A Manager Must Decide On Shipping Options
A Manager Must Make A Decision On Shipping There Are Two Shippers A
A manager must make a decision on shipping. There are two shippers, A and B. Both offer a two-day rate: A for $504 and B for $526. In addition, A offers a three-day rate of $472 and a nine-day rate of $410, and B offers a four-day rate of $452 and a seven-day rate of $428. Annual holding costs are 30 percent of unit price.
Three hundred and sixty boxes are to be shipped, and each box has a price of $150. Which shipping alternative would you recommend? (Round your intermediate calculations to 3 decimal places and final answers to 2 decimal places. Omit the "$" sign in your response.)
Paper For Above instruction
The decision to select the optimal shipping method for a shipment of 360 boxes involves analyzing both the shipping costs associated with different options and the holding costs of inventory. Given that each box costs $150 and the annual holding cost rate is 30%, it's crucial to evaluate these options not only based on freight charges but also considering how inventory costs impact overall expenses, especially if shipping times are flexible.
First, let's outline the available options:
- Shipper A:
- 2-day rate: $504
- 3-day rate: $472
- 9-day rate: $410
- Shipper B:
- 2-day rate: $526
- 4-day rate: $452
- 7-day rate: $428
Since the shipment involves 360 boxes, it is essential to compute total costs, including shipping rates and inventory holding costs, for each option.
Calculating Average Inventory and Holding Costs
The critical factor here is that holding costs accrue based on the average number of days inventory is held before shipping, and these costs can significantly influence total expenses, especially at a 30% annual rate.
The annual holding cost rate of 30% corresponds to a daily holding cost of:
\[ \text{Daily cost} = \frac{0.30 \times 150}{365} \approx 0.123 \text{ per dollar per day} \]
Thus, for each box, the daily holding cost is:
\[ 150 \times 0.123 \approx 18.45 \text{ cents} \]
Since holding costs depend on the duration of storage, an average approach is to consider the average number of days inventory is held before shipping, which varies by shipping method.
Total Cost Calculation
Shipper A:
- 2-day shipping:
- Freight cost: $504
- Inventory holding cost:
- Average inventory days: 2 days / 2 = 1 day
- Total inventory value: 360 boxes × $150 = $54,000
- Holding cost:
\[
\text{Cost} = 54,000 \times 0.30 \times \frac{2}{365} = 54,000 \times 0.30 \times 0.00548 \approx 88.71
\]
- 3-day shipping:
- Freight cost: $472
- Inventory holding cost:
\[
54,000 \times 0.30 \times \frac{3}{365} \approx 133.07
\]
- 9-day shipping:
- Freight cost: $410
- Inventory holding cost:
\[
54,000 \times 0.30 \times \frac{9}{365} \approx 399.21
\]
Shipper B:
- 2-day shipping:
- Freight cost: $526
- Inventory holding cost (same as for A):
\[
88.71
\]
- 4-day shipping:
- Freight cost: $452
- Inventory holding cost:
\[
54,000 \times 0.30 \times \frac{4}{365} \approx 177.62
\]
- 7-day shipping:
- Freight cost: $428
- Inventory holding cost:
\[
54,000 \times 0.30 \times \frac{7}{365} \approx 311.53
\]
Total Costs
| Option | Shipping Cost | Holding Cost | Total Cost |
|---------|----------------|----------------|------------|
| A - 2 days | 504 | 88.71 | 592.71 |
| A - 3 days | 472 | 133.07 | 605.07 |
| A - 9 days | 410 | 399.21 | 809.21 |
| B - 2 days | 526 | 88.71 | 614.71 |
| B - 4 days | 452 | 177.62 | 629.62 |
| B - 7 days | 428 | 311.53 | 739.53 |
Recommendation:
The lowest total combined cost is with Shipper A at the 2-day rate, totaling approximately $592.71. This option balances relatively low freight charges with minimal inventory holding costs, making it the most economical choice considering both shipping and inventory costs.
Therefore, I recommend shipping via Shipper A's 2-day rate at $504.
References
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