Question

5. Consider the following case, where

D = 10,000 units (annual demand)

S = $20 to place each order

i = 20 percent of unit price/cost (annual holding cost: storage, interest, obsolescence, etc.)

C = unit price (according to the order size)

orders of 0 to 499 units, $5.00 per unit;

orders of 500 to 999, $4.50 per unit;

orders of 1,000 and up, $3.90 per unit

What quantity should be ordered?

Answer 1

Based on given data, we first consider C = $5

H = 20%*5 = $1

Hence, we get the EOQ = = = 632.45 units

Next, we find EOQ for C = $4.50

H = 20%*4.5 = $0.9

Hence, we get the EOQ = = = 666.66 units

For other ranges, the change of Price is very less compared to change in the extreme point of the range. e.g. Change for the next range is directly to 1000 and next lower range is 499 whereas the price is changing only from 4.50 to 3.90 in 1st case and 4.50 to 5.00 in 2nd case. Hence, there will not be a major change in EOQ, and EOQ will remain in range of 500 to 999 only. Hence, we will not calculate EOQ for the Price of other ranges.

Further, EOQ = 666.66 is valid for the highest range of 500 to 999 units

Hence, the points in other ranges where the Cost may be lowest are extreme point nearest to EOQ in respective ranges i.e.

Range of less than 0 to 499 = In this range, Discount is not available and the price is more than the EOQ range of 500 to 999 as well as total inventory costs will also be more since it is not EOQ. Hence, total cost will be higher for both purchase cost and inventory costs. Hence, we will not evaluate this range.

Range of 500 to 999 = 666.66

Range of 1,000 and up = 1000

We calculate the total costs for each of this point as shown below:

EOQ = 632.45:

Price P = $4.50

H = 20%*4.50 = $0.9

Total Cost = D*P + = 10000 * 4.50 + = 45000 + 300 + 300 = $45,600

Q = 1000:

Price P = $3.90

H = 20%*3.90 = $0.78

Total Cost = D*P + = 10000 * 3.90 + = 39000 + 200 + 390 = $39590

As seen from above, the total cost for an order quantity of 1000 is the least.

Hence, the Quantity of 1000 units should be ordered.