Demand Forecasting in Demand Forecasting in a Supply Chain a Supply Chain

Demand Forecasting in Demand Forecasting in a Supply Chain a Supply Chain

Presented byPresented byProf. M. K. TiwariProf. M. K. Tiwari

At the end of session you will…

• Understand the role of forecasting for both an enterprise and a Supply Chain (SC)

• Identify the components of a demand forecasts.

• Forecast demand in a SC given historical demand data using time series methodologies.

• Analyze demand forecasts to estimate forecast error.

Forecasting!......why?• Push system requires planning about:

– Level of production

• Pull system requires planning about:– Level of available capacity– Level of inventory

• Both require future demand of customers.

• Either Pull or push, both processes are driven by customer demand.

Example of Dell Computer: Mastering Pull

and Push

• Dell orders components anticipating customers order (Push)

• It determines capacity of assembly plants on customer demand basis. (Pull)

• For both purposes it requires demand forecasting.

Forecasting: Definition and its role

Definition: In its simplest form “It is estimation of expected demand over a specified future period.” – If each SC stage makes own demand

forecast variation is unavoidable. – Collaborative forecasts tend to be more

accurate.

• Role: – This accuracy enables SC to be more

responsible and efficient in serving their customers.

Forecasting makes decisions about:

1. Production: scheduling, inventory control, aggregate planning, purchasing.

2. Marketing: sales-force allocation, promotions, new product introduction.

3. Finance: plant/equipment investment, budgetary planning.

4. Personal: workforce planning, hiring, layoffs.

Characteristics of

forecasts 1. Should include both expected and

measure of forecast error (demand uncertainty).

• Consider, two car dealers• One expects sales between 100 and 1900• Other expects sales between 900 and 1100.

• Even though for both average sales is 1000, sourcing strategy will be different.

• First dealer will have to arrange more resources due to higher forecasting error.

High Uncertaint

y

LowUncertainty

2. Long term forecasts are usually less accurate than short term forecasts.

3. For same percentage error, aggregate forecasts (e.g. GDP of a country) are usually more accurate than disaggregate forecasts (e.g. yearly revenue of company or product wise details).

Characteristics of forecasts

• The classic example of summing up the forecast error is bullwhip effect. Here order variation is amplified as they move up in SC from the end customers.

• Mature products with stable demand are usually easiest to forecast.

• Forecasting is difficult when either the supply of raw materials or the demand for the finished products is highly variable.

Characteristics of

forecasts

Factors related to demand forecast

• Past demand • Lead time of products• Planned advertising or

marketing efforts • State of the economy• Planned price discounts• Actions competitors have

taken.

Classification of forecasting methods

• Qualitative:– Methods are subjective and rely on

human judgment.– Appropriate when there is little

historical data available or experts have market intelligence.

– Used to forecast demand several years into the future in a new industry.

Classification of forecasting methods…• Time series:

– Uses historical demand to make forecasts.

– Based on assumption that past demand history is a good indicator of future demand.

– Appropriate when the basic demand pattern does not vary significantly from one period to next.

– Simple to use and can serve as a good starting point.

• Causal– Assumes that demand forecast is

highly correlated with certain factors in the environment (e.g. state of economy, interest rates etc.).

– This method find the correlation between demand and environment and use estimates of environment factors to forecast future demand.

Classification of forecasting methods…

• Simulation– These methods imitate consumer choices

that give rise to demand to arrive at a forecast.

– Using it a firm can combine time series

and causal method to answer:

1. What will be impact of price promotion?2. What will be the impact of a competitor opening

a store nearby?3. Airlines simulate customers buying behavior to

forecast demand for higher fare seats.

Classification of forecasting methods…

Appropriate method

• Several studies have indicated that using multiple forecasting method is more effective than any individual method.

• Deal with time series method when future forecast is expected to follow historical method.

• Historical demand, growth pattern, any seasonal pattern influence the forecast.

Components of demand

• Observation demand can be broken into two components.– Observed demand (0)=systematic (S)

+random (R)• Systematic component measures

the expected value of demand. • Random component is that part of

forecast that deviate from the systematic part. Company

can not forecast

this value.

Basic approach

• Step 1: Understand the objective of forecasting

• Step 2: Integrate demand planning

and forecasting through the SC

• Step 3: Understand and identify customers segments

Basic approach…• Step 4: Identify the major factors

that influence the demand forecast

• Step 5: Determine the appropriate forecasting technique

• Step 6: Establish performance and error measure for the forecast.

Step 1: Understand the objective of forecasting • Clearly identify the decisions such as:

– How much of a particular product to make? – How much to inventory?– How much to order?

• It is important that all parties must come up with a common forecast demand.

• Failure to make such decisions jointly may results either too much or too little product in various stages of supply chain.

Step 2: Integrated demand planning and forecasting through SC

• A company should link its forecast to all planning activities throughout SC.

• Link should exist at both the information system and human resource system.

• As a variety of functions are affected by the outcomes of the planning process, it is important that all of them are integrated into the forecasting process.

Step 3: Understand and identify customers segments

• Customers may be grouped by similarities in service requirements, demand volumes, order frequency, demand volatility, seasonality.

• Companies may use different forecasting methods for different segments.

• Clear understanding facilitates an accurate and simplified approach for forecasting.

Step 4: Identify major factors that influence the demand forecasts

• A proper analysis of major factors is central to developing an appropriate forecasting technique.

• The main factors are demand, supply, and product-related phenomena.

• On the demand side, a company must ascertain whether demand is growing, declining or has a seasonal pattern.

• Must be based on demand– not sales data.

Step 5: Supply side Vs Product side

• On the supply side, a company must consider available supply sources to decide on accuracy of forecast desired.– If alternative supply sources with short

lead time is available, a highly accurate forecast may not be specially important.

• On the product side, firm must know the number of variants of a product being sold.– If demand for a product influences or is

influenced by demand of another product, two forecasts are made jointly.

Step 6: Determine appropriate forecasting technique • A company should first understand

the dimensions that will be relevant to forecasts.

• These dimensions include geographical area, product groups, and customers groups.

• A firm should be wise enough to have different forecasts and techniques for each dimension.

Step 7: Establish performance and error measure of forecast

• These measures should evaluate accuracy and timeliness of forecast.

• Measure should correlate with the objective of the business decisions based on the forecasts.

• Example:– A mail order company uses forecast to place

orders to suppliers. – Orders are send to the suppliers with two months

lead time– Orders are to provide company with a quantity

minimizing both extra product left over at the end of sale season and any lost sale due to unavailability.

– At the end of season the company must compare actual demand to forecasted demand to estimate the accuracy of forecast.

– The observed accuracy should be compared with the desired and resulting gap should be used to identify corrective action that company needs to take.

Step 7: Establish performance and error measure of forecast…

Time series forecast methods

• Goal of forecasting is to predict systematic component demand and estimate the random component.

• In general, systematic component data contains 3 factors:– level factor (L)– trend factor (T) , and – seasonal factor (S).

Forms of seasonal component

• Multiplicative: systematic component=level * trend * seasonal factor

• Additive: systematic component=level + trend + seasonal factor

• Mixed: systematic component=(level + trend)* seasonal factor

Static methods

For static methods, the level, trend, and seasonality within systematic component is estimated on the basis of historical data and then same values are used for future forecasts.

Mathematical model

• The forecast in period t for demand in period t+l

Ft+1=[L+(t+l)T]St+1

where,L=estimate of level at t=0T=estimate of trendSt=estimate of seasonal factor for period t

Dt= actual demand observed for period t

Ft=forecast for demand for period t

Example problem to estimate L, T, and S.

• Tahoe , a producer of salt noticed that his retailers always overestimated the demand. This lead to his excess inventory holding costs of rock salt used in the production of salt. To reduce his inventory costs. Tahoe decided to produce a collaborative demand forecast.

• The demand is measured on quarterly basis and demand pattern repeats every year (i.e. p =4). p is the periodicity defined as the number of periods after which seasonal cycle repeats itself.

Quarterly demand for Tahoe salt Year Quarter Period Demand Dt

2000 2 1 8,000

2000 3 2 13,000

2000 4 3 23,000

2001 1 4 34,000

2001 2 5 10,000

2001 3 6 18,000

2001 4 7 23,000

2002 1 8 38,000

2002 2 9 12,000

2002 3 10 13,000

2002 4 11 32,000

2003 1 12 41,000

Estimation of three parameters

• Two steps1. Deseasonalize demand and run

linear regression to estimate level and trend.

1. Estimate seasonal factors.

Estimating level at period 0 and trend

• First, deseasonalize the demand data.

• Deseasonalized demand represents the demand that would have been observed in the absence of a seasonal fluctuations.

Method • To ensure that each season is given

equal weight when deseasonalizing the demand, take average of p consecutive periods.

• Average of demand from period l+1 to l + p provides deseasonalized demand for period l+(1 + p)/2.

• This method provides deseasonalized demand – for existing period, if p is odd, – at a point between period l+(p)/2 and l +1+ (

p)/2 , if p is even,

Method…

• By taking the average of deseasonalized demand provided by periods l+1 to (l + p) and l+2 to (l+ p+1) we obtain deseasonalized demand for period l+1+(p/2) .

i t 1 (p / 2)

t t p / 2 t p / 2 ii t 1 (p / 2)

t p / 2

ii t p / 2

D D D 2D / 2p if p is even

D / p, for p odd

Contd...

For example, in the case of Tahoe salt where p=4, for t=3 the decentralized demand is given by

4

3 1 5 ii 2

D D D 2D / 8

Deseasolized demand for Tahoe Demand

Period Demand Dt Deseasonalized demand

1 8,000

2 13,000

3 23,000 19,750

4 34,000 20,625

5 10,000 21,250

6 18,000 21,750

7 23,000 22,500

8 38,000 22,125

9 12,000 22,625

10 13,000 24,125

11 32,000

12 41,000

• Once the demand is deseasonalized it is either growing or declining at a steady rate. It can be expressed as follows:

Where,L= level or deseasonalized demand at period t.T=rate of growth of deseasonalized demand or

trend

tD L Tt

L and T estimation • For previous formula, need to estimate

the values of L and T.

• Use linear regression with deseasonalized demand( using excel sheet).

• For the example of salt, L=18439, T=524

tD 18,439 524t

Deseasonalized demand and seasonal factor for Tahoe

Salt

Period Demand Dt Deseasonalized

demand

Seasonal Factor

1 8,000 18,963 0.42

2 13,000 19,487 0.67

3 23,000 20,011 1.15

4 34,000 20,535 1.66

5 10,000 21,059 0.47

6 18,000 21,583 0.83

7 23,000 22,107 1.04

8 38,000 22,631 1.68

9 12,000 23,155 0.52

10 13,000 23,679 0.55

11 32,000 24,203 1.32

12 41,000 24,727 1.66

Estimating seasonal factors

• The seasonal factor for period t is the ratio of actual demand to deseasonalized demand and is given as follows:

• For a given periodicity, p, we can obtain the seasonal factor for a given period by averaging seasonal factors corresponding to similar periods.

• Example ,if periodicity p=4, the periods 1,5,and 9 will have similar seasonal factors. The seasonal factor for these periods is obtained as the average of the 3 seasonal factors.

t t tS D / D

_

tS

Estimating seasonal factors

• Given r seasonal cycles in data, for all periods of the form we obtain the seasonal

factor as:

• For the Tahoe salt example, a total of 12 periods and periodicity of 4 implies r=3 therefore we get

_ _ _

1 1 5 9( ) / 3 (0.42 0.47 0.52) / 3 0.47S S S S

r 1

i jp ij 0

S S / r

,1pt i i p

Adaptive forecasting

• In this, the estimates of level, trend, and seasonality are updated after each demand observation.

• In most general setting, systematic component of demand data contains a level, a trend, and a seasonal factor.

• Can be easily modified for other cases also.

• We have historical data for n periods and demand is periodic with periodicity p

Mathematical model• In adaptive methods the forecast for period t+1is

given as follows:

where– Lt=estimate of level at the end of period t– Tt=estimate of trend at the end of period t– St=estimate of seasonal factor at the end of period t – Dt= Actual demand observed at the end of period t– Ft=forecast for demand at the end of period t– Et=forecast for demand at the end of period t

( )t l t t t lF L lT S

Steps in adaptive forecasting framework

1. Initialize: 1. Compute initial estimates of level

(L0), trend (T0), seasonal factor (S1,…, SP) from given data.

2. Forecast:1. Given the estimates in period t,

forecast demand for t+1. 2. First forecast if for period 1 and is

made with the estimates of level, trend, and seasonal factor at period 0.

Steps…3. Estimate error

Record the actual demand Dt+1 for period t+1 and compute the error Et+1 in the forecast for period t+1 as the difference between the forecast and actual demand. The error for period t+1 is stated as follows:

Et+1= Ft+1- Dt+1

Steps…4. Modifying estimates

o Modify estimates of level (Lt+1), trend (Tt+1), and seasonal factor (St+p+1) for a given error Et+1 .

o Desirable modifications can be such that • If the demand is lower than forecast,

estimates are revised downward. • If demand is higher than forecast, estimates

are revised upward.

• Revised estimates in period t+1 are then used to make forecast for period t+2.

• Steps 2, 3, 4 are repeated until all historical data upto period n have been covered.

Moving Average • Used when demand has no observable

trend or seasonality.i.e. Systematic components of

demand=level – Estimate level in period t is given as the

average demand over most recent N periods.

1 1( ... ) /t t t t NL D D D N

Moving average…

• The current forecast of all future periods is same and is based on current estimate of level. The forecast is stated as follows:

• To compute new moving average, simply add the latest observation and drop the oldest one. Revised moving average serves as the next forecast.

1t tF L t n tF L and

1 1 2 2 1( ... ) / ,t t t t N t tL D D D N F L

Simple exponential smoothing

• Appropriate when demand has no observable trend or seasonality.

i.e. Systematic component=level

• Initial estimate of level, L0, is taken to be the average of all historical data.

• The current forecast for all the future periods is equal to the current estimate of level is as follows

n

0 ii 1

1L D

n

1t tF L t n tF L and

Simple exponential smoothing

• After observing demand Dt+1 for period t+1, estimate the level as

is the smoothing constant for the level,0< <1• Revised value of level is a weighted average of

observed value of level Dt+1 and old estimates of level (Lt) in period t.

• Higher value of corresponds to a forecast that is more responsive to recent observation and vice-versa.

t 1n

t 1 t 1 ni 0

1L ( )(1 ) D

n

1 1 (1 )t t tL D L

Trend corrected exponential smoothing (Holt’s method)

• Appropriate when demand is assumed to have a level and a trend in systematic component but no seasonality. i.e. Systematic component of demand=level + trend

– Initial estimation of level and trend by running a linear regression between demand Dt and time period t

Dt=at+b where ‘b’ mesures the estimate of the

demand at period t=0 and is our estimate of initial level L0and

slope ‘a’ measure the rate of change in demand per period and is our intial estimate of trend T0.

Holt’s model• Running a linear regression

between demand and time periods is appropriate since demand has a trend but no seasonality.

• Forecast for future periods is Ft+1=Lt+Tt and Ft+n=Lt +nTt

Holt’s Method… • After observing the demand for

period t, we estimate the level and trend as follows

Lt+1=αDt+1+(1-α)(Lt +Tt)Tt+1=β(Lt+1-Lt)+(1- β)Tt

α is the smoothing constant for the level 0<α<1

β is the smoothing constant for the trend 0< β <1

Trend and seasonality exponential smoothing (winter’s

model)

• Appropriate when systematic component of demand assumed to be have a level, a trend, seasonal factor.

• Systematic component of demand=(level + trend) X seasonal factor– Initiate with the estimation of level and

trend, and seasonal factor.– Forecast for future periods

Ft+1=(Lt +Tt)St and Ft+1= (Lt +lTt)St+1

Winters model

• Lt+1=α(Dt+1/St+1)St +(1-α) (Lt+Tt)

• Tt+1= β(Lt+1 - Lt)St +(1-β)Tt

• St+p+1= γ(Dt+1/Lt+1)St +(1- γ)St+1

α is the smoothing constant for the level 0<α<1β is the smoothing constant for the trend 0<β<1γ is the smoothing constant for the level 0< γ

<1

Forecast error • Every demand has a random component. A

good forecast method should capture the systematic component of the demand but not the random component. The random component manifests itself in the form of forecast error.

• Reasons for the error analysis of forecast. – Use error analysis to determine Whether the current

forecasting method is accurately predicting the systematic component of demand. E.g. If a forecasting method continues to give positive error appropriate measures can be taken by the manager.

– Estimate forecast error because any contingency plan must account for such an error

Measures of forecast error

• Observed error are within historical error estimates, firms can continue to use their current forecasting method.

• In the other case, finding may indicate forecasting method is no more appropriate.

• Forecast error Et for tth time period is given as the difference between the forecast for period t and actual demand.

1 1 1t t tE F D

Mean Squared Error (MSE)

• One measure of forecast error is the mean squared error (MSE) and is given by :

n2

n ti 1

1MSE E

n

Absolute deviation

• Absolute deviation is the absolute value of error in period t

• Mean absolute deviation (MAD) to be average of absolute deviation over all periods

• MAD can be used to estimate the SD of random component assuming it to be normally distributed.

t tA E

n

n tt 1

1MAD A

n

Mean percentage of error

• Is the average absolute error as a percentage of demand

• We can use the sum of forecast errors to evaluate the bias

• The bias will fluctuate around 0 if the error is truly random and not biased one way or the other.

nt

t 1 tn

E100

DMAPE

n

n

n tt 1

bias E

Tracking signal

• The tracking signal is the ratio of the bias and the MAD and is given as follows:

tt

t

biasTS

MAD

Tracking signal

• If the TS at any period is outside the range +6, this signal that the forecast is biased and is either under-forecasting (TS below -6) or over forecasting (TS below -6) .

• In such a case, a firm will choose a new fore casting method.

Specialty Packaging Corporation: A Case Study

Company Profile• Manufacturer of disposable containers• Major customers are from the food industry• Main raw material is Polystyrene resin • Manages inventory through a make-to-

stock policy

Specialty Packaging Corporation: A Case Study

Manufacturing Process• Polystyrene is stored in the form of resin

pallets • Extruder generates rolled sheets, which

may be stored or further processed• Thermo-setting press trims the rolls into

containers

ResinStorage

RollStorage

ExtruderThermo-SettingPress

Fig. Manufacturing Process at SPC

Specialty Packaging Corporation: A Case Study

Market Scenario• Steady growth in demand, which will

stabilize after 2005• Unable to meet the peak demand,

extrusion becomes a bottleneck• Lost sales occur frequently

PlasticPlastic

ClearClear BlackBlack

GroceryStore

GroceryStore BakeryBakery RestaurantsRestaurants Grocery

Store

GroceryStore CateringCatering

Fig. Customer Base

Peak demand in summerPeak demand in fall

Specialty Packaging Corporation: A Case Study

GoalSynergizing marketing and customer feedbacks to improve supply chain performance by adequate demand matching

ObjectiveForecasting quarterly demand during 2003-2005 for both types of containers

Results• Method of forecasting• Likely forecast errors