Solutions to Inventory Practice Problems
1. If D = 1,000 per year, S = $62.50 per order, and H = $0.50 per unit per year, what is
the economic order quantity?
We’ll use these symbols to represent the parameters of inventory systems:
Q = Number of units per order
Q* = Optimum value for Q (EOQ)
D = Annual demand in units
S = Setup or ordering cost per order
H = Holding or carrying cost per unit per year
I = Percent holding cost
C = Price per unit
d = Daily demand
L = Lead time in days
Q*

2 DS
H
2 *1000 * 62.5
0.5
 500

2. If D = 8,000 per month, S = $45 per order, and H = $2 per unit per year, what is the
economic order quantity?
Note that annual demand is 12 * 8,000 = 96,000.
Q*

2 DS
H

2 * 96,000 * 45
2
 2,078
3. If the economic order quantity = 300, annual demand = 8,000 units, and order costs
= $45 per order, what is the annual per unit holding cost?
Q*

2 DS
H
300

2 * 8000 * 45
H
90,000
90,000 * H
H
720,000
H
 720,000

8
4. Kara Chubrik uses 1,500 per year of a certain subassembly that has an annual per
unit holding cost of $45 per unit. Each order placed costs Kara $150. She operates
300 days per year, and has found that an order must be placed with her supplier 6
working days before she can expect to receive that order. For this subassembly, find
(a) Economic Order quantity
Q*

2 DS
H

2 *1500 *150
45
 100
(b) Total annual holding cost
Annual holding cost

Q
H
2
100
* 45
2
 $2,250

(c) Annual ordering cost
Annual ordering cost

D
S
Q
1,500
*150
100
 $2,250

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(d) Reorder point
R
 dL

1,500
*6
300
 30
5. Lead time for one of your fastest-moving products is 21 days. Demand during this
period averages 100 units per day. What would be an appropriate reorder point?
R
 dL
 100 * 21
 2,100
6. Cong Manufacturing has gone out to bid for a regulator component. Expected
demand is 700 units per month. The item can be purchased either from Vesey
Manufacturing or from Vaccaro manufacturing. Their price lists are shown below.
Ordering cost is $50, and annual holding cost per unit is $5.
Vesey Mfg.
Quantity
Unit Price
1-499
$16.00
500-999
15.50
1000+
15.00
Vaccaro Mfg.
Quantity
Unit Price
1-399
$16.10
400-799
15.60
800+
15.10
(a) What is the economic order quantity?
Note that D = 12*700 = 8,400.
Q*

2 DS
H

2 * 8,400 * 50
5
 410
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(b) Which supplier should be used? Why?
Step 1. Calculate a value for Q* (we did this in part (a) above).
Step 2: For any discount, if the order quantity is too low to qualify for the discount, adjust
Q upward to the lowest feasible quantity.
For Vesey:
Quantity Min Unit Price
1-499
1
16.00
500-999 500
15.50
1000+ 1000
15.00
Q* Adjusted Q*
410
410
410
500
410
1000
Quantity Min Unit Price
1-399
1
16.10
400-799 400
15.60
800+
800
15.10
Q* Adjusted Q*
410
410
410
410
410
800
For Vaccaro:
(c) What is the optimal order quantity and the total annual cost?
Step 3: Calculate the total annual cost for each Q*.
Total annual cost = Ordering Cost + Holding Cost + Purchasing Cost

D
Q
S  H  CD
Q
2
For Vesey:
Quantity Min Unit Price Q* Ordering Cost Holding Cost Purchasing Cost
1-499
1
$ 16.00
410
$ 1,025
$ 1,025
$ 134,400
500-999 500
$ 15.50
500
$ 840
$ 1,250
$ 130,200
1000+ 1000 $ 15.00
1000
$ 420
$ 2,500
$ 126,000
Total
$136,449
$132,290
$128,920
For Vaccaro:
Quantity Min Unit Price
1-399
1
$ 16.10
400-799 400 $ 15.60
800+
800 $ 15.10
Q* Ordering Cost Holding Cost
410
$ 1,025
$ 1,025
410
$ 1,025
$ 1,025
800
$ 525
$ 2,000
Purchasing Cost
Total
$ 135,240
$137,289
$ 131,040
$133,089
$ 126,840
$129,365
Step 4: Select the Q* with the lowest total annual cost.
It looks like the thing to do is to order 1,000 at a time from Vesey Manufacturing.
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7. Costello Engineering has summarized the price list from four potential suppliers of
a valve assembly. See the table below. Annual usage is 2,400 valves; order cost is
$10 per order; and annual inventory holding costs are $3.33 per unit.
Which vendor should be selected, and what order quantity is best if Costello wants to
minimize total cost?
Vendor A
Quantity
Price
1-49
$35.00
50-74
$34.75
75-149
$33.55
150-299
$32.35
300-499
$31.15
500+
$30.75
Vendor B
Quantity
Price
1-74
$34.75
75-149
$34.00
150-299
$32.80
300-499
$31.60
500+
$30.50
Vendor C
Quantity
Price
1-99
$34.50
100-199
$33.75
200-399
$32.50
400+
$31.10
Vendor D
Quantity
Price
1-199
$34.25
200-399
$33.00
400+
$31.00
Step 1. Calculate a value for Q*:
Q*

2DS
H

2 * 2,400 *10
3.33
 120
Step 2: For any discount, if the order quantity is too low to qualify for the discount, adjust
Q upward to the lowest feasible quantity.
Step 3: Calculate the total annual cost for each Q*.
Vendor A
Quantity
1-49
50-74
75-149
150-299
300-499
500+
Price Min Q* Adj. Q* Holding Cost Ordering Cost Purchasing Cost
$35.00
1 120
120
$ 199.90
$ 199.90
$ 84,000.00
$34.75 50 120
120
$ 199.90
$ 199.90
$ 83,400.00
$33.55 75 120
120
$ 199.90
$ 199.90
$ 80,520.00
$32.35 150 120
150
$ 249.75
$ 160.00
$ 77,640.00
$31.15 300 120
300
$ 499.50
$ 80.00
$ 74,760.00
$30.75 500 120
500
$ 832.50
$ 48.00
$ 73,800.00
Total Cost
$84,399.80
$83,799.80
$80,919.80
$78,049.75
$75,339.50
$74,680.50
Price Min Q* Adj. Q* Holding Cost Ordering Cost Purchasing Cost
$34.75
1 120
120
$ 199.90
$ 199.90
$ 83,400.00
$34.00 75 120
120
$ 199.90
$ 199.90
$ 81,600.00
$32.80 150 120
150
$ 249.75
$ 160.00
$ 78,720.00
$31.60 300 120
300
$ 499.50
$ 80.00
$ 75,840.00
$30.50 500 120
500
$ 832.50
$ 48.00
$ 73,200.00
Total Cost
$83,799.80
$81,999.80
$79,129.75
$76,419.50
$74,080.50
Vendor B
Quantity
1-74
75-149
150-299
300-499
500+
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Vendor C
Quantity
1-99
100-199
200-399
400+
Price Min Q* Adj. Q* Holding Cost Ordering Cost Purchasing Cost
$34.50
1 120
120
$ 199.90
$ 199.90
$ 82,800.00
$33.75 100 120
120
$ 199.90
$ 199.90
$ 81,000.00
$32.50 200 120
200
$ 333.00
$ 120.00
$ 78,000.00
$31.10 400 120
400
$ 666.00
$ 60.00
$ 74,640.00
Total Cost
$83,199.80
$81,399.80
$78,453.00
$75,366.00
Quantity Price Min Q* Adj. Q* Holding Cost Ordering Cost Purchasing Cost
1-199
$34.25
1 120
120
$ 199.90
$ 199.90
$ 82,200.00
200-399 $33.00 200 120
200
$ 333.00
$ 120.00
$ 79,200.00
400+
$31.00 400 120
400
$ 666.00
$ 60.00
$ 74,400.00
Total Cost
$82,599.80
$79,653.00
$75,126.00
Vendor D
Step 4: Select the Q* with the lowest total annual cost.
Go with Vendor B; order in quantities of 500.
8. Demand during lead time for one brand of TV is normally distributed with a mean
of 36 TVs and a standard deviation of 15 TVs. What safety stock should be carried
for a 90% service level? What is the appropriate reorder point?
R
 dL  z 
 36  1.2815
 55
9. Based on available information, lead time demand for CD-ROM drives averages 50
units (normally distributed), with a standard deviation of 5 drives. Management
wants a 97% service level.
(a) What value of z should be applied?
The appropriate z-value is approximately 1.88.
(b) How many drives should be carried as safety stock?
z s
 1.88 * 5
9
(c) What is the appropriate reorder point?
R
 dL  z 
 50  9
 59
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10. Using the fixed-time period inventory model, and given daily demand with an
average of 300 units and standard deviation of 12 units, 4 days between inventory
reviews, 5 days for lead time, 1,200 units of inventory on hand, a stockout
probability of 0.05, what quantity should be ordered?
Q
 dT  L   zT L  I


 3004  5  1.645 4  5 * 12  1200
 2700  59.2  1200
 1,559.2
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