Operations Management

1. Inventory Management

2. What Is Inventory?
• Stock of items kept to meet future demand
• Purpose of inventory management
• how many units to order
• when to order
13-2

3. Types of Inventory
13-3
▶ Raw material
▶ Purchased but not processed
▶ Work-in-process (WIP)
▶ Undergone some change but not completed
▶ A function of cycle time for a product
▶ Maintenance/repair/operating (MRO)
▶ Necessary to keep machinery and processes productive
▶ Finished goods
▶ Completed product awaiting shipment

4. Demand Types
Independent demand – the
demands for various items are
unrelated to each other
• For example, a workstation may
produce many parts that are
unrelated but meet some external
demand requirement
Dependent demand – the need for
any one item is a direct result of the
need for some other item
• Usually a higher-level item of
which it is part

5. Inventory Costs
• Carrying cost
• cost of holding an item in inventory
• Ordering cost
• cost of replenishing inventory
• Shortage cost
• temporary or permanent loss of sales when demand cannot be met
13-5

6. Inventory Control Systems
• Continuous system (fixed-order-quantity)
• constant amount ordered when inventory declines to predetermined
level
• Periodic system (fixed-time-period)
• order placed for variable amount after fixed passage of time
13-6

7. • Inventory remaining must be
continually monitored
• Has a smaller average
inventory
• Favors more expensive
items
• Is more appropriate for
important items
• Requires more time to
maintain – but is usually
more automated
• Is more expensive to
implement
– Counting takes place only at the
end of the review period
– Has a larger average inventory
– Favors less expensive items
– Is sufficient for less-important
items
– Requires less time to maintain
– Is less expensive to implement
Continuous system
Fixed-Order Quantity
Continuous system
Fixed-Time Period

8. Comparison

9. ABC Classification
• Class A
• 5 – 15 % of units
• 70 – 80 % of value
• Class B
• 30 % of units
• 15 % of value
• Class C
• 50 – 60 % of units
• 5 – 10 % of value
13-9

10. ABC Classification
1 $ 60 90
2 350 40
3 30 130
4 80 60
5 30 100
6 20 180
7 10 170
8 320 50
9 510 60
10 20 120
PART UNIT COST ANNUAL USAGE
13-10

11. ABC Classification
9 $30,600 35.9 6.0 6.0
8 16,000 18.7 5.0 11.0
2 14,000 16.4 4.0 15.0
1 5,400 6.3 9.0 24.0
4 4,800 5.6 6.0 30.0
3 3,900 4.6 13.0 43.0
6 3,600 4.2 18.0 61.0
5 3,000 3.5 13.0 71.0
10 2,400 2.8 12.0 83.0
7 1,700 2.0 17.0 100.0
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE
A
B
C
$85,400
13-11

12. ABC Classification
Example 10.1
% OF TOTAL % OF TOTAL
CLASS ITEMS VALUE QUANTITY
A 9, 8, 2 71.0 15.0
B 1, 4, 3 16.5 28.0
C 6, 5, 10, 7 12.5 60.0
13-12

13. Economic Order Quantity
(EOQ) Models
• EOQ
• continuous inventory system
• optimal order quantity that will minimize total inventory costs
• Basic EOQ model
• Production quantity model
• Order cycle
• the time between receipt of orders in an inventory system
13-13

14. Assumptions of Basic EOQ Model
• Demand is known with certainty and is constant over time
• No shortages are allowed
• Lead time for the receipt of orders is constant
• Order quantity is received all at once
• Only variable cost is holding and ordering cost
• Quantity discounts are not allowed
13-14

15. Inventory Order Cycle
13-15

16. EOQ Cost Model
13-16
Annual ordering cost =
CoD
Q
Annual carrying cost =
CcQ
2
Total cost = +
CoD
Q
CcQ
2
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity

17. EOQ Cost Model
TC = +
CoD
Q
CcQ
2
= – +
CoD
Q2
Cc
2
TC
Q
0 = – +
C0D
Q2
Cc
2
Qopt =
2CoD
Cc
Deriving Qopt Proving equality of
costs at optimal point
=
CoD
Q
CcQ
2
Q2 =
2CoD
Cc
Qopt =
2CoD
Cc
13-17

18. EOQ Cost Model
13-18

19. EOQ Example
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
Qopt =
2CoD
Cc
Qopt =
Qopt =
TCmin = +
CoD
Q
CcQ
2
TCmin =
TCmin =
Orders per year = D/Qopt Order cycle time =
13-19

20. EOQ Example
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
Qopt =
2CoD
Cc
Qopt =
2(150)(10,000)
(0.75)
Qopt = 2,000 gallons
TCmin = +
CoD
Q
CcQ
2
TCmin = +
(150)(10,000)
2,000
(0.75)(2,000)
2
TCmin = $750 + $750 = $1,500
Orders per year = D/Qopt
= 10,000/2,000
= 5 orders/year
Order cycle time = 311 days/(D/Qopt)
= 311/5
= 62.2 store days
13-20

21. Production Quantity Model
• Order is received gradually, as inventory is
simultaneously being depleted
• non-instantaneous receipt model
• assumption that Q is received all at once is relaxed
• p - daily rate at which an order is received over time,
the production rate
• d - daily rate at which inventory is demanded
13-21

22. Production Quantity Model
13-22

23. Production Quantity Model
p = production rate d = demand rate
Maximum inventory level = Q - d
= Q 1 -
Q
p
d
p
Average inventory level = 1 -
Q
2
d
p
TC = + 1 -
d
p
CoD
Q
CcQ
2
Qopt =
2CoD
Cc 1 -
d
p
13-23

24. Production Quantity Model
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = =
2CoD
Cc 1 - d
p
TC = + 1 - =
d
p
CoD
Q
CcQ
2
Production run = =
Q
p
13-24

25. Production Quantity Model
Number of production runs = =
D
Q
Maximum inventory level = Q 1 - =
d
p
13-25

26. Production Quantity Model
Cc = $0.75 per gallon Co = $150 D = 10,000 gallons
d = 10,000/311 = 32.2 gallons per day p = 150 gallons per day
Qopt = = = 2,256.8 gallons
2CoD
Cc 1 - d
p
2(150)(10,000)
0.75 1 -
32.2
150
TC = + 1 - = $1,329
d
p
CoD
Q
CcQ
2
Production run = = = 15.05 days per order
Q
p
2,256.8
150
13-26

27. Production Quantity Model
Number of production runs = = = 4.43 runs/year
D
Q
10,000
2,256.8
Maximum inventory level = Q 1 - = 2,256.8 1 -
= 1,772 gallons
d
p
32.2
150
13-27

28. Reorder Point
• Inventory level at which a new order is placed
R = dL
where
d = demand rate per period
L = lead time
13-28

29. Reorder Point
Demand = 10,000 gallons/year
Store open 311 days/year
Daily demand =
Lead time = L = 10 days
R = dL =
13-29

30. Reorder Point
Demand = 10,000 gallons/year
Store open 311 days/year
Daily demand = 10,000 / 311 = 32.154
gallons/day
Lead time = L = 10 days
R = dL = (32.154)(10) = 321.54 gallons
13-30

31. Safety Stock
• Safety stock
• buffer added to on hand inventory during lead time
• Stockout
• an inventory shortage
• Service level
• probability that the inventory available during lead time will meet
demand
• P(Demand during lead time <= Reorder Point)
13-31