inventory management and forecasting

11 – 1

Inventory Management and Inventory Management and ForecastingForecasting

Dr. R K SinghDr. R K Singh

11 – 2

Functions of InventoryFunctions of Inventory

1.1. To decouple or separate various To decouple or separate various parts of the production processparts of the production process

2.2. To decouple the firm from To decouple the firm from fluctuations in demand and fluctuations in demand and provide a stock of goods that will provide a stock of goods that will provide a selection for customersprovide a selection for customers

3.3. To take advantage of quantity To take advantage of quantity discountsdiscounts

4.4. To hedge against inflationTo hedge against inflation

11 – 3

Reduce VariabilityReduce Variability

Inventory levelInventory level

Process downtimeScrap

Setup time

Late deliveries

Quality problems

11 – 4

Inventory Inventory levellevel

Reduce VariabilityReduce Variability

Scrap

Setup time

Late deliveries

Quality problems

Process downtime

11 – 5

Types of InventoryTypes of Inventory Raw materialRaw material

Purchased but not processedPurchased but not processed WorkWork--inin--processprocess

Undergone some change but not completedUndergone some change but not completed Maintenance/repair/operating (MRO)Maintenance/repair/operating (MRO)

Necessary to keep machinery and processes Necessary to keep machinery and processes productiveproductive

Finished goodsFinished goods Completed product awaiting shipmentCompleted product awaiting shipment

11 – 6

ABC AnalysisABC Analysis Divides inventory into three classes Divides inventory into three classes

based on annual dollar volumebased on annual dollar volume Class A Class A -- high annual dollar volumehigh annual dollar volume Class B Class B -- medium annual dollar medium annual dollar

volumevolume Class C Class C -- low annual dollar volumelow annual dollar volume

Used to establish policies that focus Used to establish policies that focus on the few critical parts and not the on the few critical parts and not the many trivial onesmany trivial ones

11 – 7

ABC AnalysisABC Analysis

A ItemsA Items

B ItemsB ItemsC ItemsC Items

Perc

ent o

f ann

ual d

olla

r usa

gePe

rcen

t of a

nnua

l dol

lar u

sage

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 items

11 – 8

Independent Versus Independent Versus Dependent DemandDependent Demand

Independent demand Independent demand -- the the demand for item is independent demand for item is independent of the demand for any other of the demand for any other item in inventoryitem in inventory

Dependent demand Dependent demand -- the the demand for item is dependent demand for item is dependent upon the demand for some upon the demand for some other item in the inventoryother item in the inventory

11 – 9

Holding, Ordering, and Holding, Ordering, and Setup CostsSetup Costs

Holding costs -- the costs of holding the costs of holding or “carrying” inventory over timeor “carrying” inventory over time

Ordering costs -- the costs of the costs of placing an order and receiving placing an order and receiving goodsgoods

Setup costs -- cost to prepare a cost to prepare a machine or process for machine or process for manufacturing an ordermanufacturing an order

11 – 10

Basic EOQ ModelBasic EOQ Model

1.1. Demand is known, constant, and Demand is known, constant, and independentindependent

2.2. Lead time is known and constantLead time is known and constant3.3. Receipt of inventory is instantaneous and Receipt of inventory is instantaneous and

completecomplete4.4. Quantity discounts are not possibleQuantity discounts are not possible5.5. Only variable costs are setup and holdingOnly variable costs are setup and holding6.6. Stockouts can be completely avoidedStockouts can be completely avoided

Important assumptionsImportant assumptions

11 – 11

Inventory Usage Over TimeInventory Usage Over Time

Order Order quantity = Q quantity = Q (maximum (maximum inventory inventory

level)level)

Usage rateUsage rate Average Average inventory inventory on handon hand

QQ22

Minimum Minimum inventoryinventory

Inve

ntor

y le

vel

Inve

ntor

y le

vel

TimeTime00

11 – 12

The EOQ ModelThe EOQ ModelQQ = Number of pieces per order= Number of pieces per order

Q*Q* = Optimal number of pieces per order (EOQ)= Optimal number of pieces per order (EOQ)DD = Annual demand in units for the inventory item= Annual demand in units for the inventory itemSS = Setup or ordering cost for each order= Setup or ordering cost for each orderHH = Holding or carrying cost per unit per year= Holding or carrying cost per unit per year

Annual setup cost Annual setup cost == ((Number of orders placed per yearNumber of orders placed per year) ) x (x (Setup or order cost per orderSetup or order cost per order))

Annual demandAnnual demandNumber of units in each orderNumber of units in each order

Setup or order Setup or order cost per ordercost per order==

Annual setup cost = SDQ

= (= (SS))DDQQ

11 – 13



Annual holding cost Annual holding cost == ((Average inventory levelAverage inventory level) ) x (x (Holding cost per unit per yearHolding cost per unit per year))

Order quantityOrder quantity22= (= (Holding cost per unit per yearHolding cost per unit per year))

= (= (HH))QQ22


Annual holding cost = HQ2

11 – 14

Minimizing CostsMinimizing CostsObjective is to minimize total costsObjective is to minimize total costs

Ann

ual c

ost

Ann

ual c

ost

Order quantityOrder quantity

Curve for total Curve for total cost of holding cost of holding

and setupand setup

Holding cost Holding cost curvecurve

Setup (or order) Setup (or order) cost curvecost curve

Minimum Minimum total costtotal cost

Optimal order Optimal order quantity (Q*)quantity (Q*)

11 – 15



Optimal order quantity is found when annual setup cost Optimal order quantity is found when annual setup cost equals annual holding costequals annual holding cost


Annual holding cost = HQ2

DDQQ SS = = HHQQ

22Solving for Q*Solving for Q* 22DS = QDS = Q22HH

QQ22 = = 22DS/HDS/HQ* = Q* = 22DS/HDS/H

11 – 16

An EOQ ExampleAn EOQ Example

Determine optimal number of needles to orderDetermine optimal number of needles to orderD D = 1,000= 1,000 unitsunitsS S = $10= $10 per orderper orderH H = $.50= $.50 per unit per yearper unit per year

Q* =Q* = 22DSDSHH

Q* =Q* = 2(1,000)(10)2(1,000)(10)0.500.50 = 40,000 = 200= 40,000 = 200 unitsunits

11 – 17


Determine number of ordersDetermine number of ordersD D = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsS S = $10= $10 per orderper orderH H = $.50= $.50 per unit per yearper unit per year

= N = == N = =Expected Expected number of number of

ordersorders

DemandDemandOrder quantityOrder quantity

DDQ*Q*

N N = = 5= = 5 orders per year orders per year 1,0001,000200200

11 – 18


Determine expected time between ordersDetermine expected time between ordersD D = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsS S = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearH H = $.50= $.50 per unit per year, Number of working days=250per unit per year, Number of working days=250

= T == T =Expected Expected

time between time between ordersorders

Number of working Number of working days per yeardays per year

NN

T T = = 50 = = 50 days between ordersdays between orders25025055

11 – 19


Determine total annual costDetermine total annual costD D = 1,000= 1,000 unitsunits Q*Q* = 200= 200 unitsunitsS S = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearH H = $.50= $.50 per unit per yearper unit per year TT = 50= 50 daysdays

Total annual cost = Setup cost + Holding costTotal annual cost = Setup cost + Holding cost

TC = S + HTC = S + HDDQQ

QQ22

TC TC = ($10) + ($.50)= ($10) + ($.50)1,0001,000200200

20020022

TC TC = (5)($10) + (100)($.50) = $50 + $50 = $100= (5)($10) + (100)($.50) = $50 + $50 = $100

11 – 20

Robust ModelRobust 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

11 – 21


Management underestimated demand by 50%Management underestimated demand by 50%D D = 1,000= 1,000 units units Q*Q* = 200= 200 unitsunitsS S = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearH H = $.50= $.50 per unit per yearper unit per year TT = 50= 50 daysdays


QQ22

TC TC = ($10) + ($.50) = $75 + $50 = $125= ($10) + ($.50) = $75 + $50 = $1251,5001,500200200

20020022

1,500 1,500 unitsunits

Total annual cost increases by only 25%Total annual cost increases by only 25%

11 – 22


Actual EOQ for new demand is Actual EOQ for new demand is 244.9244.9 unitsunitsD D = 1,000= 1,000 units units Q*Q* = 244.9= 244.9 unitsunitsS S = $10= $10 per orderper order NN = 5= 5 orders per yearorders per yearH H = $.50= $.50 per unit per yearper unit per year TT = 50= 50 daysdays


QQ22

TC TC = ($10) + ($.50)= ($10) + ($.50)1,5001,500244.9244.9

244.9244.922

1,500 1,500 unitsunits

TC TC = $61.24 + $61.24 = $122.48= $61.24 + $61.24 = $122.48

Only 2% less than the total cost of $125

when the order quantity

was 200

11 – 23

Reorder PointsReorder Points

EOQ answers the “how much” questionEOQ answers the “how much” question The reorder point (ROP) tells when to The reorder point (ROP) tells when to

orderorder

ROP ROP == Lead time for a Lead time for a new order in daysnew order in days

Demand Demand per dayper day

== d x Ld x L

d = d = DDNumber of working days in a yearNumber of working days in a year

11 – 24

Reorder Point CurveReorder Point Curve

Q*Q*

ROP ROP (units)(units)In

vent

ory

leve

l (un

its)

Inve

ntor

y le

vel (

units

)

Time (days)Time (days)Lead time = LLead time = L

Slope = units/day = dSlope = units/day = d

11 – 25

Reorder Point ExampleReorder Point ExampleDemand Demand = 8,000= 8,000 iPods per yeariPods per year250250 working day yearworking day yearLead time for orders is Lead time for orders is 33 working daysworking days

ROP =ROP = d x Ld x L

d =d =DD

Number of working days in a yearNumber of working days in a year

= 8,000/250 = 32= 8,000/250 = 32 unitsunits

= 32= 32 units per day x units per day x 33 days days = 96= 96 unitsunits

11 – 26

Safety Safety Stock Stock • Safety stock

–– buffer added to on hand inventory during buffer added to on hand inventory during lead timelead time

• Stockout –– an inventory shortagean inventory shortage

• Service level –– probability that the inventory available probability that the inventory available

during lead time will meet demandduring lead time will meet demand

.

11 – 27

Variable Demand Variable Demand With Reorder With Reorder PointPoint

Reorderpoint, R

Q

LTTime

LT

Inve

ntor

y le

vel

0

11 – 28

Reorder Point With Reorder Point With Variable Variable DemandDemand

R = dL + zd L

whered = average daily demandL = lead timed = the standard deviation of daily demand

z = number of standard deviationscorresponding to the service levelprobability

zd L = safety stock

11 – 29

Reorder Point Reorder Point For a For a Service Service LevelLevel

Probability of meeting demand during lead time = service level

Probability of a stockout

R

Safety stock

dLDemand

zd L

11 – 30

Reorder Point Reorder Point For Variable For Variable DemandDemand

The paint store wants a reorder point with a 95% service level and a 5% stockout probability

d = 30 gallons per dayL = 10 daysd = 5 gallons per day

For a 95% service level, z = 1.65

R = dL + z d L

= 30(10) + (1.65)(5)( 10)

= 326.1 gallons

Safety stock = z d L

= (1.65)(5)( 10)

= 26.1 gallons

11 – 31

What is Forecasting?What is Forecasting?

Process of Process of predicting a future predicting a future eventevent

Underlying basis of Underlying basis of all business all business decisionsdecisions ProductionProduction InventoryInventory PersonnelPersonnel FacilitiesFacilities

??

11 – 32

ShortShort--range forecastrange forecast Up to 1 year, generally less than 3 monthsUp to 1 year, generally less than 3 months Purchasing, job scheduling, workforce Purchasing, job scheduling, workforce

levels, job assignments, production levelslevels, job assignments, production levels MediumMedium--range forecastrange forecast

1 year to 3 years1 year to 3 years Sales and production planning, budgetingSales and production planning, budgeting

LongLong--range forecastrange forecast 33++ yearsyears New product planning, facility location, New product planning, facility location,

research and developmentresearch and development

Forecasting Time HorizonsForecasting Time Horizons

11 – 33

Elements of a Good ForecastElements of a Good Forecast

Timely

AccurateReliable

Written

11 – 34

Influence of Product Life Influence of Product Life CycleCycle

Introduction and growth require longer Introduction and growth require longer forecasts than maturity and declineforecasts than maturity and decline

As product passes through life cycle, As product passes through life cycle, forecasts are useful in projectingforecasts are useful in projecting Staffing levelsStaffing levels Inventory levelsInventory levels Factory capacityFactory capacity

Introduction – Growth – Maturity – Decline

11 – 35

Overview of Quantitative Overview of Quantitative ApproachesApproaches

1.1. Naive approachNaive approach2.2. Moving averagesMoving averages3.3. Exponential Exponential

smoothingsmoothing4.4. Linear regressionLinear regression

TimeTime--Series Series ModelsModels

Associative Associative ModelModel

11 – 36

Naive ForecastsNaive Forecasts

Uh, give me a minute.... We sold 250 wheels lastweek.... Now, next week we should sell....

The forecast for any period equals the previous period’s actual value.

e.g., If January sales were 68, then e.g., If January sales were 68, then February sales will be 68February sales will be 68

11 – 37

MA is a series of arithmetic means MA is a series of arithmetic means Used if little or no trendUsed if little or no trend Used often for smoothingUsed often for smoothing

Provides overall impression of data Provides overall impression of data over timeover time

Moving Average MethodMoving Average Method

Moving average =Moving average =∑∑ demand in previous n periodsdemand in previous n periods

nn

11 – 38

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 33--MonthMonthMonthMonth Shed SalesShed Sales Moving AverageMoving Average

(12 + 13 + 16)/3 = 13 (12 + 13 + 16)/3 = 13 22//33(13 + 16 + 19)/3 = 16(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 (16 + 19 + 23)/3 = 19 11//33

Moving Average ExampleMoving Average Example

101012121313

((1010 + + 1212 + + 1313)/3 = 11 )/3 = 11 22//33

11 – 39

Used when trend is present Used when trend is present Older data usually less importantOlder data usually less important

Weights based on experience and Weights based on experience and intuitionintuition

Weighted Moving AverageWeighted Moving Average

WeightedWeightedmoving averagemoving average ==

∑∑ ((weight for period nweight for period n))x x ((demand in period ndemand in period n))

∑∑ weightsweights

11 – 40

JanuaryJanuary 1010FebruaryFebruary 1212MarchMarch 1313AprilApril 1616MayMay 1919JuneJune 2323JulyJuly 2626

ActualActual 33--Month WeightedMonth WeightedMonthMonth Shed SalesShed Sales Moving AverageMoving Average

[(3 x 16) + (2 x 13) + (12)]/6 = 14[(3 x 16) + (2 x 13) + (12)]/6 = 1411//33[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 19) + (2 x 16) + (13)]/6 = 17[(3 x 23) + (2 x 19) + (16)]/6 = 20[(3 x 23) + (2 x 19) + (16)]/6 = 2011//22

Weighted Moving AverageWeighted Moving Average

101012121313

[(3 x [(3 x 1313) + (2 x ) + (2 x 1212) + () + (1010)]/6 = 12)]/6 = 1211//66

Weights Applied Period3 Last month2 Two months ago1 Three months ago6 Sum of weights

11 – 41

Form of weighted moving averageForm of weighted moving averageWeights decline exponentiallyWeights decline exponentiallyMost recent data weighted mostMost recent data weighted most

Requires smoothing constant Requires smoothing constant (())Ranges from 0 to 1Ranges from 0 to 1Subjectively chosenSubjectively chosen

Involves little record keeping of past Involves little record keeping of past datadata

Exponential SmoothingExponential Smoothing

11 – 42

Exponential SmoothingExponential Smoothing

New forecast =New forecast = Last period’s forecastLast period’s forecast+ + ((Last period’s actual demand Last period’s actual demand

–– Last period’s forecastLast period’s forecast))

FFtt = F= Ft t –– 11 ++ ((AAt t –– 11 -- FFt t –– 11))

wherewhere FFtt == new forecastnew forecastFFt t –– 11 == previous forecastprevious forecast

== smoothing (or weighting) smoothing (or weighting) constant constant (0 (0 ≤≤ ≤≤ 1)1)

11 – 43

Exponential Smoothing Exponential Smoothing ExampleExample

Predicted demand Predicted demand = 142= 142 Ford MustangsFord MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20= .20

11 – 44


Predicted demand Predicted demand = 142= 142 Ford CarsFord CarsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20= .20

New forecastNew forecast = 142 + .2(153 = 142 + .2(153 –– 142)142)

11 – 45


Predicted demand Predicted demand = 142= 142 Ford MustangsFord MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20= .20

New forecastNew forecast = 142 + .2(153 = 142 + .2(153 –– 142)142)= 142 + 2.2= 142 + 2.2= 144.2 ≈ 144 cars= 144.2 ≈ 144 cars

11 – 46

Effect ofEffect ofSmoothing ConstantsSmoothing Constants

Weight Assigned toWeight Assigned toMostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th Most

RecentRecent RecentRecent RecentRecent RecentRecent RecentRecentSmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant (()) (1 (1 -- )) (1 (1 -- ))22 (1 (1 -- ))33 (1 (1 -- ))44

= .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066

= .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031

11 – 47

Effect ofEffect ofSmoothing ConstantsSmoothing Constants

Weight Assigned toWeight Assigned toMostMost 2nd Most2nd Most 3rd Most3rd Most 4th Most4th Most 5th Most5th Most

RecentRecent RecentRecent RecentRecent RecentRecent RecentRecentSmoothingSmoothing PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriod PeriodPeriodConstantConstant (()) (1 (1 -- )) (1 (1 -- ))22 (1 (1 -- ))33 (1 (1 -- ))44

= .1= .1 .1.1 .09.09 .081.081 .073.073 .066.066

= .5= .5 .5.5 .25.25 .125.125 .063.063 .031.031

11 – 48

Common Measures of Common Measures of Forecasting ErrorForecasting Error

Mean Absolute Deviation Mean Absolute Deviation ((MADMAD))

MAD =MAD =∑∑ |Actual |Actual -- Forecast|Forecast|

nn

Mean Squared Error Mean Squared Error ((MSEMSE))

MSE =MSE =∑∑ ((Forecast ErrorsForecast Errors))22

nn

11 – 49

Common Measures of ErrorCommon Measures of Error

Mean Absolute Percent Error Mean Absolute Percent Error ((MAPEMAPE))

MAPE =MAPE =∑∑100100|Actual|Actualii -- ForecastForecastii|/Actual|/Actualii

nn

nn

i i = 1= 1

11 – 50

How strong is the linear How strong is the linear relationship between the relationship between the variables?variables?

Coefficient of correlation, r, Coefficient of correlation, r, measures degree of associationmeasures degree of associationValues range from Values range from --11 to to +1+1

CorrelationCorrelation

r = r = nnSSxyxy -- SSxxSSy y

[[nnSSxx22 -- ((SSxx))22][][nnSSyy22 -- ((SSyy))22]]

11 – 51

Correlation CoefficientCorrelation Coefficient

r = r = nnSSxyxy -- SSxxSSy y

[[nnSSxx22 -- ((SSxx))22][][nnSSyy22 -- ((SSyy))22]]

y

x(a) Perfect positive correlation: r = +1

y

x(b) Positive correlation: 0 < r < 1

y

x(c) No correlation: r = 0

y

x(d) Perfect negative correlation: r = -1

11 – 52

Coefficient of Determination, rCoefficient of Determination, r22, , measures the percent of change in measures the percent of change in y predicted by the change in xy predicted by the change in xValues range from Values range from 00 to to 11Easy to interpretEasy to interpret

CorrelationCorrelation

For the Nodel Construction example:For the Nodel Construction example:r r = .901= .901rr22 = .81= .81

11 – 53

Forecasting in the Service Forecasting in the Service SectorSector

Presents unusual challengesPresents unusual challengesSpecial need for short term recordsSpecial need for short term recordsNeeds differ greatly as function of Needs differ greatly as function of

industry and productindustry and productHolidays and other calendar eventsHolidays and other calendar eventsUnusual eventsUnusual events

11 – 54

Fast Food Restaurant Fast Food Restaurant ForecastForecast

20% 20% –

15% 15% –

10% 10% –

5% 5% –

1111--1212 11--22 33--44 55--66 77--88 99--10101212--11 22--33 44--55 66--77 88--99 1010--1111

(Lunchtime)(Lunchtime) (Dinnertime)(Dinnertime)Hour of dayHour of day

Perc

enta

ge o

f sal

esPe

rcen

tage

of s

ales

11 – 55

Computer Software for Computer Software for ForecastingForecasting

•• Examples of computer software with Examples of computer software with forecasting capabilitiesforecasting capabilities–– Auto boxAuto box–– Forecast ProForecast Pro–– Smart Forecasts for WindowsSmart Forecasts for Windows–– SASSAS–– SPSSSPSS–– SAPSAP–– POM Software LibaryPOM Software Libary

Primarily forPrimarily forforecastingforecasting

HaveHaveForecastingForecasting

modulesmodules

11 – 56

Thank you

inventory management and forecasting

Documents

inventory management

inventoryother item

time ordering costs

goodsgoods setup costs

setup costssetup costs

stock of goods

critical parts

separate various parts