3 session 3 inventory_2010

Session-3: Inventory Management
Operations Management: CFVG-2012
Dr. RAVI SHANKAR
Professor
Department of Management Studies
Indian Institute of Technology Delhi
Hauz Khas, New Delhi 110 016, India
Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m)
Fax: (+91)-(11) 26862620
Email: r.s.research@gmail.com, r.s@rediffmail.com
http://web.iitd.ac.in/~ravi1

4/10/20122 (c) Dr. Ravi Shankar, AIT (2008) 2
What is an Inventory System
Inventory is defined as the stock of any item or
resource used in an organization.
An Inventory System is made up of a set of
policies and controls designed to monitor the
levels of inventory and designed to answer
the following questions:
• What levels should be maintained?
• When stock should be replenished? and
• How large orders should be? i.e. what is the
optimal size of the order?

3
Purposes of Inventory
1. To maintain independence of operations
2. To meet variation in product demand
3. To allow flexibility in production scheduling
4. To provide a safeguard for variation in raw
material delivery time
5. To take advantage of economic purchase-
order size

Inventory issues
Demand
• Constant vs. variable
• deterministic vs. stochastic
Lead time
Review time
• Continuous vs. periodic
Excess demand
• Backorders, lost sales
Inventory change
• Perish, obsolescence
Inventory
Decisions:
When, What, and
how many to order

ABC classification system
Divides on-hand inventory into 3 classes (A = very important; B = moderately
important; C = least important) usually on a basis of annual $ volume.
Policies based on the ABC:
• Develop links with A suppliers more;
• Get tighter control of A items;
• Forecast A more carefully.

ABC Analysis
A ItemsA Items
B ItemsB Items
C ItemsC Items
PercentofannualdollarusagePercentofannualdollarusage
8080 –
7070 –
6060 –
5050 –
4040 –
3030 –
2020 –
1010 –
00 – | | | | | | | | | |
1010 2020 3030 4040 5050 6060 7070 8080 9090 100100
Percent of inventory itemsPercent of inventory items Figure 12.2Figure 12.2

ABC Analysis
Policies employed may includePolicies employed may include
More emphasis on supplierMore emphasis on supplier
development for A itemsdevelopment for A items
Tighter physical inventory control forTighter physical inventory control for
A itemsA items
More care in forecasting A itemsMore care in forecasting A items

Basic inventory elements
Carrying cost,Carrying cost, Cc
• Include facility operating costs, record
keeping, interest, etc.
Ordering cost,Ordering cost, Co
• Include purchase orders, shipping, handling,
inspection, etc.
Shortage (stock out) cost,Shortage (stock out) cost, Cs
• Sometimes penalties involved; if customer is
internal, work delays could result

Carrying Costs
Category
Cost (and Range) as a
Percent of Inventory
Value
Housing costs (including rent or depreciation,
operating costs, taxes, insurance)
6% (3 - 10%)
Material handling costs (equipment lease or
depreciation, power, operating cost)
3% (1 - 3.5%)
Labor cost 3% (3 - 5%)
Investment costs (borrowing costs, taxes, and
insurance on inventory)
11% (6 - 24%)
Pilferage, space, and obsolescence 3% (2 - 5%)
Overall carrying cost 26%

Inventory
- to study methods to deal with
“how much stock of items should be kept
on hands that would meet customer
demand”
Objectives are to determine:
a) how much to order, and
b) when to order

Inventory models
Here, we study the following two different models:
1. Basic model
2. Model with “re-order points”

1. Basic model
The basic model is known as:
“Economic Order Quantity” (EOQ) Models
Objective is to determine the optimal order size that
will minimize total inventory costs
How the objective is being achieved?

Quantity
on hand
Q
Receive
order
Place
order
Receive
order
Place
order
Receive
order
Lead time
Reorder
point
Usage
rate
Profile of Inventory Level Over Time

Profile of … Frequent Orders

Basic EOQ models
Three models to be discussed:
1 Basic EOQ model
2 EOQ model without instantaneous
receipt
3. EOQ model with shortages.

(c) Dr. Ravi Shankar, AIT (2008) 16
The Basic EOQ Model
• The optimal order size, Q, is to minimize the sum of carrying costs and ordering costs.
• Assumptions and Restrictions:
- Demand is known with certainty and is relatively constant over time.
- No shortages are allowed.
- Lead time for the receipt of orders is constant. (will consider later)
- The order quantity is received all at once and instantaneously.
How to determine
the optimal value
Q*?

Determine of Q
We try to
– Find the total cost that need to spend for keeping
inventory on hands
– = total ordering + stock on hands
– Determine its optimal solution by finding its first
derivative with respect to Q
How to get these values?
1. Find out the total carrying cost
2. Find out the total ordering cost
3. Total cost = (1) + (2)
4. Equate (1) and (2) and Find Q*

(c) Dr. Ravi Shankar, AIT (2008) 18
The Basic EOQ Model
We assumed that, we will only keep half the inventory over a year then
The total carry cost/yr = Cc x (Q/2). Total order cost = Co x (D/Q)
Then , Total cost = 2
QC
Q
DCTC co += Finding optimal Q*
c
o
c
o
C
DCQ
QC
Q
DCTC
2
2
*
min
=
+=

Cost Relationships for Basic EOQ
(Constant Demand, No Shortages)
TC–AnnualCost
Total
Cost
Carrying
Cost
Ordering
Cost
EOQ balances carrying
costs and ordering
costs in this model.
Q* Order Quantity (how much)

The Basic EOQ Model
• Total annual inventory cost is sum of ordering and carrying cost:
2
QC
Q
DCTC co +=
Figure The EOQ cost model
To order inventory
To keep inventory
Try to get this value

The Basic EOQ Model
Example
Consider the following:
daysstore62.2
5
311
*/
days311timecycleOrder
5
000,2
000,10:yearperordersofNumber
500,1$
2
)000,2(
)75.0(
000,2
000,10)150(
2
:costinventoryannualTotal
yd000,2
)75.0(
)000,10)(150(22*:sizeorderOptimal
10,000ydD$150,C$0.75,C:parametersModel
*
*
min
oc
===
==
=+=+=
===
===
QD
Q
D
Q
C
Q
DCTC
C
DCQ
opt
co
c
o
No. of working days/yr
*
Note: You should pay attention that
all measurement units must be the same
Consider the same example, with yearly

The Basic EOQ Model
EOQ Analysis with monthly time frame
$1,500($125)(12)costinventoryannualTotal
monthper125$
2
)000,2(
)0625.0(
000,2
)3.833(
)150(
2
*
*
:costinventorymonthlyTotal
yd000,2
)0625.0(
)3.833)(150(22*:sizeorderOptimal
monthperyd833.3Dorder,per$150Cmonth,perydper$0.0625C:parametersModel
min
oc
==
=+=+=
===
===
Q
C
Q
DCTC
C
DCQ
co
c
o
(unit be based on yearly)
12 months a year

Robustness of EOQ model
Order Quantity
Annual Cost
Total
Cost
Q*Q*-∆Q Q*+∆Q
∆TC
Would have to mis-specify Q* by quite a bit
before total annual inventory costs would
change significantly.
Very Flat Curve - Good!!

Robust Model
The EOQ model is robustThe EOQ model is robust
It works even if all parametersIt works even if all parameters
and assumptions are not metand assumptions are not met
The total cost curve is relativelyThe total cost curve is relatively
flat in the area of the EOQflat in the area of the EOQ

3. Model with “re-order points”
• The reorder point is the inventory level at which a new order is placed.
• Order must be made while there is enough stock in place to cover demand during lead time.
• Formulation: R = dL, where d = demand rate per time period, L = lead time
Then R = dL = (10,000/311)(10) = 321.54
Working days/yr

Reorder Point
• Inventory level might be depleted at slower or faster rate during lead time.
• When demand is uncertain, safety stock is added as a hedge against stockout.
Two possible scenarios
Safety stock!
No Safety
stocks!
We should then ensure
Safety stock is secured!

Determining Safety Stocks Using Service Levels
• We apply the Z test to secure its safety level,
)( LZLdR dσ+=
Reorder point
Safety stock
Average sample demand
How these values are represented in the diagram of normal distribution?

Reorder Point with Variable Demand
stocksafety
yprobabilitlevelservicetoingcorresponddeviationsstandardofnumber
demanddailyofdeviationstandardthe
timelead
demanddailyaverage
pointreorder
where
=
=
=
=
=
=
+=
LZ
Z
L
d
R
LZLdR
d
d
d
σ
σ
σ

Reorder Point with Variable Demand
Example
Example: determine reorder point and safety stock for service level of 95%.
26.1.:formulapointreorderintermsecondisstockSafety
yd1.3261.26300)10)(5)(65.1()10(30
1.65Zlevel,service95%For
dayperyd5days,10Lday,peryd30 d
=+=+=+=
=
===
LZLdR
d
dσ
σ

3 session 3 inventory_2010

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