Download - 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
Types of Inventories
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
Types of Inventories
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
= =
= =