1. 12
Inventory Management

2. Learning Objectives
Define the term inventory, list the major reasons for holding inventories, and list the main requirements for effective inventory management.
Discuss the nature and importance of service inventories
Discuss periodic and perpetual review systems.
Discuss the objectives of inventory management.
Describe the A-B-C approach and explain how it is useful.

3. Learning Objectives
Describe the basic EOQ model and its assumptions and solve typical problems.
Describe the economic production quantity model and solve typical problems.
Describe the quantity discount model and solve typical problems.
Describe reorder point models and solve typical problems.
Describe situations in which the single-period model would be appropriate, and solve typical problems.

4. Independent demand is uncertain. Dependent demand is certain.
Inventory
Independent Demand A
B(4)
C(2)
D(2)
E(1)
D(3)
F(2)
Dependent Demand
Independent demand is uncertain. Dependent demand is certain.
Inventory: a stock or store of goods

5. Inventory Models
Independent demand: finished goods, items that are ready to be sold
E.g. a computer
Dependent demand: components of finished products
E.g. parts that make up the computer

6. Types of Inventories Raw materials and purchased parts
Partially completed goods called work-in-process (WIP)
Finished-goods inventories
(manufacturing firms) or merchandise (retail stores)

7. Types of Inventories Replacement parts, tools, and supplies
Goods-in-transit to warehouses or customers

8. Functions of Inventory
To meet anticipated demand
To smooth production requirements
To decouple operations
To protect against stockouts

9. Functions of Inventory
To take advantage of order cycles
To help hedge against price increases
To permit operations
To take advantage of quantity discounts

10. Objectives of Inventory Control
To achieve satisfactory levels of customer service while keeping inventory costs within reasonable bounds
Level of customer service
Costs of ordering and carrying inventory
Inventory turnover is the ratio of the annual cost of goods sold to the average inventory investment.

11. Effective Inventory Management
A system to keep track of inventory
A reliable forecast of demand
Knowledge of lead times
Reasonable estimates of
Holding costs
Ordering costs
Shortage costs
A classification system

12. Inventory Counting Systems
Periodic System
Physical count of items made at periodic intervals
Perpetual Inventory System System that keeps track of removals from inventory continuously, thus monitoring current levels of each item

13. Inventory Counting Systems
Two-bin system: Two containers of inventory; reorder when the first is empty
Universal Product Code (UPC): Bar code printed on a label that has information about the item to which it is attached
Radio Frequency Identification
(RFID) Tags

14. Key Inventory Terms
Lead time: time interval between ordering and receiving the order
Holding (carrying) costs: cost to carry an item in inventory for a length of time, usually a year
Ordering costs: costs of ordering and receiving inventory
Shortage costs: costs when demand exceeds supply of inventory

15. ABC Classification System
Figure 12.1
Classifying inventory according to some measure of importance and allocating control efforts accordingly.
A - very important
B - moderately important
C - least important
Annual
$ value
of items A B C
High
Low
Percentage of Items

16. Cycle Counting A physical count of items in inventory
Cycle counting management
How much accuracy is needed?
When should cycle counting be performed?
Who should do it?

17. Economic Order Quantity Models
Economic order quantity (EOQ) model
The order size that minimizes total annual cost
Economic production model
Quantity discount model

18. Assumptions of EOQ Model
Only one product is involved
Annual demand requirements known
Demand is even throughout the year
Lead time does not vary
Each order is received in a single delivery
There are no quantity discounts

19. Profile of Inventory Level Over Time
The Inventory Cycle
Figure 12.2
Profile of Inventory Level Over Time
Quantity
on hand Q
Receive
order
Place
Lead time
Reorder
point
Usage
rate
Time

20. Total Cost Annual carrying cost Annual ordering cost Total cost = + Q2 H D S +
TC =
Q = Order quantity in units
H = Holding (carrying) cost per unit
D = Demand, usually in units per year
S = Ordering cost

21. Cost Minimization Goal
Figure 12.4C
The Total-Cost Curve is U-Shaped
Annual Cost
Ordering Costs
Order Quantity (Q) QO
(optimal order quantity)

22. Deriving the EOQ
Using calculus, we take the derivative of the total cost function and set the derivative (slope) equal to zero and solve for Q.

23. Minimum Total Cost
The total cost curve reaches its minimum where the carrying and ordering costs are equal. Q 2 H D S = Q

24. Economic Production Quantity (EPQ)
Production done in batches or lots
Capacity to produce a part exceeds the part’s usage or demand rate
Assumptions of EPQ are similar to EOQ except orders are received incrementally during production

25. Economic Production Quantity Assumptions
Only one item is involved
Annual demand is known
Usage rate is constant
Usage occurs continually
Production rate is constant
Lead time does not vary
No quantity discounts

26. Economic Run Size Q0 = Order quantity in units
H = Holding (carrying) cost per unit
D = Demand, usually in units per year
S = Ordering cost
p = Production or delivery rate
u = Usage rate

27. Total Costs with Purchasing Cost
Annual
carrying
cost
Purchasing
TC = + Q 2 H D S
ordering PD

28. Total Costs with PD Figure 12.7 Cost
EOQ
TC with PD
TC without PD PD
Quantity
Adding purchasing cost doesn’t change EOQ

29. Total Cost with Constant Carrying CostsOC
EOQ
Quantity
Total Cost
TCa
TCc
TCb
Decreasing
Price
CC a,b,c
Figure 12.9A

30. When to Reorder with EOQ Ordering
Reorder Point: When the quantity on hand of an item drops to this amount, the item is reordered
Safety Stock: Stock that is held in excess of expected demand due to variable demand rate and/or lead time
Service Level: Probability that demand will not exceed supply during lead time

31. Determinants of the Reorder Point
The rate of demand
The lead time
Demand and/or lead time variability
Stockout risk (safety stock)

32. Reorder Point
If demand and lead time are both constant, the reorder point is simply
ROP = d X LT
Where
d = Demand rate (units per day or week)
LT = Lead times in days or weeks

33. Safety Stock Figure 12.12 Quantity Maximum probable demandLT
Time
Expected demand
during lead time
Maximum probable demand
ROP
Quantity
Safety stock
Safety stock reduces risk of
stockout during lead time

34. Reorder Point Figure 12.13 The ROP based on a normal
Risk of
a stockout
Service level
Probability of
no stockout
Expected
demand
Safety
stock z
Quantity
z-scale
The ROP based on a normal
distribution of lead time demand

35. Fixed-Order-Interval Model
Orders are placed at fixed time intervals
Order quantity for next interval?
Suppliers might encourage fixed intervals
May require only periodic checks of inventory levels
Risk of stockout
Fill rate: the percentage of demand filled by the stock on hand

36. Fixed-Interval Benefits
Tight control of inventory items
Items from same supplier may yield savings in:
Ordering
Packing
Shipping costs
May be practical when inventories cannot be closely monitored

37. Fixed-Interval Disadvantages
Requires a larger safety stock for given risk of stockout
Increases carrying cost
Costs of periodic reviews

38. Single Period Model
Single period model: model for ordering of perishables and other items with limited useful lives
Shortage cost: unrealized profits per unit (generally)
Excess cost: difference between purchase cost and salvage value of items left over at the end of a period

39. Single Period Model Continuous stocking levels
Identifies optimal stocking levels
Optimal stocking level balances unit shortage and excess cost
Discrete stocking levels
Service levels are discrete rather than continuous
Desired service level is matched or exceeded

40. Optimal Stocking Level
Figure 12.16
Service level = Cs
Cs + Ce
Cs = Shortage cost per unit Ce = Excess cost per unit Ce Cs
Service Level
Quantity So
Balance point

41. Example 15 Ce = $0.20 per unit Cs = $0.60 per unit
Service level = Cs/(Cs+Ce) = .6/(.6+.2)
Service level = .75
Service Level = 75%
Quantity Ce Cs
Stockout risk = 1.00 – 0.75 = 0.25

42. Operations Strategy Too much inventory Wise strategy
Tends to hide problems
Easier to live with problems than to eliminate them
Costly to maintain
Wise strategy
Reduce lot sizes
Reduce safety stock
Accurate and up-to-date inventory records