Part A: The Shoe Department Buyer At Feets Has Determined Th ✓ Solved
Part A The Shoe Department Buyer At Feets Has Determined That Feets S
The shoe department buyer at Feets has determined that Feets should buy 98,000 pairs of athletic shoes from their vendor, Adidas. The shoes are shipped and packed 10 pairs to a shipping box. Each shipping box has a value of $517. The buyer estimates that about $59 is spent on the ordering and sourcing decisions per shipping box. The annual percentage holding cost is 35%. Does that forecast pass the reasonability test? Include with your answer: What is the optimal number of boxes to order each time an order is placed? What is the total annual ordering cost?
Sample Paper For Above instruction
Introduction
Effective inventory management is crucial for retail operations, especially in sectors like footwear that experience seasonal fluctuations and high demand for popular items. Feets' decision to optimize order quantity and supplier choice directly impacts its costs and customer satisfaction. This paper evaluates the reasonableness of Feets' forecasted order quantity, calculates the optimal order size, estimates total ordering costs, and recommends the most economical shipping option considering freight rates and holding costs.
Part A: Analysis of Order Quantity and Cost
Estimating the Forecast's Reasonability
Feets plans to purchase 98,000 pairs of athletic shoes annually, supplied by a vendor, Adidas. The shoes are shipped in boxes containing 10 pairs each, resulting in 9,800 boxes annually (98,000 pairs / 10 pairs per box). The forecast appears reasonable given market demand, but it must be evaluated against economic order quantity (EOQ) principles to ensure cost efficiency.
Calculating the Economic Order Quantity (EOQ)
The EOQ model facilitates finding the optimal order size that minimizes total inventory costs, which include ordering and holding costs. The EOQ is given by the formula:
EOQ = sqrt((2 D S) / H)
Where:
- D: Annual demand (units) = 9,800 boxes
- S: Ordering cost per order = $59 per shipping box
- H: Holding cost per unit per year = percentage of inventory value
Given:
- Value per box = $517
- Annual holding cost percentage = 35%
Calculating the holding cost per unit:
H = 0.35 * $517 = $180.95
Now, calculating EOQ:
EOQ = sqrt((2 9,800 59) / 180.95) ≈ sqrt((1,156,400) / 180.95) ≈ sqrt(6392.87) ≈ 79.96 boxes
Thus, the optimal order quantity is approximately 80 boxes per order.
Assessment of Forecast Reasonability
The forecasted order size is 9,800 boxes annually, which, divided into EOQ of approximately 80 boxes per order, implies about 122 orders per year (9,800 / 80). This high number of orders suggests frequent replenishment, which could be operationally feasible given the low order cost, but it might also increase total ordering costs significantly.
Comparing the forecasted order quantity to EOQ indicates that the forecasted annual purchase aligns reasonably well with cost-efficient inventory practices. However, to optimize costs further, Feets should consider adjusting their order quantity towards the EOQ value.
Calculating Total Annual Ordering Cost
Total ordering cost is computed as:
Total Ordering Cost = Number of Orders * Order Cost
Number of orders:
N = D / EOQ = 9,800 / 80 ≈ 122.5 orders
Therefore, total ordering cost:
Total Ordering Cost = 122.5 * $59 ≈ $7,237.50
Part B: Vendor Shipping Alternatives
Comparing Shipping Options
Feets must decide between two freight options from Oakland, CA to Sacramento, CA:
- 2-day freight at \$13.562 per box
- 5-day freight with a flat \$1,500 per order (up to 123 boxes)
The annual demand remains 9,800 boxes, and the annual holding cost per box is $180.95.
Calculating Total Shipping Costs for Each Option
Option 1: 2-day Freight
Total shipping cost:
Total Shipping Cost = D Cost per box = 9,800 $13.562 ≈ $133,031.60
Assuming ordering in EOQ units (~80 boxes per order), the number of orders is:
N = 9,800 / 80 ≈ 122.5
Total annual shipping cost for EOQ:
Total shipping cost = 122.5 80 $13.562 ≈ 9,800 * $13.562 = $133,031.60
Option 2: 5-day Flat Rate Freight
Flat rate per order: $1,500 for up to 123 boxes.
Number of orders:
N = 9,800 / 80 ≈ 122.5
Total shipping cost:
Total shipping cost = N $1,500 ≈ 122.5 $1,500 = $183,750
Cost Comparison and Recommendation
The 2-day freight option results in an annual shipping cost of approximately $133,031.60, whereas the 5-day flat rate totals around $183,750. Therefore, the 2-day freight option is more economical under the frequency of orders calculated, offering significant savings over the flat-rate alternative.
Conclusion
Based on the cost analysis, Feets should opt for the 2-day freight option, as it offers lower annual shipping costs despite potentially higher per-unit freight charges. The frequent replenishment aligns with the EOQ model, balancing ordering and holding costs efficiently. Implementing this approach helps minimize total inventory costs and ensures timely stock availability for customers.
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