3445 inventory management

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POM II

INDEPENDENT DEMAND

INVENTORY



INVENTORY

Inventory is the stock of any item or resource used in an organization andcan include: raw materials, finished

products, component parts, supplies-in-transit and work-in-process.

An inventory management system is theset of policies and controls that monitor

levels of inventory and determines whatlevels should be maintained, whenstock should be replenished, and howlarge orders should be



WHY INVENTORY

1. To maintain independence of operations

2. To meet variation in product demand, production rate and

lead time

3. To allow flexibility in production scheduling

4. To provide a safeguard for variation in raw material delivery

time

5. To take advantage of volume discounts

6. Hedge against inflation

7. Disruptions

8. Reduces no of ordering / set up



NEGATIVE ASPECTS

Quality of product service bundle

Hide operational problems

High cost Obsolescence

Damage during storage

Cost of tracking New product / technology introduction



STOCK POINTS

SUPPLIERS DISTRIBUTOR RETAILER

RM, RM, INPROCESS INV PRODUCT PRODUCT

COMPONENTS COMPONENTS PIPELINE INV

VALUE ADDING S YSTEM

FINISHED GOODS



E(1

)

Independent vs. Dependent

Demand

Independent Demand (Demand for the final end-

product or demand not related to other items)

Dependent

Demand

(Derived demand

items for component

parts,

subassemblies,

raw materials,

etc)

Finished

product

Component parts



Inventory Systems

Single-Period Inventory Model

± One time purchasing decision (Example:

vendor selling t-shirts at a cricket game)

± Seeks to balance the costs of inventory

overstock and under stock

Multi-Period Inventory Models

± Fixed-Order Quantity Models

Event triggered (Example: running out of

stock)

± Fixed-Time Period Models

Time triggered (Example: Monthly sales call

by sales representative)



INVENTORY CONTROL SYSTEM

When to order

How much to order

Buffer Stock

Maximum Inventory

How often to review stock



COSTS

Holding (or carrying) costs

± Costs for storage, handling, insurance, etc

Setup (or production change) costs

± Costs for arranging specific equipment

setups, etc

Ordering costs

± Costs of someone placing an order,transportation etc

Shortage costs



SINGLE PERIOD

d + z *



Single-Period Inventory Model

uo

u

C C

C P

e

sold beunit willy that theProbabilit

estimatedunder demandof unit per CostCestimatedover demandof unit per CostC

:Where

u

o

!

!

!

P



Single Period Model Example

Our college basketball team is playing in atournament game this weekend. Based on our

past experience we sell on average 2,400 shirtswith a standard deviation of 350. We makeRs100 on every shirt we sell at the game, but loseRs50 on every shirt not sold. How many shirtsshould we make for the game?

C u = Rs100 and C o = Rs50; P 100 / (100 + 50) = .667

Z.667 = .432 (use NORMSINV(.667))

therefore we need 2,400 + .432(350) = 2,551 shirts



UNCERTAIN DEMAND

UNIT COST = 1

SALE PRICE = 2

PURCHASE 30

DEMAND PROB SOLD EARN COST PROFIT

profit10 0.05 10 20 30 -10 -0.5

20 0.15 20 40 30 10 1.5

30 0.3 30 60 30 30 9

40 0.2 30 60 30 30 6

50 0.1 30 60 30 30 3

60 0.1 30 60 30 30 3

70 0.1 30 60 30 30 3

Probable profit 25



UNCERTAIN DEMAND

UNIT COST = 1

SALE PRICE = 2

PURCHASE 30

DEMAND PROB SOLD EARN COST PROFITO

PORT

UNITY

LOST

Probableprofit

10 0.05 10 20 30 -10 0 -0.5

20 0.15 20 40 30 10 0 1.5

30 0.3 30 60 30 30 0 9

40 0.2 30 60 30 30 -10 4

50 0.1 30 60 30 30 -20 1

60 0.1 30 60 30 30 -30 0

70 0.1 30 60 30 30 -40 -1

Probable profit 14



Fixed-Order Quantity Model

Assumptions Demand for the product is constant

and uniform throughout the period

Lead time (time from ordering toreceipt) is constant

Price per unit of product is constant

Instantaneous replacement



FIXED ORDER QU ANTITY

QTY

TIME

ORDER

QU ANTITY

AVERAGE

INVENTORY

REORDER

POINT



Fixed-Order Quantity Model Assumptions

Inventory holding cost is based onaverage inventory

Ordering or setup costs are constant

All demands for the product will be

satisfied (No back orders are allowed)



TOTAL COST

H2Q +S

QD +DC=TC

Total Annual =Cost

AnnualPurchase

Cost

AnnualOrdering

Cost

AnnualHolding

Cost+ +



Q = 2DSH

= 2(Annual Demand)(Order or Setup Cost)Annual Holding CostOPT

EOQ



Cost Minimization

Ordering Costs

Holding

Costs

Order Quantity (Q)

COST

Annual Cost of

Items (DC)

Total Cost

QOPT



REORDER POINT

Reorder point, R = d L _

d = average daily demand (constant)

L = Lead time (constant)

_



EOQ Example

Annual Demand = 1,000 unitsCost to place an order = Rs10

Holding cost per unit per year = Rs2.50

Lead time = 7 days

Cost per unit = Rs15

Given the information below, what are the EOQ and

reorder point?

Q =((2*1000*10)/2.5)^1/2 = 4000

ROP= (1000/250)*7 = 28



PRICE DISCOUNT

0

5000

10000

15000

20000

25000

30000

35000

40000

45000

50000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

OQ

CO

IC

PC

TC



Price-Break Example Problem

A company has a chance to reduce their costs by

placing larger quantity orders using the price-break

order quantity schedule below. What should their

optimal order quantity be if this company purchases

this single inventory item with an ordering cost of

Rs4, a carrying cost rate of 2% of the inventory cost

of the item, and an annual demand of 10,000 units?

Order Quantity(units) Price/unit(Rs)0 to 2,499 Rs1.202,500 to 3,999 1.004,000 or more .98



Price-Break

units1,826=0.02(1.20)

4)2(10,000)( =

iC

2DS =QOPT

Annual Demand (D)= 10,000 unitsCost to place an order (S)= Rs4

First, plug data into formula for each price-break value of ³C´

units2,000=0.02(1.00)

4)2(10,000)( =

iC

2DS =QOPT

units2,020=0.02(0.98)

4)2(10,000)( =

iC

2DS =QOPT

Carrying cost % of total cost (i)= 2%Cost per unit (C) = $1.20, $1.00, $0.98

Interval from 0 to 2499, theQopt value is feasible

Interval from 2500-3999, theQopt value is not feasible

Interval from 4000 & more, theQopt value is not feasible

Next, determine if the computed Qopt values are feasible or not



Price-Break

Since the feasible solution occurred in the first price-break, it means that all the other true Qopt values occur

at the beginnings of each price-break interval. Why?

0 1826 2500 4000 Order Quantity

Totalannualcosts So the candidates

for the price-

breaks are 1826,2500, and 4000

units

Because the total annual cost function isa ³u´ shaped function



Price-Break

iC2

Q +S

Q

D +DC=TC

TC(0-2499)=(10000*1.20)+(10000/1826)*4+(1826/2)(0.02*1.20)

= Rs12,043.82TC(2500-3999)= Rs10,041

TC(4000&more)= Rs9,949.20



SENSITIVITY ANALYSIS

Deviation from EOQ may becomeinevitable

- Truck load requirement- Space in warehouse

It will result in increase in cost

Sensitivity analysis to be done to estimate

increase in cost



VARIABLE LEAD TIME ,DEMAND

QTY

TIME

SAFETY

STOCK

REORDER

POINT

ORDER

QU ANTITY



SAFETY STOCK

Safety Stock - Stock that is held inexcess of expected demand due tovariable demand rate and/or lead time.

Service Level - Probability that demandwill not exceed supply during lead time.



OP for Discrete DDLT

DistributionOne of Sharp Retailer¶s inventory items isnow being analyzed to determine anappropriate level of safety stock. The

manager wants an 80% service level duringlead time. The item¶s historical DDLT is:

DDLT (units) Occurrences3 8

4 65 46 2



OP for Discrete DDLT

Distribution

Probability Probability of

DDLT (cases) of DDLT DDLT or Less

3 .4 .44 .3 .75 .2 .9

6 .1 1.0To provide 80% service level, OP = 5

cases



REORDER POINT

ROP

Risk of a stockout

Service level

Probability of

no stockout

Expected

demand Safety

stock

0 z

Quantity

z-scale

The ROP based on a normalDistribution of lead time demand



SAFETY STOCKVARIABLE DEMAND

Average demand during lead time

Standard deviation of Demand During lead

time



SAFETY STOCKVARIABLE DEMAND

ROP = Average demand during lead time + z * standard deviation of demand during lead time

-

ROP = d + z * sd( demand during lead time)

sd (demand during lead time ) =



Set safety stock level at a percentage of EDDLT

ROP = EDDLT + j(EDDLT)

where j is a factor between 0 and 3.

Set safety stock level at square root of

RO OP = EDDLT + EDDLT

Rules of Thumb in Setting ROP

EDDLT



FIXED PERIOD MODEL

L L T L

T T



FIXED REORDER CYCLE

D = demand for the year

T = Time between orders ( fraction of year)

Average inventory = D*T/2

Orders per year = 1/T

Total Inv Cost = CO * (1/T) +(D*T/2) * IC



order )onitems(includeslevelinventorycurrent=I

timeleadandreviewover thedemandof deviationstandard=

y probabilitservicespecifiedafor deviationsstandardof number the=zdemanddailyaverageforecast=d

daysintimelead=L

reviews betweendaysof number the=T

ordered betoquantitiy=Q:Where

I-Z+L)+(Td=Q

L+T

L+T

W

W

q = Average demand + Safety stock ± Inventory currently on hand

FIXED PERIOD MODEL



Maximum Inventory Level, M

Optional Replenishment System

MActual Inventory Level, I

q = M - I

I

Q = minimum acceptable order quantity

If q > Q, order q, otherwise do not order any.



ABC Classification System

Items kept in inventory are not of equalimportance in terms of:

± Rupees invested

± profit potential

± sales or usage volume

± stock-out penalties

0

30

60

30

60

AB

C

% of

Rs Value

% of Use

So, identify inventory items based on percentage of total

consumption, where ³A´ items are roughly top 80 %, ³B´

items as next 15 %, and the lower 5% are the ³C´ items



Inventory Accuracy and Cycle Counting

Inventory accuracy refers to how

well the inventory records agreewith physical count

Cycle Counting is a physical

inventory-taking technique in whichinventory is counted on a frequent

basis rather than once or twice a

year



Inventory Counting Systems

P eriodic System

Physical count of items made at periodicintervals

P erpetual Inventory SystemSystem that keeps trackof removals from inventorycontinuously, thus

monitoringcurrent levels of each item



Inventory Counting Systems

Tw o-Bin System - Two containers of inventory; reorder when the first is empty

Universal Bar Code - Bar code

printed on a label that hasinformation about the itemto which it is attached

0

214800 232087768

3445 inventory management

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