1. OPIM 310-Lecture #5 Instructor: Jose Cruz
Inventory Management
OPIM 310-Lecture #5
Instructor: Jose Cruz

2. Inventory Stock of items held to meet future demand
Inventory management answers two questions
How much to order
When to order

3. Types of Inventory Raw materials Purchased parts and supplies Labor
In-process (partially completed) products
Component parts
Working capital
Tools, machinery, and equipment

4. Reasons to Hold Inventory
Meet unexpected demand
Smooth seasonal or cyclical demand
Meet variations in customer demand
Take advantage of price discounts
Hedge against price increases
Quantity discounts

5. Two Forms of Demand Dependent Independent
Items used to produce final products
Independent
Items demanded by external customers

6. Inventory Costs Carrying Cost Ordering Cost Shortage 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

7. 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

8. 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
The order quantity is received all at once

9. The Inventory Order Cycle
Demand rate
Time
Lead time
Order placed
Order receipt
Inventory Level
Reorder point, R
Order quantity, Q
Figure 10.1

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

11. EOQ Cost Model TC = + CoD Q CcQ 2 = + Q2 Cc TC Q 0 = + C0D Qopt == Q2 Cc
TC Q
0 =
C0D
Qopt =
2CoD
Deriving Qopt
Proving equality of costs at optimal point =
CoD Q
CcQ 2
Q2 =
2CoD Cc
Qopt =
Co - cost of placing order D - annual demand
Cc - annual per-unit carrying cost Q - order quantity
Annual ordering cost =
CoD Q
Annual carrying cost =
CcQ 2
Total cost =

12. EOQ Cost Model Annual cost ($) CoD Q Ordering Cost = Order Quantity, Q
Figure 10.2

13. EOQ Cost Model Annual cost ($) CcQ 2 Carrying Cost = CoD Q
Order Quantity, Q
Annual cost ($)
Carrying Cost =
CcQ 2
Ordering Cost =
CoD Q
Figure 10.2

14. EOQ Cost Model Slope = 0 Total Cost Order Quantity, Q Annual cost ($)
Minimum total cost
Optimal order
Qopt
Carrying Cost =
CcQ 2
Ordering Cost =
CoD Q
Figure 10.2

15. EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Qopt = 2CoD
2(150)(10,000)
(0.75)
Qopt = 2,000 yards
TCmin =
CoD Q
CcQ 2
TCmin =
(150)(10,000)
2,000
(0.75)(2,000)
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
Example 10.2

16. EOQ with Noninstantaneous Receipt
Q(1-d/p)
Inventory
level
(1-d/p) Q 2
Time
Order
receipt period
Begin
order
receipt
End
Maximum
inventory level
Average
Figure 10.3

17. EOQ with Noninstantaneous Receipt
p = production rate d = demand rate
Maximum inventory level = Q d
= Q 1 - Q p d
Average inventory level = 2
TC =
CoD
CcQ
Qopt =
2CoD
Cc 1 - d p

18. Production Quantity Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Qopt = = = 2,256.8 yards
2CoD
Cc 1 - d p
2(150)(10,000)
32.2
150
TC = = $1,329 d p
CoD Q
CcQ 2
Production run = = = days per order Q p
2,256.8
150
Example 10.3

19. Production Quantity Cc = $0.75 per yard Co = $150 D = 10,000 yards
d = 10,000/311 = 32.2 yards per day p = 150 yards per day
Number of production runs = = = 4.43 runs/year D Q
10,000
2,256.8
Maximum inventory level = Q = 2,
= 1,772 yards d p
32.2
150
Qopt = = = 2,256.8 yards
2CoD
Cc 1 - d p
2(150)(10,000)
32.2
150
TC = = $1,329
CoD Q
CcQ 2
Production run = = = days per order
2,256.8
Example 10.3

20. P = per unit price of the item
Quantity Discounts
Price per unit decreases as order quantity increases
TC = PD
CoD Q
CcQ 2
where
P = per unit price of the item
D = annual demand

21. P = per unit price of the item
Quantity Discounts
Price per unit decreases as order quantity increases
TC = PD
CoD Q
CcQ 2
where
P = per unit price of the item
D = annual demand
ORDER SIZE PRICE
$10
(d1)
(d2)

22. Quantity Discount Model
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
Figure 10.4

23. Quantity Discount Model
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
Figure 10.4

24. Quantity Discount QUANTITY PRICE 1 - 49 $1,400 50 - 89 1,100 90+ 900
$1,400
,100
Co = $2,500
Cc = $190 per computer
D = 200
Qopt = = = 72.5 PCs
2CoD Cc
2(2500)(200)
190
TC = PD = $233,784
CoD
Qopt
CcQopt 2
For Q = 72.5
TC = PD = $194,105
CoD Q
CcQ 2
For Q = 90
Example 10.4

25. When to Order
Reorder Point is the level of inventory at which a new order is placed
R = dL
where
d = demand rate per period
L = lead time

26. Reorder Point Example Demand = 10,000 yards/year
Store open 311 days/year
Daily demand = 10,000 / 311 = yards/day
Lead time = L = 10 days
R = dL = (32.154)(10) = yards
Example 10.5

27. Safety Stocks Safety stock Stockout Service level
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

28. Variable Demand with a Reorder Point
point, R Q LT
Time
Inventory level
Figure 10.5

29. Reorder Point with a Safety Stock
point, R Q LT
Time
Inventory level
Safety Stock
Figure 10.6

30. Reorder Point With Variable Demand
R = dL + zd L
where
d = average daily demand
L = lead time
d = the standard deviation of daily demand
z = number of standard deviations
corresponding to the service level
probability
zd L = safety stock

31. Reorder Point for a Service Level
Probability of
meeting demand during
lead time = service level
a stockout R
Safety stock dL
Demand
zd L
Figure 10.7

32. Reorder Point for Variable Demand
The carpet store wants a reorder point with a 95% service level and a 5% stockout probability
d = 30 yards per day
L = 10 days
d = 5 yards per day
For a 95% service level, z = 1.65
R = dL + z d L
= 30(10) + (1.65)(5)( 10)
= yards
Safety stock = z d L
= (1.65)(5)( 10)
= 26.1 yards
Example 10.6

33. Order Quantity for a Periodic Inventory System
Q = d(tb + L) + zd tb + L - I
where
d = average demand rate
tb = the fixed time between orders
L = lead time
sd = standard deviation of demand
zd tb + L = safety stock
I = inventory level

34. Fixed-Period Model with Variable Demand
d = 6 bottles per day
sd = 1.2 bottles
tb = 60 days
L = 5 days
I = 8 bottles
z = 1.65 (for a 95% service level)
Q = d(tb + L) + zd tb + L - I
= (6)(60 + 5) + (1.65)(1.2)
= bottles

35. ABC Classification System
Demand volume and value of items vary
Classify inventory into 3 categories, typically on the basis of the dollar value to the firm
PERCENTAGE PERCENTAGE
CLASS OF UNITS OF DOLLARS A
B 30 15 C

36. ABC Classification PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40
1 $ 60 90
PART UNIT COST ANNUAL USAGE
Example 10.1

37. ABC Classification PART UNIT COST ANNUAL USAGE 1 $ 60 90 2 350 40
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
Example 10.1

38. ABC Classification A B C PART UNIT COST ANNUAL USAGE 1 $ 60 90
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
Example 10.1

39. ABC Classification A B C PART UNIT COST ANNUAL USAGE 1 $ 60 90
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

40. ABC Classification C B A % of Value | | | | | | 0 20 40 60 80 100
100 –
80 –
60 –
40 –
20 –
0 –
| | | | | |
% of Quantity
% of Value A B C

41. 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
The order quantity is received all at once