Problem 4. A company considers two options for an SKU with an annual demand of 1
ID: 361739 • Letter: P
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Problem 4. A company considers two options for an SKU with an annual demand of 15,000 units, each costing $2. Ordering costs are $60 per order and the cost of carrying inventory is 25%. Option A no discount. Option B: a 3% discount for orders of 5,000 units at a time. Calculate the costs without (option A) and with the discount (option B), suggest which option is better and the saving compared to the other option. Question # 9. Option A: Total cost without discount 10. Option B: Total cost with discount 11. Which option is better? 12. What is the saving? Answer/SolutionExplanation / Answer
For the given problem quantity discount or price-volume range model is applied.
Quantity Discount Model
1. For each price range (C), compute EOQ
2. If EOQ < Minimum quantity for price range, adjust the quantity to Q = Minimum for discount. If the EOQ > Maximum quantity for discount, adjust the quantity to Q = Maximum for discount. If the EOQ is within the range, then adjust Q = EOQ.
3. For each EOQ or adjusted Q, compute Total cost
4. Choose the lowest-cost quantity.
Annual Demand
A
15000.00
Ordering cost
S
$60.00
Holding cost per year
I
25.00%
Quantity Range
Unit Price (C)
EOQ
order quantity
Annual Material Cost
(AMC)
Annual Ordering Cost (AOC)
Annual Carrying Cost (ACC)
Annual Inventory cost
Total Annual cost ($)
(2*A*S/C*I)
(Q)
A*C
(A/Q)*S
(Q/2)*H
(AOC + ACC)
(AOC + ACC + AMC)
No Discounts
$2
1897
1897
$30,000
$474
$474
$949
$30,949
3% discount if 5000 units order at a time
$2 x (1 – 0.03)
= $1.94
1926
5,000
$29,100
$180
$1,213
$1,393
$30,493
Since EOQ is less than minimum order quantity of 5000 units for discount option, the revised order quantity = 5000 units.
9. Option A Total cost without discount
$30,949
10. Option A Total cost without discount
$30,493
11. Which option is better?
Option B: Order quantity = 5000 at the 3% discounted price
12. What is saving?
30,949 – 30,493 = $456
Annual Demand
A
15000.00
Ordering cost
S
$60.00
Holding cost per year
I
25.00%
Quantity Range
Unit Price (C)
EOQ
order quantity
Annual Material Cost
(AMC)
Annual Ordering Cost (AOC)
Annual Carrying Cost (ACC)
Annual Inventory cost
Total Annual cost ($)
(2*A*S/C*I)
(Q)
A*C
(A/Q)*S
(Q/2)*H
(AOC + ACC)
(AOC + ACC + AMC)
No Discounts
$2
1897
1897
$30,000
$474
$474
$949
$30,949
3% discount if 5000 units order at a time
$2 x (1 – 0.03)
= $1.94
1926
5,000
$29,100
$180
$1,213
$1,393
$30,493
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