1. Solved Problem 1
Nelson’s Hardware Store stocks a 19.2 volt cordless drill that is a popular seller. Annual demand is 5,000 units, the ordering cost is $15, and the inventory holding cost is $4/unit/year.
a. What is the economic order quantity?
b. What is the total annual cost for this inventory item?
SOLUTION
a. The order quantity is
EOQ = =
2DS H
2(5,000)($15) $4
= ,500 = or 194 drills
b. The total annual cost is
C = (H) (S) = Q 2 D
($4) ($15) = $774.60
194 2
5,000

2. Solved Problem 2
For a product managed according to the Economic Order Quantity method, the table shows monthly demand rates for the last two years
The product is bought at 20 Euros per unit. Set up cost is 105 Euros and holding cost is 35% of the purchasing price.
Service level decided by management is 95%.
Delivery lead time is 1 month.
Calculate EOQ, Number of orders and time between orders
Calculate the reorder point ROP
Trace the inventory profile
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Year 1 80 70
110
100 90
120
130
Year 2 50
140

3. Solved Problem 2 Solution:
Total demand of the 1st year: 1200 (sum of the 1st row)
Total demand of the 2nd year: 1210 (sum of the 2st row)
Mean year demand: D = ( )/2 = 1205 per year
Mean monthly demand: d = ( )/24 = 100,4167 ≈ 100 prod/month
Economic Order Quantity:
EOQ = = = 190,1315 ≈ 190
Number of orders = D/EOQ = 1205/190 ≈ 6,3 orders per year
Time between orders = EOQ / D = 0,15 year or similarly EOQ/D*(12 months/year) = 1,89 months ≈ 2 months

4. Solved Problem 2 Calculation of Reorder Point
ROP = Average demand during lead time + Safety Stock
The lead time L is 1 month, and we also know the mean monthly demand d. Therefore, the average demand during lead time is d*L = 100.

5. Solved Problem 2
We also need to determine the safety stock S. The formula for the safety stock is S = z * standard deviation of the demand during lead time (sd).
The term z can be obtained from normal distribution tables. For a given service level of 95% z = 1,645. On the other hand, the monthly standard deviation of the demand can be calculated from the table of the monthly demand rates using the formula below.
Thereafter, S = 1,645*23,86177 = 39,2526 ≈ 40 products
As such, ROP = = 140
To trace the inventory, we start at the replenishment level (which is EOQ + safety stock) and we draw a graph similar to that of the slides.

6. Solved Problem 3
Our company manages an inventory of light bulbs. A particular lamp is bought at 10 cents. Ordering cost is 150 cents and holding cost is 20% of unit price per unit and year.
The factory works 12 months per year, steady production and management requires an 80% service level for this particular item. Delivery lead time from the supplier is 1,5 months.
The monthly demand over the last 24 months is as follows: 
500, 500, 425, 425, 450, 425, 425, 475, 475, 425, 425, 425, 475, 525, 425, 425, 450, 475, 425, 425, 475, 450, 425, 425.
Compute the following:
Economic order quantity
Reorder point

7. Solved Problem 3 SOLUTION Total demand: 10800 (sum of 24months)
Mean year demand: D = (10800)/2 = 5400 lamps per year
Mean monthly demand: d = 5400/12 = 450 lamps/month 
Economic Order Quantity:
EOQ = = = 900 lamps
Number of orders = D/EOQ = 5400/900 ≈ 6 orders per year
Time between orders = EOQ / D = 0,167 year or approximately ≈ 2 months

8. Solved Problem 3 Calculation of Reorder Point
ROP = Average demand during lead time + Safety Stock
The lead time L is 1,5 month. The mean monthly demand d is 450. Therefore, the average demand during lead time is d*L = 675.

9. Solved Problem 3
We also need to determine the safety stock S. The formula for the safety stock is S = z * standard deviation of the demand during lead time (sd). The term z can be obtained from normal distribution tables. For a given service level of 80% z = 0,84. On the other hand, the monthly standard deviation of the demand can be calculated from the table of the monthly demand rates using the formula below.
Thereafter, S = 0,84*sd* = 31,70 ≈ 32 lamps
As such, ROP = = 932

10. Solved Problem 4
Grey Wolf Lodge is a popular 500-room hotel in the North Woods. Managers need to keep close tabs on all room service items, including a special pine-scented bar soap. The daily demand for the soap is 275 bars, with a standard deviation of 30 bars. Ordering cost is $10 and the inventory holding cost is $0.30/bar/year. The lead time from the supplier is 5 days, with a standard deviation of 1 day. The lodge is open 365 days a year.
a. What is the economic order quantity for the bar of soap?
b. What should the reorder point be for the bar of soap if management wants to have a 99 percent cycle-service level?
c. What is the total annual cost for the bar of soap, assuming a Q system will be used?

11. Solved Problem 4
SOLUTION a. We have D = (275)(365) = 100,375 bars of soap; S = $10; and H = $0.30. The EOQ for the bar of soap is
EOQ = =
2DS H
2(100,375)($10)
$0.30
= 6,691, = 2, or 2,587 bars

12. Solved Problem 4
b. We have d = 275 bars/day, σd = 30 bars, L = 5 days, and σLT = 1 day.
σdLT = Lσd2 + d2σLT2 =
(5)(30)2 + (275)2(1)2 = bars
Consult the body of the Normal Distribution appendix for The closest value is , which corresponds to a z value of We calculate the safety stock and reorder point as follows:
Safety stock = zσdLT =
(2.33)(283.06) = or 660 bars
Reorder point = dL + Safety stock =
(275)(5) = 2,035 bars

13. Solved Problem 4 c. The total annual cost for the Q system is
C = (H) (S) + (H)(Safety stock) Q 2 D
C = ($0.30) ($10) + ($0.30)(660) = $974.05
2,587 2
100,375

14. Solved Problem 5 ABC Classification: Example
1 $ 60 90
PART UNIT COST ANNUAL USAGE

15. Solved Problem 5 ABC Classification: Example (cont.)
1 $ 60 90
PART UNIT COST ANNUAL USAGE
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE
9 $30,
8 16,
2 14,
1 5,
4 4,
3 3,
6 3,
5 3,
10 2,
7 1,
$85,400 A B C
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8,
B 1, 4,
C 6, 5, 10,
Example 10.1