Athe Uptown Kiln Is An Importer Of Ceramics From Overseas

Athe Uptown Kiln Is An Importer Of Ceramics From Overseas It Hasarra

Athe Uptown Kiln is an importer of ceramics from overseas. It has arranged to purchase a particular type of ceramic pottery from a Korean artisan. The artisan makes the pottery in 120-unit batches and will ship only that exact amount. The transportation and handling cost of a shipment is $7,600 (not including the unit cost). The Uptown Kiln estimates its annual demand to be 900 units. What storage and handling cost per unit does it need to achieve in order to minimize its inventory cost?

The I-75 Carpet Discount Store has an annual demand of 10,000 yards of Super Shag carpet. The annual carrying cost for a yard of this carpet is $0.75, and the ordering cost is $150. The carpet manufacturer normally charges the store $8 per yard for the carpet; however, the manufacturer has offered a discount price of $6.50 per yard if the store will order 5,000 yards. How much should the store order, and what will be the total annual inventory cost for that order quantity?

The bookstore at State University purchases sweatshirts emblazoned with the school name and logo from a vendor. The vendor sells the sweatshirts to the store for $38.00 each. The cost to the bookstore for placing an order is $120.00, and the carrying cost is 25% of the price paid per shirt. The bookstore manager estimates that 1,700 sweatshirts will be sold during the year. The vendor has offered the bookstore the following volume discount schedule. The manager wants to determine the bookstore’s optimal order quantity given the foregoing quantity discount information.

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Minimizing Inventory Costs for Athe Uptown Kiln and Other Retailers

Managing inventory efficiently is crucial for businesses to minimize costs and maximize profitability. In this analysis, we evaluate the inventory management strategies for three different retail scenarios: an importer of ceramics, a carpet store, and a university bookstore. Each case involves calculating the optimal order quantity and the associated cost parameters to help these businesses make informed purchasing decisions.

Part A: Cost Minimization for Athe Uptown Kiln

Athe Uptown Kiln sources ceramics in batches of 120 units from a Korean artisan. The total transportation and handling cost per shipment is $7,600, and the annual demand is 900 units. To minimize inventory costs, the business needs to determine the suitable storage and handling cost per unit that align with its procurement strategy.

The total number of shipments per year is calculated as:

Number of Shipments (N) = Annual Demand / Batch Size = 900 / 120 = 7.5, which rounds up to 8 shipments per year.

The total transportation cost annually is:

Transportation Cost = Number of Shipments × Cost per shipment = 8 × $7,600 = $60,800.

To balance ordering costs with holding costs, we can use the Economic Order Quantity (EOQ) model. EOQ is given by:

EOQ = √(2DS / H)

Where:

• D = 900 (annual demand)
• S = $7,600 (ordering or shipment cost)
• H = holding or storage cost per unit annually

Rearranged to solve for H (storage and handling cost per unit):

H = (2DS) / (EOQ)^2

Since the batch size is fixed at 120 units, the EOQ approximates this size, but for optimality, we can set EOQ equal to batch size or solve for H accordingly. Using batch size (Q) = 120 units:

H = (2 × 900 × 7,600) / (120)^2 = (2 × 900 × 7,600) / 14,400 = (13,680,000) / 14,400 ≈ $950 per unit per year.

This figure indicates that to minimize costs around this batch size, the per-unit storage and handling cost should be approximately $950 annually. However, such a high cost per unit suggests that the batch size logistics directly influence cost structure, and the business should aim for a balance where the total cost is minimized, often through adjusting batch size or cost parameters.

Part B: EOQ and Discount Analysis for I-75 Carpet

The store's annual demand is 10,000 yards, with an ordering cost of $150 and a holding cost of $0.75 per yard annually. The standard price is $8 per yard, but a bulk discount offers a reduced price of $6.50 per yard if the store orders 5,000 yards.

Calculating the EOQ without discounts:

EOQ = √(2DS / H) = √(2 × 10,000 × 150 / 0.75) = √(3,000,000 / 0.75) = √4,000,000 = 2,000 yards.

This EOQ exceeds the discounted order size (5,000 yards). To maximize savings, the store should consider ordering at the discounted volume of 5,000 yards.

Cost analysis for ordering 5,000 yards:

• Number of orders = Demand / Order Quantity = 10,000 / 5,000 = 2
• Total ordering cost = 2 × $150 = $300
• Average inventory level = 5,000 / 2 = 2,500 yards
• Total holding cost = 2,500 × $0.75 = $1,875
• Cost of goods = 10,000 × $6.50 = $65,000
• Total annual inventory cost (excluding purchase cost) = holding + ordering = $1,875 + $300 = $2,175

Thus, ordering 5,000 yards balances the discounted price and inventory costs efficiently, resulting in a total annual inventory-related expense of approximately $2,175.

Part C: Optimal Order Quantity with Volume Discounts at the University Bookstore

The bookstore's demand is 1,700 sweatshirts, with an ordering cost of $120 per order and a unit cost of $38. The carrying cost is 25% of the unit price, amounting to $9.50 per sweatshirt annually.

The vendor offers a volume discount schedule, which typically reduces the price at specific order quantities, such as:

• Order up to 1,000 units: no discount
• Order 1,001–2,000 units: 5% discount
• Order above 2,000 units: 10% discount

Calculating EOQ without discounts:

EOQ = √(2 × 1,700 × 120 / 9.50) ≈ √(408,000 / 9.50) ≈ √42,947 ≈ 207 units

Since the demand is low, the EOQ suggests ordering approximately 207 units; however, due to the volume discounts, larger order quantities may be more cost-effective. For example, ordering 1,000 units with no discount might be suboptimal since the discount applies at higher quantities. Ordering at the 1,001–2,000 units range yields a 5% discount on the $38 price, reducing it to $36.10 per sweatshirt.

Calculating total costs for 1,000 units:

• Number of orders = 1.7, approximated as 2
• Total ordering cost = 2 × $120 = $240
• Average inventory = 1,000 / 2 = 500 units
• Total holding cost = 500 × $9.50 = $4,750
• Total purchase cost = 1,700 × $36.10 ≈ $61,387

Alternatively, ordering closer to 2,000 units at a 10% discount (price = $34.20) may reduce overall costs. The optimal order quantity should be a balance between the EOQ and the discount thresholds, often determined through cost optimization models incorporating volume discount schedules.

Therefore, the bookstore’s optimal order quantity should be determined by analyzing the trade-offs between purchase discounts, order costs, and carrying costs, with the likely optimal range near the 1,000 unit or 2,000 unit thresholds depending on the exact discount structure.

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