1. Roberta Russell & Bernard W. Taylor, III
Chapter 11
Forecasting
Operations Management - 5th Edition
Roberta Russell & Bernard W. Taylor, III

2. Forecasting Predicting the Future Qualitative forecast methods
subjective
Quantitative forecast methods
based on mathematical formulas

3. Forecasting and Supply Chain Management
Accurate forecasting determines how much inventory a company must keep at various points along its supply chain
Continuous replenishment
supplier and customer share continuously updated data
typically managed by the supplier
reduces inventory for the company
speeds customer delivery
Variations of continuous replenishment
quick response
JIT (just-in-time)
VMI (vendor-managed inventory)
stockless inventory

4. Forecasting and TQM
Accurate forecasting customer demand is a key to providing good quality service
Continuous replenishment and JIT complement TQM
eliminates the need for buffer inventory, which, in turn, reduces both waste and inventory costs, a primary goal of TQM
smoothes process flow with no defective items
meets expectations about on-time delivery, which is perceived as good-quality service

5. Types of Forecasting Methods
Depend on
time frame
demand behavior
causes of behavior

6. Time Frame Indicates how far into the future is forecast
Short- to mid-range forecast
typically encompasses the immediate future
daily up to two years
Long-range forecast
usually encompasses a period of time longer than two years

7. Demand Behavior Trend Random variations Cycle Seasonal pattern
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

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

9. Forecasting Methods Qualitative Time series Regression methods
use management judgment, expertise, and opinion to predict future demand
Time series
statistical techniques that use historical demand data to predict future demand
Regression methods
attempt to develop a mathematical relationship between demand and factors that cause its behavior

10. Qualitative Methods
Management, marketing, purchasing, and engineering are sources for internal qualitative forecasts
Delphi method
involves soliciting forecasts about technological advances from experts

11. Is accuracy of forecast acceptable?
Forecasting Process
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

12. Time Series
Assume that what has occurred in the past will continue to occur in the future
Relate the forecast to only one factor - time
Include
moving average
exponential smoothing
linear trend line

13. Moving Average Naive forecast Simple moving average
demand the current period is used as next period’s forecast
Simple moving average
stable demand with no pronounced behavioral patterns
Weighted moving average
weights are assigned to most recent data

14. Moving Average: Naïve Approach
Jan 120
Feb 90
Mar 100
Apr 75
May 110
June 50
July 75
Aug 130
Sept 110
Oct 90
ORDERS
MONTH PER MONTH -
120 90
100 75
110 50
130
Nov
FORECAST

15. n = number of periods in the moving average
Simple Moving Average
MAn = n
i = 1  Di
where
n = number of periods in the moving average
Di = demand in period i

16. 3-month Simple Moving Average
MA3 = 3
i = 1  Di =
= 110 orders
for Nov
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

17. 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
MA5 = 5
i = 1  Di =
= 91 orders
for Nov

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

19. Weighted Moving Average
WMAn =
i = 1 
Wi Di
where
Wi = the weight for period i, between 0 and 100 percent
 Wi = 1.00
Adjusts moving average method to more closely reflect data fluctuations

20. Weighted Moving Average Example
MONTH WEIGHT DATA
August 17% 130
September 33% 110
October 50% 90
WMA3 = 3
i = 1 
Wi Di
= (0.50)(90) + (0.33)(110) + (0.17)(130)
= orders
November Forecast

21. Exponential Smoothing
Averaging method
Weights most recent data more strongly
Reacts more to recent changes
Widely used, accurate method

22. Exponential Smoothing (cont.)
Ft +1 = Dt + (1 - )Ft
where:
Ft +1 = forecast for next period
Dt = actual demand for present period
Ft = previously determined forecast for present period
= weighting factor, smoothing constant

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

24. Exponential Smoothing (α=0.10)
PERIOD MONTH DEMAND
1 Jan 120
2 Feb 90
3 Mar 100
4 Apr 75
5 May 110
6 Jun 50
7 Jul 75
8 Aug 130
9 Sep 110
10 Oct 90
F2 = D1 + (1 - )F1
= (0.10)(120) + (0.90)(120)
= 120
F3 = D2 + (1 - )F2
= (0.10)(90) + (0.90)(120)
= 117
F11 = D10 + (1 - )F10
= (0.10)(90) + (0.90)(105.34) =

25. 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

26. 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

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

28. 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

29. Linear Regression y = a + bx a = y - b x b = xy - nxy x2 - nx2
where
a = intercept
b = slope of the line
x = = mean of the x data
y = = mean of the y data
xy - nxy
x2 - nx2
x n
y

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

31. 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

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

33. 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

34. 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