost for Popinjay = $139.23 + 254.73 = $393.96$
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Calculate shipping cost per territory per week
Weight of Dandy products = Quantity $\times$ Weight per unit = $3 \times 0.2 = 0.6$ pounds Weight of Popinjay products = Quantity $\times$ Weight per unit = $25 \times 0.1 = 2.5$ pounds Total weight = $0.6 + 2.5 = 3.1$ pounds Shipping cost per week = $0.75 + 0.33 \times 3.1 = 0.75 + 1.023 = $1.773$
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Calculate annual shipping cost per territory
Annual shipping cost = Shipping cost per week $\times$ Number of weeks = $1.773 \times 52 = $92.20$ (rounded)
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Calculate total annual cost per territory
Total annual cost = Total holding cost + Annual shipping cost = $393.96 + 92.20 = $486.16$
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Calculate total annual cost for all territories
Since the problem does not specify the number of territories, we cannot calculate the total annual cost for all territories. Assuming there was a typo in the Dandy product cost (350 should be 35), the total annual cost per territory is $486.16.
$486.16
More Information
The overall annual cost is the sum of holding costs for Dandy and Popinjay products and the annual shipping costs, which sums up our final answer. The number of territories influences the final value.
Tips
A common mistake is to not calculate the safety stock correctly, or to forget to include it when calculating the average inventory. Another common mistake is to not consider the annual holding cost percentage, and the UPS shipping cost function correctly. Finally, forgetting to multiply the shipping cost per week by the number of weeks in a year would lead to an incorrect answer. Also, confusing Dandy product cost may cause issues.
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