Question

The TransCanada Lumber Company and Mill processes 10,000 logs annually, operating 250 days per year. Immediately upon receiving an order, the logging company’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 $1600 per order, and the cost of carrying logs in inventory before they are processed is $15 per log on an annual basis.

a.The optimal order size?

Answer 1

Given values:

Annual demand (D) = 10,000 logs

Number of working days = 250 days per year

Daily demand (d) = Annual demand / Number of working days = 10,000 / 250

Daily demand (d) = 40 logs per day

Daily production (p) = 60 logs per day

Ordering cost (Co) = $1600 per order

Cost of carrying (Cc) = $15 per log

Solution:

The optimal order size (Q) is calculated as below,

Q = SQRT [(2 x D x Co) / Cc x (1 - d/p)]

Putting the given values in the above formula, we get,

Q = SQRT [(2 x 10,000 x $1600) / $15 x (1 - 40/60)]

Q = SQRT (6,399,999.999)

Q = 2,529.82 or 2,530 (Rounding off to the nearest whole number)

Optimal order size = 2,530 logs