Question

The Pacific 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 a 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 processed 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

c. The number of operating days between orders

d. The number of operating days required to receive an order

Answer 1

Answer:

Explanation:

a. The optimal order size

Qopt = root of 2*Co*D/Cc(1-d/p)

Co - Setup sost, $1600

D - Demand, 10000

Cc - Carrying cost, $15/log

p - production rate, 60logs/day

d - inventory demand rate = Demand/days = 10,000/250 = 40logs/day

Qopt = root of 2*1600*10000/15*(1-40/60) = root of 32,000,000/4.95 = 2543logs

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

TC = Co*D/Qopt + [Cc*Qopt/2 ] *(1 - d/p)

TC = 1600*10000/2543 + [15*2543/2] *(1-40/60) = 6291.78 + 6293.76 = 12585.54

c. The number of operating days between orders

N = D/Qopt

N = 10000/2543 = 4 (optimal number of orders per year)

T = Days/N = 250/4 = 62.5 days