The Woody Woodpecker Lumber Company processes 10,000 logs annually, operating 25

Question

The Woody Woodpecker Lumber Company processes 10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, Woody’s supplier begins delivery to the lumber mill at the rate of 60 logs per day. The lumber mill has determined that the ordering cost is $1,600 per order, and the cost of carrying logs in inventory before they are processes is $15 per log on an annual basis. Determine the following:

a. The optimal order size

b. The total inventory cost associated with the optimal order quantity

Explanation / Answer

Annual demand (D) = 10000 logs

Ordering cost (S) = $1600 per order

Carrying cost (H) = $15

a) Optimal order size(Q) = sqrt of (2DS /H)

= sqrt of [(2 x 10000 x 1600)/15]

= 1460.60 or rounded to 1461 logs

b) Annual Ordering cost = (D/Q)S = (10000/1461)1600 = $10951.40

Annual carrying cost = (Q/2)H = (1461/2)15 = $10957.5

Total inventory cost = Ordering cost + carrying cost

= $10951.40 + $10957.5

= $21908.9

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