2. Inv.Control - Objectives
Introduction
Purpose of Inventories
Inventory Cost Structures
Independent versus Dependent Demand
Economic Order Quantity
Continuous Review System
Periodic Review System
Using P and Q System in Practice
Selective Inventory Control Systems
3. Introduction
Inventory: a stock of materials used to
facilitate production or to satisfy customer
demand.
Types of inventory
–
–
–
–
Raw materials (RM)
Work in process (WIP)
Finished goods (FG)
Maintenance, repair & operating supplies (MRO)
5. A Water Tank Analogy for Inventory
Inventory Level
Supply Rate
Inventory Level
Demand Rate
6. Purpose of Inventories
To protect against uncertainties
–
–
–
–
in demand (finished goods, MRO)
supply (RM, MRO)
lead times (RM/PP or WIP)
schedule changes (WIP)
To allow economic production and
purchase (as in discounts for buying RM/PP
in bulk)
7. Purpose of Inventories (Contd.)
To cover anticipated changes in demand (as
in a level strategy) or supply
– finished goods
– RM/PP
To provide for transit (pipeline inventories)
–
–
–
RM/PP
finished goods
WIP (independence of operations)
8. Inventory Cost Structures
Ordering (or setup) cost
– Paperwork, worker time (ordering)
– worker time, downtime (setup)
– Typically expressed as a fixed cost per order or
setup.
9. Inventory Cost Structures(contd.)
Carrying (or holding) cost:
– Cost of capital (market rate or internal rate of return)
– Cost of storage (building, utilities, insurance, handling)
– Cost of obsolescence, deterioration, and loss
(shrinkage)
– Management cost (record keeping, counting)
Typically expressed as a percentage of SKU cost.
Average in INDIA is estimated to be 25 percent
per year.
Businesses often use only cost of capital
(understatement).
10. Inventory Cost Structures(contd.)
How the 25 percent carrying cost is distributed
Cost of Capital—15 percent
Obsolescence—2 percent
Storage—5 percent
Materials Handling—2 percent
Shrinkage/pilferage—1 percent
Insurance—1 percent
11. Inventory Cost Structures(contd.)
Stock out Cost (Back order or Lost sales or
Understocking Cost)
–
–
–
–
record maintenance
lost income
customer dissatisfaction
Typically expressed as a fixed cost per backorder
or as a function of aging of backorders.
13. Forms of Demand
Independent demand
–
–
–
–
finished goods, spare parts, MRO
based on market demand
requires forecasting
managed using ‘replenishment philosophy’, i.e.
reorder when you reach a pre-specified level.
14. Forms of Demand(contd.)
Dependent demand
– parts that go into the finished products, RM/PP
or WIP
– dependent demand is a known function of
independent demand
– calculate instead of forecast
– Managed using a ‘requirements philosophy’,
i.e. only ordered as needed for higher level
components or products.
15. Economic Order Quantity (EOQ)
Developed in 1915 by F.W. Harris
Answers the question ‘How much do I order?’
Used for independent demand items.
Objective is to find order quantity (Q) that minimizes
the total cost (TC) of managing inventory.
Must be calculated separately for each SKU.
Widely used and very robust (i.e. works well in a lot
of situations, even when its assumptions don’t hold
exactly).
16. Economic Order Quantity (EOQ)
Basic Model Assumptions
Demand rate is constant, recurring, and known.
Lead time is constant and known.
No stockouts allowed.
Material is ordered or produced in a lot or batch
and the lot is received all at once
Costs are constant
–
–
–
Unit cost is constant (no quantity discounts)
Carrying cost is a constant per unit (SKU)
Ordering (setup) cost per order is fixed
The item is a single product or SKU.
17. EOQ Lot Size Choice
There is a trade-off between frequency of
ordering (or the size of the order) and the
inventory level.
– Frequent orders (small lot size) lead to a lower
average inventory size, i.e. higher ordering cost
and lower holding cost.
– Fewer orders (large lot size) lead to a larger
average inventory size, i.e. lower ordering cost and
higher holding cost.
18. Notations and measurement
units in EOQ
D = Demand rate, units per year
S = Cost per order placed, or setup cost,
Rupees per order
C = Unit cost, Rupees per unit
i = Carrying rate, percent of value per year
Q = Lot size, units
TC= total of ordering cost plus carrying cost
19. Cost Equations in EOQ
Ordering cost = (cost per order) x orders per
year) = SD/Q
Carrying cost per year = (annual carrying rate) x
(unit cost) x average inventory = iCQ/2
Total annual cost (TC) = ordering cost per year
+ carrying cost per year = SD/Q + iCQ/2
21. TC and EOQ
TC = ordering cost + holding cost
= S*(D/Q) + iC*(Q/2)
EOQ = Q =
2 SD
iC
note: Although we have used annual costs, any time period is all
right. Just be consistent! The same is true for currency
designations.
22. Continuous Review System
Relax assumption of constant demand.
Demand is assumed to be random.
Check inventory position each time there is a
demand (i.e continuously).
If inventory position drops below the reorder
point, place an order for the EOQ.
Also called fixed-order-quantity or Q system
(the fixed order size is EOQ).
23. A Continuous Review (Q) System
R = Reorder Point
Q = Order Quantity
L = Lead time
24. A Continuous Review (Q) System
Amount to order = EOQ
Order when inventory position = reorder point.
Reorder point = lead time * demand/period
= R = lead time demand (when demand is
constant)
Reorder point is independent of EOQ!
EOQ tells how much to order.
Reorder point tells when to order.
25. Periodic Review System
Instead of reviewing continuously, we review
the inventory position at fixed intervals. For
example, the bread truck visits the grocery
store on the same days every week.
Also known as “P system”, “Fixed-orderinterval system” or “Fixed-order-period
system”
26. Periodic Review System
(contd.)
Each time we review the inventory, we either
order or don’t. The decision depends upon our
reorder point.
The amount we order is the amount needed to
bring us up to a target (T).
28. Using P and Q System in Practice
Use P system when orders must be placed at
specified intervals.
Use P systems when multiple items are
ordered from the same supplier (jointreplenishment).
Use P system for inexpensive items.
29. Using P and Q Systems in
Practice
P may be easier to use since levels are
reviewed less often.
P requires more safety stock since may only
order at fixed points.
P is more likely to run out since cannot
respond to increases in demand
immediately
Either may be more costly: P in safety
stock, Q in monitoring cost.
30. FORMULAE –
INVENTORY MANAGEMENT
E.O.Q. =
2 X Annual Demand X Ordering cost
Unit Price X Inv. Carr. Cost (%)
Fixed order Qty model ( “Q” System)
o Order Qty = E.O.Q.
o Reorder Point = Average Daily Demand X Lead-time in days
Total Annual Cost = Annual
+ Annual + Annual
Purchase
Ordering
Inventory
Cost
Cost
Carr. Cost
(i.e. Annual
Demand X
Unit Cost)
31. o Safety Stock = Constant based X Std. deviation
on Service level
in demand
Fixed order Qty model with safety stock
o Reorder Point = (Average daily demand + Safety
X
lead-time in days)
Stock
Fixed – Time Period Model with Safety Stock (“P” System)
o Safety stock = Constant based X
on Service level
*
Where
=
* Std. deviation
(during Review
period + leadtime )
(R.P. + L.T.) X (Std. Dev.) 2
32. o Optimal Order Qty (Q) =
Average Daily Demand X (Review Period +Leadtime) +
(Plus)
Safety Stocks
– (minus)
Current Inventory Status
(Physical Stocks + Quantity on order)
33. Selective Inventory Control System
Methods of classification:-
Title
Basis
Main Use
A-B-C
Value of Consumption
To control- raw material/ w.i.p/
components
H-M-L (High-MedLow)
Unit price of the material
Mainly to control purchase
X-Y-Z
Value of items in storage
To review the inventories & their
uses at scheduled intervals
V-E-D (vital/essen/
desirable
Criticality of the component
To determine stock levels of spare
parts
F-S-N (fast/slow/nonmoving)
Consumption pattern of the
component
To control obsolescence
S-D-E
(scarce/diff/easy)
Problems faced in procurement
Lead-time analysis & purchasing
strategy
G-O-L-F
(govt/open/local/fore
ign)
Source of materials
Procurement strategies
S-0-S (seasonal/ off
seasonal)
Nature of supplies
Procurement stocking strategies for
seasonal items like agricultural
V-E-I-N (vital/ essen/
imp/normal)
Plant &machinery
Production Machinery
& Services
34. Cumulative % of Annual consumption value
A-B-C Analysis
100
Class ‘C’
90
Class
‘B’
65
Class
‘A’
0
15
40
Cumulative % of Total number of items
100
35. ABC Inventory Management
Based on “Pareto” concept (80/20 rule) and
total usage in dollars of each item.
Classification of items as A, B, or C based on
usage.
Purpose is to set priorities on effort used to
manage different SKUs, i.e. to allocate scarce
management resources.
36. ABC Inventory Management
(contd.)
‘A’ items: 20% of SKUs, 80% of
Ann.Con.Value
‘B’ items: 30 % of SKUs, 15% of
Ann.Con.Value
‘C’ items: 50 % of SKUs, 5% of A.C.Value
Three classes is arbitrary; could be any number.
Percents are approximate.
Danger: Consumption Value may not reflect
importance of any given SKU!
38. The Two-Bin System
Q
Re-order point shifts with usage
First Bin
Re-order Level
Normal
Lead-time
Usage
Time
Second Bin
O
Lead-time
Safety stock
39. Inventory Accuracy and Cycle
Counting
Inventory accuracy refers to how
well the inventory records agree
with physical count
Cycle Counting is a physical
inventory-taking technique in which
inventory is counted on a frequent
basis rather than once or twice a
year
40. 40
Question Bowl
The average cost of inventory in India
is which of the following?
a. 10 to 15 percent of its cost
b. 15 to 20 percent of its cost
c. 20 to 25 percent of its cost
d. 25 to 30 percent of its cost
e. 30 to 35 percent of its cost
Answer: d. 25 to 30 percent of its cost
41. 41
Question Bowl
a.
b.
c.
d.
e.
Which of the following is a reason why firms
keep a supply of inventory?
To maintain independence of operations
To meet variation in product demand
To allow flexibility in production scheduling
To take advantage of economic purchase
order size
All of the above
Answer: e. All of the above (Also can include to provide a
safeguard for variation in raw material delivery time.)
42. 42
Question Bowl
An Inventory System should include policies
that are related to which of the following?
a.
How large inventory purchase orders should
be
b.
Monitoring levels of inventory
c.
Stating when stock should be replenished
d.
All of the above
e.
None of the above
Answer: d. All of the above
43. 43
Question Bowl
Which of the following is an Inventory Cost item
that is related to the managerial and clerical
costs to prepare a purchase or production order?
a.
Holding costs
b.
Setup costs
c.
Carrying costs
d.
Shortage costs
e.
None of the above
Answer: e. None of
the above (Correct
answer is Ordering
Costs.)
44. 44
Question Bowl
Which of the following is considered a
Independent Demand inventory item?
a.
Bolts to a automobile manufacturer
b.
Timber to a home builder
c.
Windows to a home builder
d.
Containers of milk to a grocery store
e.
None of the above
Answer: d. Containers of milk to a grocery store
45. 45
Question Bowl
If you are marketing a more expensive
independent demand inventory item, which
inventory model should you use?
a.
Fixed-time period model
b.
Fixed-order quantity model
c.
Periodic system
d.
Periodic review system
e.
P-model
Answer: b. Fixed-order quantity model
46. 46
Question Bowl
If the annual demand for an inventory item is
5,000 units, the ordering costs are Rs100 per
order, and the cost of holding a unit is stock for a
year is Rs10, which of the following is
approximately the Qopt?
a.
b.
c.
d.
e.
5,000 units
Rs5,000
500 units
316 units
None of the above
Answer: d. 316
units
(Sqrt[(2x5000x1
00)/10=316.227
7)
47. 47
Question Bowl
The basic logic behind the ABC Classification
system for inventory management is which of the
following?
a.
Two-bin logic
b.
One-bin logic
c.
Pareto principle
d.
All of the above
e.
None of the above
Answer: c. Pareto principle
48. 48
Question Bowl
a.
b.
c.
d.
e.
A physical inventory-taking technique in
which inventory is counted frequently rather
than once or twice a year is which of the
following?
Cycle counting
Mathematical programming
Pareto principle
ABC classification
Stockkeeping unit (SKU)
Answer: a. Cycle counting
49. 49
Solved Problems – OPERATIONS MANAGEMENT
(Class of 2010)
Q1. A supplier is offering stainless steel bars at Rs 95 per kg for order of upto 100kg each,
and at Rs 80 per kg for orders of 101kg and above. Your annual requirement is 1200kg.
If your ordering cost is Rs 300 per order, and holding cost is 20%, what would be the
most economical quantity to order?
(10 Marks)
Answer.
E.O.Q(1) = √2 × Annual Demand × Ordering Cost
√Unit Cost × Holding Cost
E.O.Q = √2 × 1200 × 300
√95 × 0.20
E.O.Q = 195 units
E.O.Q(2) = √2 × 1200 × 300
√80 × 0.20
= 212 units
50. 50
Now, E.O.Q (1), i.e. 195 units does not fall in the category of upto 100kg
Therefore here consider it’s optimum E.O.Q as 100 units so that it falls under the
category of Rs 95 per kg
Now, find the Total Cost
For 100 units
• Ordering Cost = 1200 × 300 = Rs 3600/100
• Purchase Cost = 1200 × 95 = Rs 1,14,000/• Holding Cost = 100 × 0.2 × 95 = Rs 950/Therefore Total Cost = Rs 1,18,550/-
For 212 units
• Ordering Cost = 1200 × 300 = Rs 1698/212
• Purchase Cost = 1200 × 80 = Rs 96,000/-
51. 51
• Holding Cost = 212 × 0.2 × 80 = Rs 1696/2
Therefore Total Cost = Rs 99,394/Therefore most Economic Order Quantity to order is 212 kgs
