3 session 3 inventory_2010

Session-3: Inventory Management

Operations Management: CFVG-2012

Dr. RAVI SHANKARProfessor

Department of Management Studies

Indian Institute of Technology DelhiHauz Khas, New Delhi 110 016, India

Phone: +91-11-26596421 (O); 2659-1991(H); (0)-+91-9811033937 (m)Fax: (+91)-(11) 26862620

Email: [email protected], [email protected]://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 timeReview 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

Perc

en

t o

f an

nu

al d

ollar

usag

eP

erc

en

t o

f an

nu

al d

ollar

usag

e

80 80 –

70 70 –

60 60 –

50 50 –

40 40 –

30 30 –

20 20 –

10 10 –

0 0 – | | | | | | | | | |

1010 2020 3030 4040 5050 6060 7070 8080 9090 100100

Percent of inventory itemsPercent of inventory itemsFigure 12.2Figure 12.2

ABC Analysis

�� Policies employed may includePolicies employed may include

�� More emphasis on supplier More emphasis on supplier development for A itemsdevelopment for A items

�� Tighter physical inventory control for Tighter 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

orderPlace

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 = 2Q

CQDCTC co += Finding optimal Q*

c

o

co

CDCQ

QCQDCTC

2

2

*

min

=

+=


Cost Relationships for Basic EOQ(Constant Demand, No Shortages)

TC

–A

nn

ual

Co

st

Total Cost

CarryingCost

OrderingCost

EOQ balances carryingcosts 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:

2Q

CQDCTC co +=

Figure The EOQ cost model

To order inventory

To keep inventory

Try to get this value


The Basic EOQ ModelExample

Consider the following:

days store 62.2 5

311*/

days 311 timecycleOrder

5000,2000,10

:yearper orders ofNumber

500,1$2

)000,2()75.0(

000,2000,10

)150(2

:costinventory annual Total

yd 000,2)75.0(

)000,10)(150(22* :sizeorder Optimal

10,000yd D $150, C $0.75, C :parameters Model

*

*

min

oc

===

==

=+=+=

===

===

QD

QD

QC

QD

CTC

CDC

Q

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 ModelEOQ Analysis with monthly time frame

$1,500 ($125)(12) cost inventory annual Total

monthper 125$2

)000,2()0625.0(

000,2)3.833(

)150(2*

* :costinventory monthly Total

yd 000,2)0625.0(

)3.833)(150(22* :sizeorder Optimal

monthper yd 833.3 D order,per $150 C month,per ydper $0.0625 C :parameters Model

min

oc

==

=+=+=

===

===

QC

QD

CTC

CDC

Q

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 parameters It works even if all parameters and assumptions are not metand assumptions are not met

�� The total cost curve is relatively The 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

yprobabilit level service toingcorrespond deviations standard ofnumber

demanddaily ofdeviation standard the

timelead

demanddaily average

pointreorder

where

=

=

=

=

=

=

+=

LZ

Z

L

d

R

LZLdR

d

d

d

σ

σ

σ


Reorder Point with Variable DemandExample

Example: determine reorder point and safety stock for service level of 95%.

26.1. : formulapoint reorder in termsecond isstock Safety

yd 1.3261.26300)10)(5)(65.1()10(30

1.65 Zlevel, service 95%For

dayper yd 5 days, 10 L day,per yd 30 d

=+=+=+=

=

===

LZLdR

d

dσ

σ

3 session 3 inventory_2010

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