1. Forecasting Demand in a Supply Chain4.
Forecasting Demand in a Supply Chain

2. Learning Objectives
Understand the role of forecasting for both an enterprise and a supply chain.
Identify the components of a demand forecast.
Forecast demand in a supply chain given historical demand data using time-series and regression methodologies.
Analyze demand forecasts to estimate forecast error.

3. Overview of Forecasting Methods

4. Role of Forecasting in a Supply Chain
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

5. Role of Forecasting in a Supply Chain – Some Examples
Inventory Management
Accurate forecasting determines how much inventory a company must keep at various points along its supply chain
Quality Management
Accurately forecasting customer demand is a key to providing good quality service
Strategic Planning
Successful strategic planning requires accurate forecasts of future products and markets

6. Characteristics of Forecasts
Forecasts are always inaccurate and should thus include both the expected value of the forecast and a measure of forecast error
Long-term forecasts are usually less accurate than short- term forecasts
Aggregate forecasts are usually more accurate than disaggregate forecasts
In general, the farther up the supply chain a company is, the greater is the distortion of information it receives

7. Types of Forecasting Methods
Depend on
Time frame (how far into the future)
Short- to mid-range forecast (immediate future - up to two years)
Long-range forecast
Demand behavior
Causes of behavior

8. Types of Forecasting Methods
Demand Behavior
Trend
a gradual, long-term up or down movement of demand
Random variations
movements in demand that do not follow a pattern
Cycle
an up-and-down repetitive movement in demand
Seasonal pattern
an up-and-down repetitive movement in demand occurring periodically

9. Types of Forecasting Methods
Time
(a) Trend
(d) Trend with seasonal pattern
(c) Seasonal pattern
(b) Cycle
Demand
Random movement
Forms of Forecast Movement

10. Components and Methods
Companies must identify the factors that influence future demand and then ascertain the relationship between these factors and future demand, for example:
Past demand
Lead time of product replenishment
Planned advertising or marketing efforts
Planned price discounts
State of the economy
Actions that competitors have taken
Notes:

11. Components and Methods
Qualitative
Primarily subjective
Rely on judgment
Time Series
Use historical demand only
Best with stable demand
Causal – Regression
Relationship between demand and some other factor
Simulation
Imitate consumer choices that give rise to demand
Notes:

12. 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 component (size and variability)
Forecast error – difference between forecast and actual demand
A good forecast has an error whose size is comparable to the random component

13. Time-Series Methods Use historical data only
Relate the forecast to the time only
Linear Trend Line method
Static Methods
Additive Methods

14. Time-Series Techniques
Best -> Forecast DES: MAPE 8.177

15. Time-Series Forecasting Methods
Assumption: what has occurred in the past will continue to occur in the future
Relate the forecast to only one factor - time
Linear trend line method
Additive methods
Static methods
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

16. Linear Trend Line Method
= b
a = y - b x
where
n = number of periods
x = = mean of the x values
y = = mean of the y values
xy - nxy
x2 - nx2
x n
y
S = level + trend
y = a + bx
where
a = intercept coefficient
b = slope of the line
x = time period (variable coefficient)
y = forecast for demand for period x

17. Linear Trend Line Method
x(PERIOD) y(DEMAND) xy x2
Least Squares Example

18. Linear Trend Line Method
Least Squares Example (cont.)
x = = 6.5
y = = 46.42
b = = =1.72
a = y - bx
= (1.72)(6.5) = 35.2
(12)(6.5)(46.42)
(6.5)2
xy - nxy
x2 - nx2 78 12
557

19. Linear trend line y = 35.2 + 1.72x Forecast for period 13
= units
70 –
60 –
50 –
40 –
30 –
20 –
10 –
0 –
| | | | | | | | | | | | |
Actual
Demand
Period

20. Adaptive Forecasting Methods
The estimates of level, trend, and seasonality are adjusted after each demand observation
Estimates incorporate all new data that are observed.
Methods:
Moving Averages + Weighted Moving Averages
Simple Exponential Smoothing
Trend-Corrected Exponential Smoothing (Holt’s model)
Trend- and Seasonal-Corrected Exponential Smoothing (Winter’s model)

21. Adaptive Forecasting Methods
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

22. 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

23. Moving Average Assumption: 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
Ft+1 = Lt and 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

24. Moving Average Example I
A supermarket has experienced weekly demand of milk of D1 = 120, D2 = 127, D3 = 114, and D4 = 122 gallons over the past four weeks
What is the forecast demand for Period 5 using a 4- period moving average?
What is the forecast error if demand in Period 5 turns out to be 125 gallons?

25. Moving Average Example I
L4 = (D4 + D3 + D2 + D1)/4
= ( )/4 =
Forecast demand for Period 5:
F5 = L4 = gallons
Error if demand in Period 5 = 125 gallons
E5 = F5 – D5 = 125 – = 4.25
Revised demand
L5 = (D5 + D4 + D3 + D2)/4
= ( )/4 = 122

26. Moving Average Example II
3-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
ORDERS
MONTH PER MONTH –
103.3
88.3
95.0
78.3
85.0
105.0
110.0
MOVING
AVERAGE

27. Moving Average Example II
5-month Simple Moving Average
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
Nov -
ORDERS
MONTH PER MONTH –
99.0
85.0
82.0
88.0
95.0
91.0
MOVING
AVERAGE

28. Moving Average Example II
150 –
125 –
100 –
75 –
50 –
25 –
0 –
| | | | | | | | | | |
Jan Feb Mar Apr May June July Aug Sept Oct Nov
Actual
Orders
Month
Smoothing Effects
5-month
3-month

29. Weighted Moving Average
Enhancement: Adjusts the moving average method to more closely reflect data fluctuations
The level in period t is the weighted average demand over the last N periods
Lt = Wt Dt + Wt-1 Dt-1 + … + Wt–N+1 Dt–N+1
Ft+1 = Lt and Ft+n = Lt
Wt is the weight for period t, between 0 and 100 percent
All weights must add up to 1.

30. Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= orders
November Forecast

31. Simple Exponential Smoothing
Assumption: No observable trend or seasonality
Systematic component of demand = level
Initial estimate of level L0 is assumed to be the average of all historical data (this is optional)

32. Simple Exponential Smoothing
Given data for Periods 1 to n
(this step is optional)
Current forecast
Revised forecast using smoothing constant 0 < a < 1
Thus

33. Simple Exponential Smoothing
Use supermarket data to forecast period 5 using a=0.1
E1 = F1 – D1 = –120 = 0.75

34. Simple Exponential Smoothing
If we continue the calculations for the next periods (2, 3 & 4), we obtain F5 = a
0.1
Period Dt Lt Ft Et
120.75 1
120
120.68
0.75 2
127
121.31
-6.33 3
114
120.58
7.31 4
122
120.72
-1.42 5

35. Simple Exponential Smoothing
Effect of Smoothing Constant
0.0  1.0 If = 0.20, then Lt +1 = 0.20Dt Lt
If = 0, then Lt +1 = 0Dt + 1 Lt = Lt Forecast does not reflect recent data
If = 1, then Lt +1 = 1Dt + 0 Lt =Dt Forecast based only on most recent data

36. Simple Exponential Smoothing
Period
Month Dt Lt Ft Et
46.42 1
Jan 37
43.59
9.42 2
Feb 40
42.51
3.59 3
Mar 41
42.06
1.51 4
Apr
40.54
5.06 5
May 45
41.88
-4.46 6
Jun 50
44.32
-8.12 7
Jul 43
43.92
1.32 8
Aug 47
44.84
-3.08 9
Sep 56
48.19
-11.16 10
Oct 52
49.33
-3.81 11
Nov 55
51.03
-5.67 12
Dec 54
51.92
-2.97 13

37. Simple Exponential Smoothing
Period
Month Dt Lt Ft Et
46.42 1
Jan 37
41.71
9.42 2
Feb 40
40.85
1.71 3
Mar 41
40.93
-0.15 4
Apr
38.96
3.93 5
May 45
41.98
-6.04 6
Jun 50
45.99
-8.02 7
Jul 43
44.50
2.99 8
Aug 47
45.75
-2.50 9
Sep 56
50.87
-10.25 10
Oct 52
51.44
-1.13 11
Nov 55
53.22
-3.56 12
Dec 54
53.61
-0.78 13

38. Simple Exponential Smoothing

39. Trend-Corrected Exponential Smoothing (Holt’s Model)
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

40. Trend-Corrected Exponential Smoothing (Holt’s Model)
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 (β is a smoothing constant factor)
Lt+1 = aDt+1 + (1 – a)(Lt + Tt)
Tt+1 = b(Lt+1 – Lt) + (1 – b)Tt

41. Trend-Corrected Exponential Smoothing (Holt’s Model)
MP3 player demand
D1 = 8,415, D2 = 8,732, D3 = 9,014,
D4 = 9,808, D5 = 10,413, D6 = 11,961
a = 0.1, b = 0.2
Using regression analysis (line trend method)
L0 = 7,367 and T0 = 673
Forecast for Period 1
F1 = L0 + T0 = 7, = 8,040

42. Trend-Corrected Exponential Smoothing (Holt’s Model)
Revised estimate
L1 = aD1 + (1 – a)(L0 + T0)
= 0.1 x 8, x 8,040 = 8,078
T1 = b(L1 – L0) + (1 – b)T0
= 0.2 x (8,078 – 7,367) x = 681
With new L1
F2 = L1 + T1 = 8, = 8,759
Continuing
F7 = L6 + T6 = 11, = 12,072

43. Trend-Corrected Exponential Smoothing (Holt’s Model)
Period
Demand L T
Forecast
|Et|
Et2
(|Et|/Dt)%
35.212
1.7238
January 1 37
36.97
1.73
36.94
0.06
0.00
0.17
February 2 40
39.35
1.93
38.70
1.30
1.69
3.25
March 3 41
41.14
1.89
41.28
0.28
0.08
0.68
April 4
40.01
0.98
43.03
6.03
36.31
16.29
May 5 45
43.00
1.58
41.00
4.00
16.04
8.90
June 6 50
47.29
2.40
44.58
5.42
29.37
10.84
July 7 43
46.34
1.39
49.69
6.69
44.71
15.55
August 8 47
47.37
1.28
47.74
0.74
0.54
1.57
September 9 56
52.33
2.39
48.65
7.35
54.01
13.12
October 10 52
53.36
1.98
54.71
2.71
5.21
November 11 55
55.17
55.33
0.33
0.11
0.61
December 12 54
55.55
1.46
57.10
3.10
9.58
5.73
57.01 b
0.300
MAD
3.167 a
0.500
MSE
16.649
MAPE
6.826

44. Trend-Corrected Exponential Smoothing (Holt’s Model)

45. Trend- and Seasonality-Corrected Exponential Smoothing
Appropriate when the systematic component of demand is assumed to have a level, trend, and seasonal factor
Systematic component = (level + trend) x seasonal factor
Ft+1 = (Lt + Tt)St+1 and Ft+l = (Lt + lTt)St+l

46. Trend- and Seasonality-Corrected Exponential Smoothing
After observing demand for period t + 1, revise estimates for level, trend, and seasonal factors
Lt+1 = a(Dt+1/St+1) + (1 – a)(Lt + Tt)
Tt+1 = b(Lt+1 – Lt) + (1 – b)Tt
St+p+1 = g(Dt+1/Lt+1) + (1 – g)St+1
a = smoothing constant for level
b = smoothing constant for trend
g = smoothing constant for seasonal factor

47. Winter’s Model Tahoe Salt Example L0 = 18,439 T0 = 524
S1= 0.47, S2 = 0.68, S3 = 1.17, S4 = 1.67
F1 = (L0 + T0)S1 = (18, )(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
Year, Qtr
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
3,1 8
38,000
3,2 9
12,000
3,3 10
3,4 11
32,000
4,1 12
41,000

48. Winter’s Model
Assume a = 0.1, b = 0.2, g = 0.1; revise estimates for level and trend for period 1 and for seasonal factor for Period 5
L1 = a(D1/S1) + (1 – a)(L0 + T0)
= 0.1 x (8,000/0.47) x (18, ) = 18,769
T1 = b(L1 – L0) + (1 – b)T0
= 0.2 x (18,769 – 18,439) x 524 = 485
S5 = g(D1/L1) + (1 – g)S1
= 0.1 x (8,000/18,769) x 0.47 = 0.47
F2 = (L1 + T1)S2 = (18, )0.68 = 13,093

49. Mean Squared Error MSEt
Winter’s Model
Period t
Demand Dt
Level Lt
Trend Tt
Seasonal Factor St
Forecast Ft
Error Et
Absolute Error At
Mean Squared Error MSEt
MADt
% Error
MAPEt
TSt
18,439
524 1
8,000
18,769
485
0.47
8,913
913
832,857 11
11.41
1.00 2
13,000
19,240
482
0.68
13,093 93
420,727
503
6.06
2.00 3
23,000
19,716
481
1.17
23,076 76
282,393
360
4.15
3.00 4
34,000
20,214
484
1.67
33,730
-270
270
230,049
338
3.31
2.40 5
10,000
20,776
500
9,637
-363
363
210,321
343
3.37
1.31 6
18,000
21,797
604
14,458
-3,542
3,542
2,265,821
876 20
6.09
-3.53 7
22,127
549
26,202
3,202
3,406,502
1,208 14
7.21
0.09 8
38,000
22,683
551
37,898
-102
102
2,981,997
1,070
6.34
0.01 9
12,000
23,479
600
10,855
-1,145
1,145
2,796,424
1,078 10
6.70
-1.06
23,543
493
0.69
16,715
3,715
3,896,961
1,342 29
8.89
1.92
32,000
24,399
565
1.16
27,801
-4,199
4,199
5,145,678
1,602 13
9.27
-1.01 12
41,000
24,921
557
41,731
731
4,761,357
1,529
8.65
-0.58
12,015
17,703 15
31,167 16
45,307
alpha
0.1
Beta
0.2
Gamma

50. Winter’s Model

51. Time Series Models Forecasting Method Applicability Moving average
No trend or seasonality
Simple exponential smoothing
Holt’s model
Trend but no seasonality
Winter’s model
Trend and seasonality

52. Static Forecasting Methods
Static methods assumes that the estimates of level, trend, and seasonality within the systematic component do not vary as new demand is observed
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

53. Static Forecasting Methods - Tahoe Salt Example
Year
Quarter
Period, t
Demand, Dt 1 2
8,000 3
13,000 4
23,000
34,000 5
10,000 6
18,000 7 8
38,000 9
12,000 10 11
32,000 12
41,000

54. Static Forecasting Methods - Tahoe Salt Example
Observe that the demand is seasonal, the lowest occurs every second quarter of each year, and the overall demand pattern repeats every year.

55. Static Forecasting Methods - Tahoe Salt Example
How to estimate level, trend, and seasonality factors?
Basic Steps:
Deseasonalize demand and run the linear trend line method to estimate level and trend
To ensure that each season is given equal weight when deseasonalizing the demand, we must take the average of p consecutive periods of demand.
Estimate seasonal factors
The seasonal factor of a period t is the ratio between the actual demand and the deseasonalized demand

56. Static Forecasting Methods - Tahoe Salt Example
Estimate Level and Trend
Deseasonalized Demand formulas:
Periodicity p = 4, t = 3

57. Static Forecasting Methods - Tahoe Salt Example
Estimate Level and Trend

58. Static Forecasting Methods - Tahoe Salt Example
Estimate Level and Trend
A linear relationship exists between the deseasonalized demand and time based on the change in demand over time

59. Static Forecasting Methods - Tahoe Salt Example
The values of L and T for the deseasonalized demand can be estimated using the linear trend line method:
See also later slides on Linear Regression
Estimate Level and Trend

60. Static Forecasting Methods - Tahoe Salt Example
Estimating Seasonal Factors

61. Static Forecasting Methods - Tahoe Salt Example
Estimating Seasonal Factors
Given r seasonal cycles in the data, for all periods of the form pt+1,1<=i<=p, we should obtain the seasonal factor for each period:
For r = 3 (seasonal cycles) and p=4 (periods) we get:

62. Static Forecasting Methods - Tahoe Salt Example
Forecast for the next 4 periods
Given the level, trend and all seasonal factors calculated earlier, using the following formula we obtain the forecast for the next 4 quarters:

63. Static Forecasting Methods - Tahoe Salt Example

64. Forecast Errors

65. Measures of Forecast Error
Declining alpha

66. Forecast Accuracy Forecast error
difference between forecast and actual demand
MAD
mean absolute deviation
MAPD
mean absolute percent deviation
Cumulative error
Average error or bias

67. Mean Absolute Deviation (MAD)
 Dt - Ft  n
MAD =
where
t = period number
Dt = demand in period t
Ft = forecast for period t
n = total number of periods
 = absolute value

68. PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
MAD Example
– –
PERIOD DEMAND, Dt Ft ( =0.3) (Dt - Ft) |Dt - Ft|
MAD = 53.39/11 = 4.85

69. Other Accuracy Measures
Mean absolute percent deviation (MAPD)
MAPD =
|Dt - Ft|
Dt
Cumulative error
E = et
Average error
E =
et n

70. Forecast Control Tracking signal (Dt - Ft) E MAD Tracking signal = =
monitors the forecast to see if it is biased high or low
1 MAD ≈ 0.8 б
Control limits of 2 to 5 MADs are used most frequently
Tracking signal = =
(Dt - Ft)
MAD E

71. Tracking Signal Values
– – –
DEMAND FORECAST, ERROR E =
PERIOD Dt Ft Dt - Ft (Dt - Ft) MAD –
1.00
2.00
1.62
3.00
4.25
5.01
6.00
7.19
8.18
9.20
10.17
TRACKING
SIGNAL
TS3 = = 2.00
6.10
3.05
Tracking signal for period 3

72. Statistical Control Charts
 =
(Dt - Ft)2
n - 1
Using  we can calculate statistical control limits for the forecast error
Control limits are typically set at  3

73. Statistical Control Charts
Errors
18.39 –
12.24 –
6.12 –
0 –
-6.12 – – –
| | | | | | | | | | | | |
Period
UCL = +3
LCL = -3

74. Selecting the Best Smoothing Constants

75. Selecting the Best Smoothing Constant

76. Selecting the Best Smoothing Constant

77. Application at Tahoe Salt

78. Forecasting Demand at Tahoe Salt
Moving average
Simple exponential smoothing
Trend-corrected exponential smoothing
Trend- and seasonality-corrected exponential smoothing

79. Forecasting Demand at Tahoe Salt

80. Forecasting Demand at Tahoe Salt
Moving average
L12 = 24,500
F13 = F14 = F15 = F16 = L12 = 24,500
s = 1.25 x 9,719 = 12,148

81. Forecasting Demand at Tahoe Salt

82. Forecasting Demand at Tahoe Salt
Single exponential smoothing
L0 = 22,083
L12 = 23,490
F13 = F14 = F15 = F16 = L12 = 23,490
s = 1.25 x 10,208 = 12,761

83. Forecasting Demand at Tahoe Salt

84. Forecasting Demand at Tahoe Salt
Trend-Corrected Exponential Smoothing
L0 = 12,015 and T0 = 1,549
L12 = 30,443 and T12 = 1,541
F13 = L12 + T12 = 30, ,541 = 31,984
F14 = L12 + 2T12 = 30, x 1,541 = 33,525
F15 = L12 + 3T12 = 30, x 1,541 = 35,066
F16 = L12 + 4T12 = 30, x 1,541 = 36,607
s = 1.25 x 8,836 = 11,045

85. Forecasting Demand at Tahoe Salt

86. Forecasting Demand at Tahoe Salt
Trend- and Seasonality-Corrected
L0 = 18,439 T0 =524
S1 = S2 = S3 = S4 = 1.67
L12 = 24,791 T12 = 532
F13 = (L12 + T12)S13 = (24, )0.47 = 11,940
F14 = (L12 + 2T12)S13 = (24, x 532)0.68 = 17,579
F15 = (L12 + 3T12)S13 = (24, x 532)1.17 = 30,930
F16 = (L12 + 4T12)S13 = (24, x 532)1.67 = 44,928
s = 1.25 x 1,469 = 1,836

87. Forecasting Demand at Tahoe Salt

88. Forecasting Demand at Tahoe Salt
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

89. Regression Methods

90. Regression Methods Linear regression Correlation
a mathematical technique that relates a dependent variable to an independent variable in the form of a linear equation
Correlation
a measure of the strength of the relationship between independent and dependent variables

91. Linear Regression Example
(WINS) x (ATTENDANCE) y xy x2

92. Linear Regression Example (cont.)
y = =
b = =
= 4.06
a = y - bx
= (4.06)(6.125) = 49 8
346.9
xy - nxy2
x2 - nx2
(2,167.7) - (8)(6.125)(43.36)
(311) - (8)(6.125)2

93. Linear Regression Example (cont.)
| | | | | | | | | | |
60,000 –
50,000 –
40,000 –
30,000 –
20,000 –
10,000 –
Linear regression line, y = x
Wins, x
Attendance, y
y = (7)
= 46.88, or 46,880
Attendance forecast for 7 wins

94. Correlation and Coefficient of Determination
Correlation, r
Measure of strength of relationship
Varies between and +1.00
Coefficient of determination, r2
Percentage of variation in dependent variable resulting from changes in the independent variable

95. Computing Correlation
n xy -  x y
[n x2 - ( x)2] [n y2 - ( y)2]
r =
Coefficient of determination
r2 = (0.947)2 = 0.897
r =
(8)(2,167.7) - (49)(346.9)
[(8)(311) - (49)2] [(8)(15,224.7) - (346.9)2]
r = 0.947

96. Correlation Coefficienty x
(a) Perfect negative correlation y x
(e) Perfect positive correlation y x
(b) Negative correlation y x
(d) Positive correlation
High
Moderate
Low
Correlation coefficient values
| | | | | | | | |
–1.0 –0.8 –0.6 –0.4 – y x
(c) No correlation

97. Standard Error of the Estimate
A forecast is just a point estimate of a future value
This point is actually the mean of a probability distribution
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
3.25
Regression line,

98. Standard Error of the Estimate
where y = y-value of each data point
yc = computed value of the dependent variable, from the regression equation
n = number of data points

99. Standard Error of the Estimate
Computationally, this equation is considerably easier to use
We use the standard error to set up prediction intervals around the point estimate

100. Standard Error of the Estimate
4.0 –
3.0 –
2.0 –
1.0 –
| | | | | | |
Area payroll (in $ billions)
Nodel’s sales
(in$ millions)
3.25
The standard error of the estimate is $306,000 in sales

101. Regression Analysis with Excel

102. Regression Analysis with Excel
Maosplace.xls – Linear Regression

103. Study the relationship of demand to two or more independent variables
Multiple Regression
Study the relationship of demand to two or more independent variables
y = 0 + 1x1 + 2x2 … + kxk
where
0 = the intercept
1, … , k = parameters for the independent variables
x1, … , xk = independent variables

104. Multiple Regression with Excel

105. Example of Multi-Regression for Demand Forecasting
Day
Temperature
Flyer
Sales 1 63 ✓
152 2 70
168 3 73
180 4 75
235 5 80
236 6 82
225 7 85
268 8 88
330 9 90
314 10 91
306 11 92
374 12
192 13 98
340 14
100
388 15
317 16 87
283 17 84
258 18
310 19
226 20
214 21 76
198
Can we predict customer reactions or the demand for a product (ice cream)?
: Flyer was included in the local daily newspaper

106. Do you see any relationships in these data?
Day
Temperature
Flyer
Sales 1 63
152 2 70
168 3 73
180 4 75
235 5 80
236 6 82
225 7 85
268 8 88
330 9 90
314 10 91
306 11 92
374 12
192 13 98
340 14
100
388 15
317 16 87
283 17 84
258 18
310 19
226 20
214 21 76
198
Two parameters possibly affecting sales: temperature and flyer advertisement in the local daily newspaper
Flyer = 0: No flyer included in the local daily newspaper
Flyer = 1: Otherwise

107. Sales Forecast – Single Regression
Use as predictor variable the temperature, assuming a linear relationship between sales and temperature
Can I use this model to forecast the demand for a day in 2 months from now?
Can I make forecasts outside the above temperature range?
Should I cleanup the historical data (e.g. days with sold outs)?

108. Sales Forecast - Multiple Regression
Can I increase predictability by considering flyer promotions on particular days?
The relationship with TWO explanatory (predictor) variables can be formalized as follows:
Sales(t) = B0 + B1*Temperature(t)+ B2*Flyer(t)

109. Sales Forecast - Multiple Regression
Better predictability than
the original regression (R Square was )
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 21
ANOVA df SS MS F
Significance F
Regression 2
E-12
Residual 18
Total 20
Coefficients
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
E-07
Temperature
E-12
Flyer
Very small chance (<0.05) the independent values are not useful
B0; B1; B2
Significance

110. Sales Forecast - Multiple Regression

111. Application in Practice

112. Demand Forecasting
Extrapolate past demand data into the future using time-series forecasting methods:
Select a preferred forecasting method from a set of techniques
Quantify the forecasting errors to be experienced when forecasting the future
Use regression analysis to build predictive models that will relate targeted customer segments with casual variable such as price, inventory, and so on.

113. The Role of IT in Forecasting
Forecasting module is core supply chain software
Can be used to best determine forecasting methods for the firm and by product categories and markets
Real time updates help firms respond quickly to changes in marketplace
Facilitate demand planning

114. Risk Management
Errors in forecasting can cause significant misallocation of resources in inventory, facilities, transportation, sourcing, pricing, and information management
Common factors are long lead times, seasonality, short product life cycles, few customers and lumpy demand, and when orders placed by intermediaries in a supply chain
Mitigation strategies – increasing the responsiveness of the supply chain and utilizing opportunities for pooling of demand

115. Forecasting In Practice
Collaborate in building forecasts
Share only the data that truly provide value
Be sure to distinguish between demand and sales

116. Basic Approach Understand the objective of forecasting.
Integrate demand planning and forecasting throughout the supply chain.
Identify the major factors that influence the demand forecast.
Forecast at the appropriate level of aggregation.
Establish performance and error measures for the forecast.
Notes:

117. Forecasting In Practice
1. Identify the purpose of forecast
2. Collect historical data
3. Plot data and identify patterns
6. Check forecast accuracy with one or more measures
5. Develop/compute forecast for period of historical data
4. Select a forecast model that seems appropriate for data 7.
Is accuracy of forecast acceptable? No
8b. Select new forecast model or adjust parameters of existing model
Yes
9. Adjust forecast based on additional qualitative information and insight
10. Monitor results and measure forecast accuracy
8a. Forecast over planning horizon

118. Summary of Learning Objectives
Understand the role of forecasting for both an enterprise and a supply chain
Identify the components of a demand forecast
Forecast demand in a supply chain given historical demand data using time-series methodologies
Analyze demand forecasts to estimate forecast error