PIM 22-24 [Compatibility Mode] (1)

8/6/2019 PIM 22-24 [Compatibility Mode] (1)

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INVENTORY CONTROL

Physical stock of goods raw materials,

semi finished items, finished goods, etc.

For smooth and efficient running of future

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a a rs o an organ za on After receiving sales order placing order for

purchase of materials, wait for their receipt

and then start production customer has towait a long time loss of business


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INVENTORY CONTROL

Inventory Control: scientific method of findingout how much stock should be maintained in

order to meet the production demands andbe able to provide right type of material at

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competitive prices

Idle resource we have to minimize


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INVENTORY CONTROL

Q1: how much to order? - Q

Q2: When to order? r (ROL)

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Input: Demand


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INVENTORY CONTROL

Types of Inventories

1. Movement Inventories (pipe line inventories)

material in transit

2. Buffer Inventories

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Reserve stock or safety stock to meetfluctuations in demand news papers

3. Anticipation Inventories Built-up for a big selling season, a

promotion programme or a plant shut-

down period refrigerators


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INVENTORY CONTROL


4. Decoupling Inventories

To cope-up the need during failure of anymachine (in-process inventory)

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5. Cycle Inventories Quotas


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INVENTORY CONTROL


1. Raw material2. Work-in-process

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3. Finished goods

4. Spare parts

5. Tools


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INVENTORY CONTROL

Types of Models

1. Deterministic2. Stochastic

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1. Single period (Static)

2. Muti-period (Dynamic)


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INVENTORY CONTROL

Order cycle time period betweenplacement of two successive orders

Inventory review systems:

a) Fixed-order quantity system (two-bin system)

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Inventory level checked continuously Reorder point

b) Periodic review system Inventory levels are reviewed at fixed time

intervals

Order size is not fixed


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INVENTORY CONTROL

Lead time time gap between the moment ofplacing an order or deciding for production

and the moment of receiving the item intoinventory

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probabilistic

Lead time zero instantaneous production

no need to place an order in advance


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INVENTORY CONTROL

Stock replenishment the rate at whichitems are added to inventory

Instantaneous (when purchased) or uniform

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w en pro uce


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INVENTORY CONTROL

Inventory Costs

1. Cost of item C

2. Ordering cost Co Rs./order

Acquisition costs or set-up costs

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People, stationery, communication fax,follow-up travel, transportation,inspection, delay, rejection and rework

Independent of quantity ordered orproduced


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INVENTORY CONTROL

Inventory Costs

3. Carrying cost / Holding Cost Cc

Rs./unit/period

Cost of ca ital s ace eo le stationer

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power, special requirements air-conditioners, dust-free environment,insurance, pilferage, obsolescence

Cost of capital dominates (interest rate, i)

c

C iC=


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INVENTORY CONTROL

Inventory Costs

4. Shortage cost / back-order Cost Cs

Rs./unit/period

Shorta e: lost sales loss of rofit loss of

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opportunity

Backorder: Delay in meeting the demand

Loss of goodwill, increased transportationcosts, extra costs associated with urgent(often small) quantity, etc.


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INVENTORY CONTROL

Inventory CostsCo = Rs. 100 per order; Q = 6000 units/year

Cu = Rs. 10 per unit;i= 12%

No. of

orders

Ordering

Quantity

Ordering

Cost

Carrying

Cost

Total

Cost

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1 6000 100 3600 3700

2 3000 200 1800 2000

6 1000 600 600 1200

12 500 1200 300 1500


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INVENTORY CONTROL

Deterministic Models

(known demand)

Probabilistic (Stochastic)

Models

Inventory Models

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emen aryModels o e s w r ce- rea s(Quantity discounts) o e s wrestrictions

InstantaneousProduction

FiniteProduction rate

With shortages With shortagesWithout shortages


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INVENTORY CONTROL

Model I: Harris-Wilsons Model

Single item, uniform demand, instantaneous

production, no shortages Annual demand: D

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* 2

2

O

C

O C

DCQ EOQ

C

TC DC C

= =

=


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INVENTORY CONTROL

Model I: Harris-Wilsons ModelI

n

v

e

n

t

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tt t

Q

TTime

ry


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INVENTORY CONTROL

Model-ICo = Rs. 300 per order; D = 10,000 units/year

Cu

= Rs. 20 per unit;i= 20%

* 2 10000 300

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At the optimum, the order cost and thecarrying cost components become equal

.

4

2 10000 300 4 .4898.98 / TC Rs year = =


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INVENTORY CONTROL

Model II

Single item, uniform demand, Instantaneous

replenishment, backordering is allowed Annual demand: D

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Maximum inventory level: Im

Backorder quantity: s


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INVENTORY CONTROL

Model IIIn

v

e

n

t

o

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Time

y

ttt

T

t1 t2

Q

m

s


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INVENTORY CONTROL

Model II

( )* 2 c so

c s

C CDCQ C C

+

=

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( )

( )2

o sm

c c s

s

o c

c s

IC C C

CTC DC C C C

=

+

=

+


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INVENTORY CONTROL

Model-IICo = Rs. 300 per order; D = 10,000 units/year

Cu

= Rs. 20 per unit;i

= 20%; Cs

= Rs. 25/unit/year

*1319.09Q =

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Order cost = inventory cost + backorder cost

*

181.9435

1137.15

.4548.72 /

m

s

I Q s

TC Rs year

=

= =

=


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INVENTORY CONTROL

Model-II

Period of holding inventory is less and the

maximum inventory is also less

-

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, .

Model-I is a restricted version of Model-II

Model-II is a relaxed version of Model-I

Limiting value of Cs is , where Models I

and II are same


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INVENTORY CONTROL

Model III Basic production-Consumption Model

Single item, uniform demand, finite production

rate, backordering is not allowed When inventory builds up over a period of

time or when units are roduced and sold at a

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constant rate Annual demand: D

Ordering quantity: Q Maximum inventory level: Im

Production rate: P/year


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INVENTORY CONTROL

Model III

P>D: otherwise, no inventory builds up andstock outs will occur

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INVENTORY CONTROL

Model IIIIn

v

e

n

t

o

P

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t2t1 tT Time

y

P-D

DIm

Q


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INVENTORY CONTROL

Model III

* 2 oDCQD

=

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2 1

c

o c

P

DTC DC C

P

=


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INVENTORY CONTROL

Model-IIICo = Rs. 300 per setup; D = 10,000 units/year

Cu = Rs. 20 per unit; i = 20%; P = 20,000 units/year

*1732.05Q =

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1

2

.

0.08666

0.08666

.3464.10 /

m

t year

t year

TC Rs year

=

=

=


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INVENTORY CONTROL

Model IV Production-Consumption Modelwith Backordering

Single item, uniform demand, finiteproduction rate, backordering is allowed

Annual demand: D

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Ordering quantity: Q

Maximum inventory level: Im

Production rate: P/year Backorder quantity: s


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INVENTORY CONTROL

Model IV

P

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t1

t

DP-D

Im

s t3t2 t4


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INVENTORY CONTROL

Model IV

( )* 2

1

c so

sc

C CDCQ

D CCP

+

=

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( )

( )

21

2 1

o s

c c s

s

o c

c s

DC C Ds

C P C C

CDTC DC C

P C C

= +

=

+


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INVENTORY CONTROL

Model-IVCo = Rs. 300 per setup; D = 10,000 units/year

Cu = Rs. 20 per unit; i = 20%; P = 20,000 units/year

Cs = Rs. 25/unit/year

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*1865.48

128.65

804.09

.3216.338 /

m

Q

s

I

TC Rs year

=

=

=

=


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INVENTORY CONTROL

Model-IIICo = Rs. 1000 per setup; D1 = 3000 units/year;

D2

= 5000 units/year; D3

= 20000 units/year;

i = 20%; C1 = Rs. 100 per unit; C2 = Rs. 200 per unit;

= =

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Apply the basic production consumption

model and verify the feasibility of thesolution.

. ,

P2 = 20,000 units/year; P3 = 50,000 units/year


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INVENTORY CONTROL

Model-III

1

1

1

1

2 2 3000 1000654.653

20 3000

20 11 100 10000

o

c

D CQ

DC

P

= = =

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2

2

2

2

3

3

3

3

577.3520 500020 11

100 20000

2 2 20000 1000

20 220 11

100

o

c

o

c

Q DC

P

D CQ

DC

P

= = =

= =

912.870000

50000

=


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INVENTORY CONTROL

Model-III

1

1

CYCLE TIME

654.653

0.21823000

577.35

Qyears

D= =

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2

3

3

.

5000

912.870.0456

20000

yearsD

Qyears

D

= =

= =

PIM 22-24 [Compatibility Mode] (1)

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