1. Inventory Management for Independent Demand
Chapter 12

2. Just-in-Time & Lean Systems
MGMT 326
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Managing
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Introduction
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Strategy
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Process
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Layout
Just-in-Time & Lean Systems

3. Chapter Outline Basic concepts ABC inventory analysis Inventory costs
Objectives of inventory management
Dependent and independent demand
ABC inventory analysis
Inventory costs
Item costs
Holding costs
Order or setup costs
Shortage costs

4. Chapter Outline (2) Inventory policy Fixed order quantity method
Economic order quantity – the optimal fixed order quantity
Reorder point
Reorder point when demand is constant
Reorder point when demand is variable
Economic production quantity – the optimal production quantity

5. Objectives of Inventory Management
Maintain good customer service
Minimize inventory investment, consistent with the required level of customer service

6. Types of Demand Dependent Demand
Demand for raw materials, component parts, and subassemblies used to make a finished product
Both the amount of demand and the date required depend on the production schedule

7. Types of Demand (2) Independent Demand
Any demand that is not used to meet a production schedule is called independent demand
Examples of independent demand: finished goods; retail and distributor inventories; service inventories; maintenance, repair, and operating (MRO) inventories
MRO includes fuels, repair parts, office supplies, cleaning supplies

8. Dependent and Independent Demand: Types of Inventory
used to meet a
production schedule
in manufacturing
Independent demand:
not used to meet a production schedule
Manufacturer
Service Company
Raw materials
Finished goods
Retail or
distributor
inventories
Component parts
MRO
Work-in-process
(WIP)
Service inventories
MRO

9. ABC Inventory Analysis
For an inventory item, the annual usage in dollars is
(annual demand)x(cost per unit).
Annual demand is also called annual usage in units.
ABC inventory analysis divides inventory items into 3 categories:
A items usually account for at least 60% of annual usage and should be controlled most closely
B items require a moderate level of control. A and B items should account for at least 80% of annual usage.
C items require less control than other items. These items are those with the least usage that were not classified as
A and B items

10. The AAU Corp. is considering doing an ABC analysis on its entire inventory but has decided to test the technique on a small sample of 15 of its SKU’s. The annual usage and unit cost of each item is shown below
© Wiley 2007

11. Steps in ABC Analysis Compute Annual Usage in Dollars for each item.
Compute Total Annual Usage.
Compute the percentage of Annual Usage for each item.
Sort the list of items by the percentage of Annual Usage in Dollars, from largest to smallest.

12. Steps in ABC Analysis (2)
Calculate the Cumulative Percentage of Annual Usage in Dollars for the first item, first 2 items, first 3 items, etc. For the last item, the cumulative % should be 100%.
Using Cumulative % as a guide, assign the items to A, B, and C categories.

13. © Wiley 2007

14. © Wiley 2007

15. Relevant Inventory Costs
Measurable Cost of Inventory =
Order Costs for
purchased items OR
Setup Costs for
items made by
your company
Shortage costs:
Administrative
& transportation
costs related to
back orders
Item Costs
Holding
Costs + + +
Shortages and back orders result in lost sales and lost goodwill. These costs are relevant but hard to measure.

16. Item Costs
Item costs
For purchased items, the item cost is the purchase price, plus shipping
For work in process, the item cost is the cost of materials and labor used in the item
For finished goods, the item cost is the cost of goods sold.

17. Inventory Holding Costs
Inventory holding costs include capital costs, storage costs, and risk costs
Capital costs:
If inventory is financed with borrowed money, the capital cost is the interest rate paid
If inventory is financed from retained earnings, the capital cost is the opportunity cost of not putting the money into other investments
Storage costs: the costs of space, people, and equipment used in inventory storage

18. Inventory Holding Costs (2)
Risk costs: cost of taxes and insurance on inventory, damage, obsolescence, and theft
Inventory holding costs are usually computed as a percentage of item costs

19. Ordering and Setup Costs
For purchased items, ordering costs are the fixed costs associated with placing an order with a supplier
For items made internally, setup costs are used instead of order costs. The setup cost is the cost of work that must be done before production actually begins.

20. Shortage Costs
Administrative and transportation costs related to back orders
Lost good will and lost sales due to product shortages – hard to measure

21. Inventory Management Policies
An inventory management policy should determine
How much to order
When to order

22. Fixed Order Quantity Method
An inventory policy for independent demand. Based on the following rules:
Order the same amount, Q, each time
Q is called the order quantity
Place an order when the amount in inventory gets down to the reorder point, R
Compute Q and R for each item.

23. Fixed Order Quantity Method (2) Relevant Costs
Assume
Quantity discounts are not available
Orders are placed early enough that shortages do not occur
Relevant costs
Order costs
Inventory holding costs

24. Fixed Order Quantity Method (3) Annual Inventory Cost
Figure 12.2, page 430
Given:
D = annual demand = 10,400
Weekly demand = 200
L = lead time = 1 week
Q = order quantity = 600
Average inventory
= (Q/2) = 600/2 = 300

25. Fixed Order Quantity Method (4) Notation
Q = order quantity
D = annual demand for the item
S = cost of placing one order
H = inventory holding cost per unit per year
(commonly called holding cost)
L = lead time (time between order placement and order receipt)
R = reorder point
TC = annual cost of placing orders
+ annual cost of holding inventory

26. Fixed Order Quantity Method (5) Costs
Annual cost of placing orders =
Annual cost of holding inventory =
Total annual cost =

27. Economic Order Quantity
The economic order quantity (EOQ) is the fixed order quantity (Q) that minimizes the total annual costs of placing orders and holding inventory (TC).

28. Economic Order Quantity Assumptions
Demand (D) is known and constant
H is known and constant
Order costs (S) are constant
The order quantity arrives in a single shipment
No quantity discounts are available
All demand will be met (no shortages)

29. We want to minimize TC
D, S, and H are constant. TC is a function of Q.

30. Economic Order Quantity (3)
Let Q* be the economic order quantity. Then
For Q*, annual order cost = annual inventory cost

31. Simple Reorder Point Use this method when daily demand is constant.
R = reorder point
d = daily demand (may have to compute this)
L = lead time (Caution: if lead time is given in weeks, convert this to days. A week may be 5, 6, or 7 days).
R = dL

32. Reorder Point with Safety Stock
Safety stock (SS) is extra inventory that is kept to meet unexpected demand.
Reorder point without
safety stock
Reorder point
with safety stock

33. Reorder Point with Safety Stock (2) How much safety stock (SS) ?
Service level is the probability of having enough inventory to meet demand during lead time
The probability of a stockout is (1 - service level)
Demand during lead time is normally distributed with mean and standard deviation sdL

34. Reorder Point with Safety Stock (2) How much safety stock (SS) ?
z is the number of standard deviations required to meet the desired service level
SS = zsdL
Reorder point with safety stock: R = zsdL

35. Reorder Point with Safety Stock Example
Given
D = annual demand = 10,000
N = number of business days per year = 250
The company operates 5 days per week
= average daily demand
sdL = standard deviation of demand during lead time = 20
L = lead time = 1 week
Service level = 96%
Find: reorder point with safety stock: R = zsdL

36. Computing Reorder Point with Safety Stock
If average daily demand ( ) is not given, compute it.
Note: = D/N and D =
= 10,000/250 = 40
If the lead time is given in weeks or months, compute lead time in days.
L = 1 week = 1(5) = 5 days
Note: 1 week is the number of days per week that the company operates. This may be 5, 6, or 7.

37. Computing Reorder Point with Safety Stock (2)
Find the z value for the service level (96%)
Appendix B gives
this area.
Probability of
a stockout =
1 – service
level = 4%
50%
46% z

38. Computing Reorder Point with Safety Stock (3)
Find the z value for the service level (96%) (cont.)
(a) Write the service level as a decimal
96% =
(b) Subtract from the service level
– =
(c) Use the table in Appendix B, page 652, to find the area that is closest to
The closest area in the table is , which occurs when z = 1.75
Use z = 1.75

39. Computing Reorder Point with Safety Stock (4)
Compute R
R = L+ zsdL
= 40(5) (20) =
= 235
Note: If the computation gives a fractional value, round up to nearest integer.
Example: Computed R =  R = 211

40. Economic Production Quantity
Key question: How many units of a part or product should be made at one time?
The economic production quantity (EPQ) is the production quantity (lot size) that minimizes the total annual cost of setups and holding inventory.

41. Economic Production Quantity (2) Notation
Q = Amount to make (lot size)
D = annual demand for the item
d = daily demand for the item
p = daily production rate
S = cost of one setup
H = inventory holding cost per unit per year
(commonly called holding cost)
TC = annual cost of setups
+ annual cost of holding inventory
The EPQ is the quantity that minimizes TC

42. Economic Production Quantity (3)
Assumption: Daily demand < daily production.
When the item is being made, some is sold or used to
make a product. The remainder goes into inventory.
When production stops, the inventory is used until
there is no inventory left. Then production resumes.
Ending inventory
= beginning
inventory
+ production
- sales or usage

43. Economic Production Quantity (4)
Length of production run = Q/p
During production, d units are sold or used each day. (p – d) units go into inventory.
Maximum inventory:
Total cost:
Economic production
quantity (EPQ):

44. EOQ vs. EPQ When to use economic order quantity (EOQ):
Demand is independent
Compute how much to order (order quantity)
When to use economic production quantity (EPQ):
Parts or products will be produced: demand is dependent
Compute how much to make at one time (production lot size)