1. Inventory Management

2. Lecture Outline Elements of Inventory Management
Inventory Control Systems
Economic Order Quantity Models
Quantity Discounts
Reorder Point
Order Quantity for a Periodic Inventory System

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

4. Types of Inventory Raw materials Purchased parts and supplies
Work-in-process (partially completed) products (WIP)
Items being transported
Tools and equipment

5. Inventory and Supply Chain Management
Bullwhip effect
demand information is distorted as it moves away from the end-use customer
higher safety stock inventories to are stored to compensate
Seasonal or cyclical demand
Inventory provides independence from vendors
Take advantage of price discounts
Inventory provides independence between stages and avoids work stop-pages

6. Two Forms of Demand Dependent Independent
Demand for items used to produce final products
Tires stored at a Goodyear plant are an example of a dependent demand item
Independent
Demand for items used by external customers
Cars, appliances, computers, and houses are examples of independent demand inventory

7. Inventory and Quality Management
Customers usually perceive quality service as availability of goods they want when they want them
Inventory must be sufficient to provide high-quality customer service in TQM

8. 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

9. 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

10. ABC Classification Class A Class B Class C 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

11. ABC Classification: Example
1 $ 60 90
PART UNIT COST ANNUAL USAGE

12. ABC Classification: Example (cont.)
1 $ 60 90
PART UNIT COST ANNUAL USAGE
TOTAL % OF TOTAL % OF TOTAL
PART VALUE VALUE QUANTITY % CUMMULATIVE 9 8 2
4 4,
3 3,
6 3,
5 3,
10 2,
7 1,
$85,400
Example 10.1

13. Economic Order Quantity (EOQ) Models
optimal order quantity that will minimize total inventory costs
Basic EOQ model
Production quantity model

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

15. Inventory Order Cycle Demand rate Time Lead time Order placed
Order receipt
Inventory Level
Reorder point, R
Order quantity, Q

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

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

18. EOQ Cost Model (cont.) Order Quantity, Q Annual cost ($) Slope = 0
Minimum total cost
Optimal order
Qopt

19. EOQ Example Cc = $0.75 per yard Co = $150 D = 10,000 yards Qopt = 2CoD
Qopt = yards
TCmin =
CoD Q
CcQ 2
TCmin =
TCmin = =
Orders per year = D/Qopt =
= orders/year
Order cycle time = days/(D/Qopt) =
= store days

20. Production Quantity Model
An inventory system in which an order is received gradually, as inventory is simultaneously being depleted
AKA 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, a.k.a. production rate
d - daily rate at which inventory is demanded

21. Production Quantity Model (cont.)
Inventory
level
(1-d/p) Q 2
Time
Order
receipt period
Begin
order
receipt
End
Maximum
inventory level
Average

22. Production Quantity Model (cont.)
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 -

23. Production Quantity Model: Example
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 = = = yards
2CoD
Cc 1 - d p
TC = = d p
CoD Q
CcQ 2
Production run = = = days per order Q p

24. Production Quantity Model: Example (cont.)
Number of production runs = = = runs/year D Q
Maximum inventory level = Q =
= yards d p

25. 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

26. Quantity Discount Model (cont.)
Qopt
Carrying cost
Ordering cost
Inventory cost ($)
Q(d1 ) = 100
Q(d2 ) = 200
TC (d2 = $6 )
TC (d1 = $8 )
TC = ($10 )
ORDER SIZE PRICE
$10
100 – (d1)
(d2)

27. Quantity Discount: Example
QUANTITY PRICE
$1,400
,100
Co = $2,500
Cc = $190 per computer
D = 200
Qopt = = = PCs
2CoD Cc
TC = PD =
CoD
Qopt
CcQopt 2
For Q = 72.5
TC = PD =
CoD Q
CcQ 2
For Q = 90

28. Reorder Point Level of inventory at which a new order is placed R = dL
where
d = demand rate per period
L = lead time

29. 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 = = yards

30. 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

31. Variable Demand with a Reorder Point
point, R Q LT
Time
Inventory level

32. Reorder Point with a Safety Stock
point, R Q LT
Time
Inventory level
Safety Stock

33. 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

34. 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

35. 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 =
R = dL + z d L =
= yards
Safety stock = z d L =
= yards

36. 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

37. 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 =
= bottles