Question

The annual demand for an item is 10,000 units. The cost to process an order is $75 and the annual inventory holding cost is 20% of item cost.

1. What is the optimal order quantity, given the following price breaks for purchasing the item?

2. What price should the firm pay per unit?

3. What is the total annual cost at the optimal behavior?

Quantity	Price
1-9	$2.95 per unit
10 - 999	$2.50 per unit
1,000 - 4,999	$2.30 per unit
5,000 or more	$1.85 per unit

Answer 1

For various prices, we calculate EOQ as follows:

C G H I A Price Order Quantity Number of orders (Annual demand / Order Quantity) Ordering Cost (number of orders x S) Carrying Cost ((Ordering quantity/2) x Carrying cost) Cost of Purchase (Price x Annual Demand) Total Cost 2.30 $ 2.50 1.85 2.95 Annual demand Da Price Carrying cost Order cost EOQ 1732.05 10,000 1594.48 1805.79 2013.47 P 1.85 6.27 5.77 5.54 4,97 470.37 S 415.33 S 180.58 $ 201.35 23,000.00 $18,500.00 25.606.22 23.595.91$19.073.84 433.01 S 4 20% S H 372.49 173.21 $ $75.00 159.45 S S SQRT(2 Da S/(H*P)) 2013.47 $29,500.00 6 25,000.00 $30,129.82

The actual quantities for EOQ for each price are shown in the table on the left. Calculation for Price of $1.85 is shown for reference. The above table in form of formulas is as shown below:

Now, as per range given, we will input the minimum or maximum no. of items to be purchased for each discount level based on the EOQ we calculated i.e. EOQ for price 2.95 is 1594.48, hence we need to put quantity as 9 since for 9 nos. the total cost will be less as compared to lesser nos. and we cannot put more than 9 nos. for this discount level as shown below:

G I H Price Order Quantity Number 1.85 2013.47 - $ D$2 / J2 J3 $D$5 1. ,95 2 5 .3 Annual demand Da 10000 1732.05 1594.48 1805.79 $D$2/G2 -G3* $D$5 G2*$D$4/2H2*$D$4 / 2 -G1*$D$2 -SUM(G4:G6 )SUM (H4: H6)-SUM (14:16) -SUM(J4:16) Price forders (Annual demand/Order Quantity) $D$2/12 - 13* $D$5 | 12*$D$4/2 | 12* $D$4/2 E11*$D$2 SD$2/H2 H3* $D$5 85 Ordering Cost (number of orders xS) Carrying Cost ((Ordering quantity/2) x Carrying cost) Cost of Purchase (Price x Annual Demand) Total Cost Carrying cost Order cost EOQ 0.2 4 H S SORT(2*Da*s/(H P))-SQRT(2*D2* D5/ (D4*D3)) H1 $D$2 J1*$D$2

2.95 $ 2.30 $ Price 2.50 1.85 Order Quantity 9 999 1805.79 5000 Number of orders (Annual demand Order Quantity) 10.01 1111.11 5.54 2.00 750.75$ 415.33 $ $ 83,333.33 $ Ordering Cost (number of orders x S) Carrying Cost ((Ordering quantity 2) x Carrying cost) Cost of Purchase (Price x Annual Demand) Total Cost 150.00 180.58 0.90 $ 99.90 $ 500.00 $ 29,500.00 $25,000.00 $23,00o.00 $18,500.00 $112,834.23 $25,850.65$23,595.91 $19,150.00

For price $2.95, we have put 9 as it is closest to calculated EOQ of 1594.48 out of discount range

For price $2.50, we have put 999 as it is closest to calculated EOQ of 1732.05 out of discount range

For price $2.30, we have retained EOQ = 1805.79 since it is fitting within discount range

For price $1.85, we have put 5000 as it is closest to calculated EOQ of 2013.47 as per discount range

As seen, the total cost for EOQ of 5000 is lowest.

Hence, we answer questions as shown below:

1. What is the optimal order quantity, given the following price breaks for purchasing the item?

Optimal order quantity = 5000 nos

2. What price should the firm pay per unit?

The firm should pay a price of $1.85

3. What is the total annual cost at the optimal behavior?

Total annual cost = $19,150