Question

IM.82 A distributor of industrial equipment purchases specialized compressors for use in air conditioners. The regular price is $40, however, the manufacturer of this compressor offers quantity discounts per the following discount schedule:

Option Plan Quantity Discount

A 1 - 299 0%

B 300 - 1,299 0.50%

C 1,300+ 1.00%

The distributor pays $80 each time it places an order with the manufacturer. Holding costs are negligible (none) but they do earn 13% annual interest on all cash balances (meaning there will be a financial opportunity cost when they put cash into inventory). Annual demand is expected to be 5,000 units.

When there is no quantity discount (Option Plan A, the first row of the schedule listed above), what is the adjusted order quantity? (Display your answer to the nearest whole number.)

Based on your answer to the previous question, and based on the annual demand as stated above, what will be the annual ordering costs? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (two questions back), what will be the average number of units held in inventory? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (three questions back), and assuming a materials cost for the given discount, what will be the annual holding cost? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (four questions back), and assuming a materials cost for the given discount, what will be the total annual inventory cost? (Display your answer to the nearest whole number.)

When there is a 0.50% discount (Option Plan B, the second row of the schedule listed above), what is the adjusted order quantity? (Display your answer to the nearest whole number.)

Based on your answer to the previous question, and based on the annual demand as stated above, what will be the annual ordering costs? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (two questions back), what will be the average number of units held in inventory? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (three questions back), and assuming a materials cost for the given discount, what will be the annual holding cost? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (four questions back), and assuming a materials cost for the given discount, what will be the total annual inventory cost? (Display your answer to the nearest whole number.)

When there is a 1.00% discount (Option Plan C, the third row of the schedule listed above), what is the adjusted order quantity? (Display your answer to the nearest whole number.)

Based on your answer to the previous question, and based on the annual demand as stated above, what will be the annual ordering costs? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (two questions back), what will be the average number of units held in inventory? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (three questions back), and assuming a materials cost for the given discount, what will be the annual holding cost? (Display your answer to the nearest whole number.)

Using the adjusted order quantity as determined above (four questions back), and assuming a materials cost for the given discount, what will be the total annual inventory cost? (Display your answer to the nearest whole number.)

Sort each option plan from left to right by dragging the MOST preferred option plan to the left, and the LEAST preferred option plan to the right: Option Plan B Option Plan C Option Plan A

Answer 1

Annual demand, D = 5000

Ordering cost, K = $ 80

Holding cost, H = 40*13% = $ 5.2

Under option plan A, optimal order quantity as per EOQ = √(2*D*k/H) = √(2*5000*80/5.2) = 392

1) Without discount, adjusted order quantity for level A = 301

2) Annual ordering cost = (D/Q)*K = (5000/392)*80 = $ 1,020.41

3) Average number of units held in inventory = 392/2 = 196

4) Annual holding cost = 196*5.2 = $ 1,019.2

5) Total annual inventory cost = Ordering cost + Holding cost + Product cost = (D/Q)*K + (Q/2)*H + P*D = 1020.41+1019.2+5000*40 = $ 202,039.61

6) For option B, unit cost = 40*(1-.5%) = $ 39.8

Holding cost, H = 39.8*13% = $ 5.174

Adjusted order quantity is the min order quantity = sqrt(2*5000*80/5.174) = 393

7) Annual ordering cost = (5000/393)*80 = $ 1,017.81

8) Average number of units held in inventory = 393/2 = 197

9) Annual holding cost = 197*5.174 = $ 1,019.29

10) Total annual inventory cost = 1017.81+1019.29+5000*39.8 = $ 201,037

11) For plan C, adjusted order quantity is the min order quantity for level C = 1300

12) Annual ordering cost = (5000/1300)*80 = $ 307.7

13) Average number of units held in inventory = 1300/2 = 650

14) Unit cost = 40*(1-1%) = $ 39.6

Holding cost per unit, H = 39.6*.13 = $ 5.148

Annual holding cost = 650*5.148 = $ 3,346.2

15) Total annual inventory cost = 307.7+3346.2+5000*39.6 = $ 201,653.9

16) Total annual inventory cost of Level B is the lowest. Therefore, choose option plan B