Question

A mail ordering company uses 800 boxes a year. The boxes can be purchased from either the supplier A or supplier B. Holding cost is 25% of unit cost and the ordering cost is $ 40 per order. The following quantity discounts are available:

Supplier A			Supplier B
Quantity	Unit Price		Quantity	Unit Price
1-199	$14.00		1-149	$14.10
200-499	$13.80		150-349	$13.90
500+	$13.60		350+	$13.70

Which supplier should be used and what is (a) the optimal order quantity and (b) the number of orders per year if the intent is to minimize the total annual cost? Use appropriate calculations to show your answers.

Answer 1

To choose between Supplier A and B, lets compute who delivers the boxes at lowest cost.

Supplier A:

Step 1:

Beginning with the lowest unit price, lets find a price which is feasible.

Minimum point

P = $13.60:

Given D = 800*12 = $ 9600

S= $40

H = 25% of purchase cost

Economic Order quantity = (2D*S/H)^0.5

= 475

This is not feasible as this price range is available only for orders with quantity above 500

Nest Minimum point: $13.8

Economic order quantity is computed using same formula to be = 472

This value is feasible as the quantity range is between 200-499.

Total cost for Q=472 and Q=500

Total Cost = Q*H/2 + D*S/Q + P*D

where H - holding cost = 0.25* 13.8 ( Unit price)

When Q is 472,

Total cost = $134107.76 ( substituting values in the total cost formula above)

When Q = 500,

Total cost = $132718

Thus, optimal quantity from supplier A is 500 with a total cost of $132718

Similarly, for supplier B,

Beginning with the lowest unit price, computing minimum points for P = $13.70 ( lowest price)

Economic Order quantity = (2* D*S/ H)^0.5

Thus EOQ- Q= 474 which is feasible as it lies in the range 350+

Total cost = Q*H/2 + D*S/Q + P*D = $133141.86

Comparing the total cost of Supplier A vs Supplier B, Supplier A should be chosen with a EOQ of 500 and 2 orders.