11 – 1 Inventory Management and Inventory Management and Forecasting Forecasting Dr. R K Singh Dr. R K Singh
Jan 28, 2016
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
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Reduce VariabilityReduce Variability
Inventory levelInventory level
Process downtimeScrap
Setup time
Late deliveries
Quality problems
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Inventory Inventory levellevel
Reduce VariabilityReduce Variability
Scrap
Setup time
Late deliveries
Quality problems
Process downtime
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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
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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
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ABC AnalysisABC Analysis
A ItemsA Items
B ItemsB ItemsC ItemsC Items
Perc
ent o
f ann
ual d
olla
r usa
gePe
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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
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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
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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
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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
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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
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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
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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 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 setup cost = SDQ
Annual holding cost = HQ2
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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*)
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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
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 setup cost = SDQ
Annual holding cost = HQ2
DDQQ SS = = HHQQ
22Solving for Q*Solving for Q* 22DS = QDS = Q22HH
QQ22 = = 22DS/HDS/HQ* = Q* = 22DS/HDS/H
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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
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An EOQ ExampleAn EOQ Example
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
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An EOQ ExampleAn EOQ Example
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
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An EOQ ExampleAn EOQ Example
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
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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
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An EOQ ExampleAn EOQ Example
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
TC = S + HTC = S + HDDQQ
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%
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An EOQ ExampleAn EOQ Example
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
TC = S + HTC = S + HDDQQ
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
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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
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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
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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
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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
.
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Variable Demand Variable Demand With Reorder With Reorder PointPoint
Reorderpoint, R
Q
LTTime
LT
Inve
ntor
y le
vel
0
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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
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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
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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
??
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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
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Elements of a Good ForecastElements of a Good Forecast
Timely
AccurateReliable
Written
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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Exponential Smoothing Exponential Smoothing ExampleExample
Predicted demand Predicted demand = 142= 142 Ford MustangsFord MustangsActual demand Actual demand = 153= 153Smoothing constant Smoothing constant = .20= .20
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Exponential Smoothing Exponential Smoothing ExampleExample
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
Exponential Smoothing Exponential Smoothing ExampleExample
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
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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
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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
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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
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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
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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]]
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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
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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
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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
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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
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f sal
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of s
ales
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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
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Thank you