Demand for a book at Amazon.com is 310 units per week. The product is supplied t

Question

Demand for a book at Amazon.com is 310 units per week. The product is supplied to Amazon from a factory. The factory charges Amazon $10 per book, while the total cost of shipping an order from the factory to the Amazon, when the shipment size is Q, is given by Shipment cost $70+2Q Assume the annual inventory carrying cost is 25 percent. a-1. What is Amazon's total cost per shipment? Cost per shipment a-2. What is the annual holding cost per book? (Round your answer to 2 decimal places.) Annual holding cost per book b. What is the optimal shipment size? (Assuming 52 weeks per year. Round your answer to the nearest whole number.) Optimal shipment size books c. What is the average throughput time? (Do not round intermediate calculations. Round your answer to 3 decimal places.) Average throughput time months

Explanation / Answer

(a-1)

Total variable cost per book = $10 + $2 = $12

So, total cost per shipment = $70 + 12 Q

(a-2)

Annual holding cost per book (H) = 10% x variable cost per book = 10% x $12 = $1.2

(b)

D=52x310=

TC = (D/Q) x (70 + 2Q) + Q.H/2
or, d(TC)/dQ = -70 D/Q2 + 0 + H/2
equating this with zero, we get

-70 D/Q2 + 0 + H/2 = 0
or, Q = SQRT(2 * D *70 / H) = SQRT(2 * 16120 * 70 / 1.2) = 1371.4 units

(c)

Time between orders = 12 / (D/Q) = 12 / (16120 / 1371.4) = 1.021 months

Average throughput time is the half of this i.e. 0.511 months.

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