Question

Target purchases home goods made by a supplier in China. Target's stores in the United States sell 200,000 units of home goods each month. Each unit costs $10 and the company has an annual holding cost of 20 percent. Placing a replenishment order incurs clerical costs of $500/order. The shipping company charges $5,000 as a fixed cost per shipment along with a variable cost of $0.10 per unit shipped. What is the optimal order size? What is the annual holding cost of the optimal policy? How many orders per year does Target place? What is the annual variable transportation cost? What is the annual clerical cost?

Answer 1

Given:

Annual Demand(D) = 200,000 × 12 = 2,400,000  units

Cost per order(S) = $500 per order

Holding cost(H) = 20% of Unit cost = $10 × 20% = $2

Unit cost =$10

Computation:

1)  Optimal Order size = $\sqrt{\frac{2DS}{H} }$

Optimal Order Size= $\sqrt{\frac{2\times 2,400,000\times 500}{2} }$

$Optimal\ Order\ Size = 34,641 Units (Approx)$

2)  $Annual\ holding\ cost = (Optimal\ Order\ Size / 2) \times Holding\ Cost$

Annual holding cost = (34,641 / 2) × 2

Annual holding cost = $34,641

3)  Number of Order per year = Annual demand / Optimal Order Quantity

Number of Order per year = 2,400,000 / 34,641

Number of Order per year = 69.2820646

Number of Order per year = 69 order (Approx)

4)  Annual variable transportation cost = Transportation per unit × Annual Demand

Annual variable transportation cost = $0.10 × 2,400,000

Annual variable transportation cost  = $240,000

5)  Annual Clerical Cost = Number of Order per year × Cost per Order

Annual Clerical Cost = 69.282 × $500

Annual Clerical Cost  = $34,641