Part A: The Shoe Department Buyer At Feets Has Determ 117383

Part A The Shoe Department Buyer At Feets Has Determined That Feets S

The shoe department buyer at Feets has determined that Feets should purchase 98,000 pairs of athletic shoes from their vendor, Adidas. The shoes are shipped in quantities of 10 pairs per shipping box, with each box valued at $517. Additionally, the buyer estimates that the sourcing and ordering costs per shipping box amount to $59. The annual holding cost rate is 35%. The key questions are whether this forecast is reasonable, what the optimal order quantity (economic order quantity, EOQ) is, and what the total annual ordering cost would be.

To evaluate the reasonability of the forecast, we first examine the fundamental inventory management principles. The EOQ model determines the most cost-efficient order quantity that minimizes total inventory costs, which include ordering costs, holding costs, and purchase costs. Assuming demand (D) is 98,000 pairs annually, packed in boxes of 10 pairs, which makes total annual boxes demanded (Q*) as:

Q_demand = 98,000 pairs / 10 pairs per box = 9,800 boxes per year

The EOQ formula is given by:

Q_opt = √(2DS / H)

Where:

• D = annual demand in units (here, boxes) = 9,800
• S = ordering cost per order = $59
• H = holding cost per unit per year = (value per box) × (holding cost rate) = $517 × 0.35 = $180.95

Calculating Q_opt:

Q_opt = √(2 × 9,800 × 59 / 180.95) ≈ √(2,908,400 / 180.95) ≈ √16,067.69 ≈ 126.88

Thus, the optimal order quantity is approximately 127 boxes per order. Since each box contains 10 pairs, this corresponds to about 1,270 pairs per order, which is reasonable considering demand and cost factors.

The total annual ordering cost is calculated as:

Number of orders per year = D / Q_opt = 9,800 / 127 ≈ 77

Total ordering cost = number of orders × S = 77 × $59 ≈ $4,543

In conclusion, the forecast of purchasing 98,000 pairs annually appears reasonable, as the EOQ calculation yields an order size that balances ordering and holding costs effectively. The total annual ordering cost at this optimal quantity is approximately $4,543.

Part B

For the shipping vendor choice between 2-day freight and 5-day flat rate freight, we analyze the total annual shipping costs based on demand, rate structures, and costs involved.

The demand remains at 9,800 boxes per year, with shipping costs structured as follows:

• 2-day freight: $13.562 per box
• 5-day freight: $1,500 per order (flat rate), applicable to orders up to 123 boxes

First, we calculate the total shipping cost with 2-day freight:

Total cost (2-day) = demand × per-box rate = 9,800 × $13.562 ≈ $132,599.60

Next, for 5-day freight, considering the flat rate per order:

Number of orders required = total demand / order size = 9,800 / 123 ≈ 79.67, rounded up to 80

Total shipping cost (5-day) = number of orders × flat rate = 80 × $1,500 = $120,000

When comparing totals, the 5-day freight option results in a lower overall shipping cost of approximately $120,000, compared to roughly $132,600 for 2-day freight.

Additionally, considerations include the urgency of delivery. If the supply chain requires rapid replenishment to avoid stockouts, 2-day freight may be justified despite higher costs. However, assuming that the relatively flexible 5-day shipping timeframe suffices, the cost savings favor choosing the 5-day freight option.

Thus, based on cost efficiency alone, the 5-day flat rate freight is recommended because it offers significant savings, reduces per-unit shipping expenses, and simplifies cost management. The decision balances inventory needs with transportation expenditure, and in this case, the flat rate freight appears optimal.

In summary, the total annual shipping cost with 2-day freight is approximately $132,600, whereas utilizing 5-day freight with flat rates would cost about $120,000 annually. Therefore, the 5-day freight is the more economical choice under the given assumptions.

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