DEM A N D FO RECA ST I N G I N A S U P P LY

CH A I N
SRI LANKA – PRICE
INCREASE DURING
COVID-19

Prices of essential commodities —

including rice, dhal, bread, sugar,
vegetables, fish — have risen several
times during the pandemic, and more
rapidly in recent weeks. Local
varieties of rice — a staple item —
currently cost about LKR 120 (₹44) a
kg, while common vegetables such as
onion and potato are priced over
LKR 200 (₹73) per kg. A kilo of fish
costs nearly LKR 700 (₹255).

Survey?
 T H I S S C H E M E W A S F I R S T
S T A R T E D O N 1 4 J A N U A R Y
1 9 4 5 , D U R I N G T H E S E C O N D
W O R L D W A R , A N D W A S
L A U N C H E D I N T H E C U R R E N T
F O R M I N J U N E 1 9 4 7 . T H E
I N T R O D U C T I O N O F R A T I O N I N G
I N I N D I A D A T E S B A C K T O
T H E 1 9 4 0 S B E N G A L F A M I N E .
T H I S R A T I O N I N G S Y S T E M W A S
R E V I V E D I N T H E W A K E O F
A C U T E F O O D S H O R T A G E
D U R I N G T H E E A R L Y 1 9 6 0 S ,
B E F O R E T H E G R E E N
R E V O L U T I O N
P RO C U R E M E N T
STOCKS
COST

FCI’s “economic cost” of procuring, handling, transporting,

storing and distributing grains was estimated at Rs 39.99
per kg for rice and Rs 27.40/kg for wheat in 2020-21.

Carrying cost of buffer”, pegged at Rs 5.40/kg in 2020-21

ROLE OF FORECASTING IN A
S U P P LY C H A I N

• The basis for all planning decisions in a supply chain

• Used for both push and pull processes
Production scheduling, inventory, aggregate planning
Sales force allocation, promotions, new production introduction
Plant/equipment investment, budgetary planning
Workforce planning, hiring, layoffs
• All of these decisions are interrelated
CHARACTERISTICS OF FORECASTS

1. Forecasts are always inaccurate and should thus include both

the expected value of the forecast and a measure of forecast
error
2. Long-term forecasts are usually less accurate than short-term
forecasts
3. Aggregate forecasts are usually more accurate than
disaggregate forecasts
4. In general, the farther up the supply chain a company is, the
greater is the distortion of information it receives
COMPONENTS AND METHODS (1 OF
2)

• Companies must identify the factors that influence future demand

and then ascertain the relationship between these factors and
future demand
Past demand
Lead time of product replenishment
Planned advertising or marketing efforts
Planned price discounts
State of the economy
Actions that competitors have taken
 Components and Methods (2 of 2)

1. Qualitative
– Primarily subjective
– Rely on judgment

2. Time Series
Use historical demand only
Best with stable demand

3. Causal
Relationship between demand and some other factor

4. Simulation
Imitate consumer choices that give rise to demand
Components of An Observation
Observed demand ( O) = systematic component ( S)
+ random component ( R)
• Systematic component – expected value of demand
– Level (current deseasonalized demand)
– Trend (growth or decline in demand)
– Seasonality (predictable seasonal fluctuation)
• Random component – part of forecast that deviates from
systematic part
• Forecast error – difference between forecast and actual
demand
F I V E I M P O RTA N T P O I N T S I N T H E
FORECASTING PROCESS

1. Understand the objective of forecasting.

2. Integrate demand planning and forecasting throughout the
supply chain.
3. Identify the major factors that influence the demand forecast.
4. Forecast at the appropriate level of aggregation.
5. Establish performance and error measures for the forecast.
TIME-SERIES FORECASTING
METHODS
• Three ways to calculate the systematic component
Multiplicative
S = level × trend × seasonal factor
Additive
S = level + trend + seasonal factor
Mixed
S = (level + trend) × seasonal factor
Static Methods
Systematic component = (level+trend)×seasonal factor

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

Where
L = estimate of level at t = 0
T = estimate of trend
St = estimate of seasonal factor for Period t
Dt = actual demand observed in Period t
Ft = forecast of demand for Period t
TA H O E S A LT (1 OF 5)

Table 7-1 Quarterly Demand for Tahoe Salt

Year Quarter Period, t Demand, Dt

1 2 1 8,000
1 3 2 13,000
1 4 3 23,000
2 1 4 34,000
2 2 5 10,000
2 3 6 18,000
2 4 7 23,000
TA H O E S A LT (2 OF 5)

Table 7-1 [continued]

Year Quarter Period, t Demand, Dt

3 1 8 38,000
3 2 9 12,000
3 3 10 13,000
3 4 11 32,000
4 1 12 41,000
Ta h o e S a l t (3 of 5)

Figure 7-1 Quarterly Demand at Tahoe Salt

1. Deseasonalize demand and run linear regression to estimate
level and trend.
2. Estimate seasonal factors.
E S T I M AT E L E V E L A N D T R E N D (1 OF
2)

Periodicity p = 4, t = 3

 p
t –1+   
 2

 Dt –  p  + Dt + p  +  2Di 
 2 2 p
i =t +1–   
  2

 (2 p ) for p even
Dt = 
 ( p –1) 
 t +  2 
 

  ( p –1) 
Di
 i =t – 
 2 


 p for p odd
E S T I M AT E L E V E L A N D T R E N D (2 OF
2)

 p
t –1+   
 
 
2

Dt –  p  + Dt + p  +  p 2Di 

  2  2  
i =t +1–  
2

Dt =
(2 p )
4
D1 + D5 +  2Di
= i =2
8
TA H O E S A LT (4 OF 5)

Figure 7-2 Excel Workbook with Deseasonalized Demand for Tahoe Salt
Ta h o e S a l t (5 of 5)

F igure 7-3 Deseasonalized Demand for Tahoe Salt

A linear relationship exists between the deseasonalized demand and time based
on the change in demand over time

Dt = L + Tt
E S T I M AT I N G S E A S O N A L F A C T O R S
(1 OF 3)

Di
St =
Dt

Figure 7-4 Deseasonalized Demand and Seasonal Factors for Tahoe Salt
E S T I M AT I N G S E A S O N A L F A C T O R S
(2 OF 3)

r –1

S
j =0
jp + i

Si =
r

(S1 + S5 + S9 ) (0.42 + 0.47 + 0.52)

S1 = = = 0.47
3 3
(S + S6 + S10 ) (0.67 + 0.83 + 0.55)
S2 = 2 = = 0.68
3 3
(S + S7 + S11 ) (1.15 + 1.04 + 1.32)
S3 = 3 = = 1.17
3 3
(S + S8 + S12 ) (1.66 + 1.68 + 1.66)
S4 = 4 = = 1.67
3 3
E S T I M AT I N G S E A S O N A L F A C T O R S
(3 OF 3)

F13 = (L + 13T )S13 = (18,439 + 13  524)0.47 = 11,868

F14 = (L + 14T )S14 = (18,439 + 14  524)0.68 = 17,527
F15 = (L + 15T )S15 = (18,439 + 15  524)1.17 = 30,770
F16 = (L + 16T )S16 = (18,439 + 16  524)1.67 = 44,794
ADAPTIVE FORECASTING (1 OF 2)

• The estimates of level, trend, and seasonality are

updated after each demand observation
• Estimates incorporate all new data that are observed
ADAPTIVE FORECASTING (2 OF 2)

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

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 for Period t
Ft = forecast of demand for Period t (made
Period t – 1 or earlier)
Dt = actual demand observed in Period t
Et = Ft – Dt = forecast error in Period t
STEPS IN ADAPTIVE
FORECASTING
• Initialize
Compute initial estimates of level ( L0), trend (T0), and
seasonal factors ( S1,…,Sp)
• Forecast
Forecast demand for period t + 1
• Estimate error
Compute error Et+1 = Ft+1 – Dt+1
• Modify estimates
Modify the estimates of level ( Lt+1), trend (Tt+1), and
seasonal factor ( St+p+1), given the error Et+1
M o v i n g Av e r a g e
• Used when demand has no observable trend or seasonality
Systematic component of demand = level
• The level in period t is the average demand over the last N periods

(Dt + Dt −1 + … + Dt – N +1 )
Lt =
N
Ft +1 = Lt and Ft + n = Lt

• After observing the demand for period t + 1, revise the estimates

(Dt +1 + Dt + … + Dt −N + 2 )
Lt +1 = , Ft + 2 = Lt +1
N
M O V I N G AV E R A G E E X A M P L E (1 OF
2)

• A supermarket has experienced weekly demand of milk

of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons
over the past four weeks
– Forecast demand for Period 5 using a four-period
moving average
– What is the forecast error if demand in Period 5
turns out to be 125 gallons?
M O V I N G AV E R A G E E X A M P L E (2 OF
2)

(D4 + D3 + D2 + D1 )
L4 =
4

=
(122 + 114 + 127 + 120 ) = 120.75
4

• Forecast demand for Period 5

F5 = L4 = 120.75 gallons
• Error if demand in Period 5 = 125 gallons
E5 = F5 – D5 = 120.75 – 125 = – 4.25
– Revised demand

(D5 + D4 + D3 + D2 )
L5 =
4

=
(125 + 122 + 114 + 127 ) = 122
4
SIMPLE EXPONENTIAL
SMOOTHING (1 OF 3)

• Used when demand has no observable trend or seasonality

Systematic component of demand = level
• Initial estimate of level, L0, assumed to be the average of all
historical data
SIMPLE EXPONENTIAL
SMOOTHING (2 OF 3)
Given data for Periods 1 to n 1 n
L0 =  Di
n i =1

Current forecast Ft +1 = Lt and Ft + n = Lt

Revised forecast using

smoothing constant (0 Lt +1 =  Dt +1 + (1 –  )Lt
< α < 1)

t –1
Thus
Lt +1 =   (1 –  )n Dt +1– n + (1 –  )t D1
n =0
Simple Exponential Smoothing (3 of 3)

• Supermarket data
4
Di
L0 =  = 120.75
i =1 4

F1 = L0 = 120.75
E1 = F1−D1 = 120.75−120 = 0.75
L1 = αD1+(1−α)L0
= 0.1×120+0.9 ×120.75=120.68
TREND-CORRECTED EXPONENTIAL
S M O O T H I N G ( H O LT ’ S M O D E L ) ( 1 O F
4)

• Appropriate when the demand is assumed to have a level and

trend in the systematic component of demand but no
seasonality
Systematic component of demand = level + trend
 Tr e n d - C o r r e c t e d E x p o n e n t i a l S m o o t h i n
(Holt’s Model) (2 of 4)
• Obtain initial estimate of level and trend by running a linear regression

Dt = at + b
T0 = a, L0 = b

• In Period t, the forecast for future periods is

Ft+1 = Lt + Tt and Ft+n = Lt + nTt

• Revised estimates for Period t

Lt +1 =  Dt +1 + (1− α ) ( Lt + Tt )
Tt +1 =  ( Lt +1 − Lt ) + (1−  )Tt
Tr e n d - C o r r e c t e d E x p o n e n t i a l S m o o t h i n g
(Holt’s Model) (3 of 4)
• Smartphone player demand

D1 = 8,415, D2 = 8,732, D3 = 9,014, D4 = 9,808,D5 = 10,413,

D6 = 11,961, α = 0.1, β = 0.2

• Using regression analysis

L0 = 7,367 and T0 = 673

• Forecast for Period 1

F1 = L0 + T0 = 7,367 + 673 = 8,040

• Period 1 error

E1 = F1 – D1 = 8,040 – 8,415 = –375

 Tr e n d - C o r r e c t e d E x p o n e n t i a l S m o o t h i n
(Holt’s Model) (4 of 4)
• Revised estimate
L1 =  D1 + (1−  ) ( L0 + T0 )
= 0.1 8,415 + 0.9  8,040 = 8,078
T1 =  ( L1 − L0 ) + (1−  )T0
= 0.2  ( 8,078 − 7,367 ) + 0.8  673 = 681

• With new L1

F2 = L1 + T1 = 8,078 + 681 = 8,759

• Continuing

F7 = L6 + T6 = 11,399 + 673 = 12,072

Tr e n d - a n d S e a s o n a l i t y - C o r r e c t e d
Exponential Smoothing (1 of 2)
• Appropriate when the systematic component of demand has a
level, trend, and seasonal factor

Systematic component = (level + trend) × seasonal factor

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

Tr e n d - a n d S e a s o n a l i t y - C o r r e c t e d
Exponential Smoothing (2 of 2)

• After observing demand for period t + 1, revise estimates

for level, trend, and seasonal factors
D 
Lt +1 =   t +1  + (1−  ) ( Lt + Tt )
 St +1 
Tt +1 =  ( Lt +1 − Lt ) + (1−  )Tt
 Dt +1 
St + p+1 =    + (1−  ) St +1
 Lt +1 
α = smoothing constant for level
β = smoothing constant for trend
γ = smoothing constant for seasonal factor
WINTER’S MODEL (1 OF 3)

L0 = 18,439 T0 = 524
S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67
F1 = (L0 + T0)S1 = (18,439 + 524)(0.47) = 8,913
The observed demand for Period 1 = D1 = 8,000
Forecast error for Period 1
= E1 = F1 – D1
= 8,913 – 8,000 = 913
WINTER’S MODEL (2 OF 3)

• Assume α = 0.1, β = 0.2, γ = 0.1; revise estimates for level and

trend for period 1 and for seasonal factor for Period 5
D 
L1 =   1  + (1−  ) ( L0 + T0 )
 S1 
  8,000  
= 0.1    + 0.9  (18,439 + 524 )  = 18,769
  0.47 
T1 =  ( L1 − L0 ) + (1− β )T0
= 0.2  (18,769 − 18,439 )  + ( 0.8  524 ) = 485
D 
S5 =   1  + (1−  ) S1
 L1 
  8,000  
= 0.1    + ( 0.9  0.47 ) = 0.47
  18,769 
WINTER’S MODEL (3 OF 3)

Forecast demand for Period 2

F2 = (L1 + T1)S2 = (18,769 + 485)(0.68) = 13,093
TIME SERIES MODELS

Forecasting Method Applicability

Moving average No trend or seasonality
Simple exponential smoothing No trend or seasonality
Holt’s model Trend but no seasonality
Winter’s model Trend and seasonality
S U M M A RY O F L E A R N I N G
OBJECTIVE 3

Time-series methods for forecasting are categorized as static or

adaptive. In static methods, the estimates of parameters are not
updated as new demand is observed. Static methods include
regression. In adaptive methods, the estimates are updated each
time a new demand is observed. Adaptive methods include moving
averages, simple exponential smoothing, Holt’s model, and Winter’s
model. Moving averages and simple exponential smoothing are best
used when demand displays neither trend nor seasonality. Holt’s
model is best when demand displays a trend but no seasonality.
Winter’s model is appropriate when demand displays both trend and
seasonality.
Measures of Forecast Error (1
of 2)

• Forecast errors contain valuable information and must

be analyzed for two reasons:
1. Managers use error analysis to determine whether the
current forecasting method is predicting the systematic
component of demand accurately
2. All contingency plans must account for forecast error
MEASURES OF FORECAST ERROR
(2 OF 2)

Et = Ft – Dt n
Et
1 n
 Dt
100

t =1
MSEn = Et2 MAPEn =
n t =1 n

At = Et
1 n
MADn =  At biasn =  Et
n t =1 t =1

 = 1.25MAD TSt
biast
MADt
 t –1 1– 
Declining alpha t = =
 +  t –1 1 –  t
S U M M A RY O F L E A R N I N G
OBJECTIVE 4
Forecast error measures the random component of
demand. This measure is important because it reveals
how inaccurate a forecast is likely to be and what
contingencies a firm may have to plan for. The M SE, MA
D, and MAPE are used to estimate the size of the fore-
cast error. The bias and TS are used to estimate if the
forecast consistently over- or under- forecasts or if
demand has deviated significantly from historical norms.
SELECTING THE BEST SMOOTHING
C O N S TA N T ( 1 O F 2 )

Figure 7-5 Selecting Smoothing Constant by Minimizing M SE

SELECTING THE BEST SMOOTHING
C O N S TA N T ( 2 O F 2 )

Figure 7-6 Selecting Smoothing Constant by Minimizing M AD

F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 1 O F 1 0 )
• Moving average
• Simple exponential smoothing
• Trend-corrected exponential smoothing
• Trend- and seasonality-corrected exponential smoothing
F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 2 O F 1 0 )

Figure 7-7 Tahoe Salt Forecasts Using Four-Period Moving Average

F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 3 O F 1 0 )

Moving average
L12 = 24,500
F13 = F14 = F15 = F16 = L12 = 24,500
σ = 1.25 × 9,719 = 12,148
F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 4 O F 1 0 )

Figure 7-8 Tahoe Salt Forecasts Using Simple Exponential Smoothing

F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 5 O F 1 0 )

Simple exponential smoothing

α = 0.1
L0 = 22,083
L12 = 23,490
F13 = F14 = F15 = F16 = L12 = 23,490
σ = 1.25 × 10,208 = 12,761
F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 6 O F 1 0 )

Figure 7-9 Trend-Corrected Exponential Smoothing

F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 7 O F 1 0 )
Trend-Corrected Exponential Smoothing
L0 = 12,015 and T0 = 1,549
L12 = 30,443 and T12 = 1,541
F13 = L12 + T12 = 30,443 + 1,541 = 31,984
F14 = L12 + 2T12 = 30,443 + 2 × 1,541 = 33,525
F15 = L12 + 3T12 = 30,443 + 3 × 1,541 = 35,066
F16 = L12 + 4T12 = 30,443 + 4 × 1,541 = 36,607
σ = 1.25 × 8,836 = 11,045
F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 8 O F 1 0 )

Figure 7-10 Trend- and Seasonality-Corrected Exponential Smoothing

F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 9 O F 1 0 )
Trend- and Seasonality-Corrected
L0 = 18,439 T0 =524
L12 = 24,791 T12 = 532
S1 = 0.47 S2 = 0.68 S3 = 1.17 S4 = 1.67
F13 = (L12 + T12)S13 = (24,791 + 532)0.47 = 11,902
F14 = (L12 + 2T12)S13 = (24,791 + 2 × 532)0.68 = 17,581
F15 = (L12 + 3T12)S13 = (24,791 + 3 × 532)1.17 = 30,873
F16 = (L12 + 4T12)S13 = (24,791 + 4 × 532)1.67 = 44,955
σ = 1.25 × 1,469 = 1,836
F O R E C A S T I N G D E M A N D AT TA H O E
S A LT ( 1 0 O F 1 0 )
Table 7-2 Error Estimates for Tahoe Salt Forecasting

Forecasting Method MAD MAPE (% ) TS Range

Four-period moving average 9,719 49 –1.52 to 2.21

Simple exponential smoothing 10,208 59 –1.38 to 2.15

Holt’s model 8,836 52 –2.15 to 2.00

Winter’s model 1,469 8 –2.74 to 4.00
T H E R O L E O F S O F T WA R E T O O L S
IN FORECASTING

• Software is important
Large amounts of data
Frequency of forecasts
Importance of high-quality results
• Can forecast demand by products and markets
• Real time updates help firms respond quickly to
changes in marketplace
• Facilitates demand planning
S U M M A RY O F L E A R N I N G
OBJECTIVE 5

Given the repetitive nature of time-series forecasting methods, they

can easily be modeled in Microsoft Excel with simple formulae that
are copied across rows or columns. For regular forecasting at
companies, however, it may be more effective to select among a
wide variety of software packages available today.