Forecasting Ppt

1. Time series
Forecasting
in a Supply Chain
Made by
Arpit Garg - CM14205

2. Components of an Observation
1
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 component

4. Time-Series Forecasting Methods
3
• Three ways to calculate the systematic
component
– Multiplicative
S = level x trend x seasonal factor
– Additive
S = level + trend + seasonal factor
– Mixed
S = (level + trend) x seasonal factor

6. Static Methods
4
Estimates of Level, trend and seasonality does not
vary as new demand is observed.
Estimation of parameters on basis of historical data
and then using same values for all future forecasts.
Assumption that demand is mixed i.e.
S = (level + trend) x seasonal factor
S: Systematic component

7. Systematic component  (level trend)seasonal factor
F  [L (t  l)T]S
tl
tl
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
In a static forecasting method, the forecast in Period t for
demand in Period t + l is a product of the level in Period t + l
and the seasonal factor for Period t + l. The level in Period t + l
is the sum of the level in Period 0 (L) and (t + l) times the trend
T. The forecast in Period t for demand in Period t + l is given.

8. Moving Average
5
• 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
Lt = (Dt + Dt-1 + … + Dt–N+1) /N
andFt+1 = Lt Ft+n = Lt
• After observing the demand for period t + 1, revise the
estimates
Lt+1 = (Dt+1 + Dt + … + Dt-N+2) / N, Ft+2 = Lt+1

9. Example
6
• 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?

10. 7
L4 = (D4 + D3 + D2 + D1)/4
= (122 + 114 + 127 + 120)/4 = 120.75
• Forecast demand for Period 5
F5 = L4 = 120.75gallons
• Error if demand in Period 5 = 125 gallons
E5 = F5 – D5 = 125 – 120.75 = 4.25
• Revised demand
L5 = (D5 + D4 + D3 + D2)/4
= (125 + 122 + 114 + 127)/4 = 122

11. Simple Exponential Smoothing
8
• 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

12. Simple Exponential Smoothing
9
t1 t1
L  D (1–)Lt
1
n i1
n
L0  Di
Given data for Periods 1 to n
t1 t
F  L and F  L
tn t
Current forecast
Revised forecast
using smoothing
constant 0 <  < 1
t1
L  n
(1– ) Dt1–n
(1– )t
D1
t–1

n0
Thus

13. 10
4
• Supermarket data
L0  Di / 4 120.75
i1
F  L 120.75
1 0
E1 = F1 – D1 = 120.75 –120 = 0.75
L  D (1–)L1 1 0
 0.11200.9120.75 120.68
ContinuedExample