Annual demand is 4,000 units, ordering cost $10, carrying cost 50 cents per unit per year.?

Question

a) Determine the ordering frequency, total ordering cost, total inventory carrying cost and total cost of running the inventory system if orders 100 units at a time.
b) Repeat (a) if orders 800 units at a time.
c) Determine the optimal inventory policy for the firm.

Answer 1

a) Number of orders to be placed = 40 and so you need to place an order every 9 days. Total ordering cost is $400, Average inventory is 50 units for the whole year and so inventory carrying cost is 25 dollars. So, total cost is $ 425.

b) Number of orders to be placed = 5 and so the ordering frequency is once 73 days. Ordering cost is $ 50.

Average inventory is 400 units and so cost of inventory is 200 dollars. Total cost is $ 250.

c) If we have to choose between a and b, choice is a. If a better policy is to be found out, graphical solutions and or linear equations are to be used.

Answer 2

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RE:
Annual demand is 4,000 units, ordering cost $10, carrying cost 50 cents per unit per year.?
a) Determine the ordering frequency, total ordering cost, total inventory carrying cost and total cost of running the inventory system if orders 100 units at a time.
b) Repeat (a) if orders 800 units at a time.
c) Determine the optimal inventory policy for the firm.

Answer 3

Ordering 100 units at a time, you'll have to place 40 orders over the course of the year: $400
Storage of 100 units: $50
Total: $450

Ordering 800 units at a time, you'll have to place 5 orders over the course of the year: $50
Storage of 800 units: $400
Total: $450

If you've noticed, ordering cost and carrying cost are inversely proportional; as one increases, the other decreases.

The formula for total cost is (x = order amount):

Total Cost = (4000/x) * 10 + x * 0.5

To find the minimal (optimal) cost, we find the derivative of the above formula and equal it to 0:

10*(-4,000/x^2) + 0.5 = 0
(-40,000/x^2) + 0.5 = 0
-40,000/x^2 = -0.5
-40,000 = -0.5 * x^2
80,000 = x^2
282.842 = x

Answer 4

Carrying Cost Formula

Answer 5

Holding Cost Formula

Answer 6

a) Ordering frequency, N = D/Q = 4000/100 = 40 orders/year
Total ordering cost = Co x N = 10 x 40 = $400
Carrying cost = Ch(Q/2) = 0.50(100/2) = $25
Total annual cost = Co(D/Q) + Ch(Q/2) = $425
b) You can do this one with the formulas and example in (a).
c) Ch = (Q*/2) = Co(D/Q*), where Q* is the optimum order quantity.
Solve for Q*
Q* = SqrRoot[(2CoD)/Ch] = √[(2 x 10 x 4000)/0.50] = 400 units/order.
and total annual cost is 10(4000/400) + 0.5(400/2) = $200