1. Operations Management Forecasting Chapter 4

2. Examples Predict the next number in the pattern:

3. Examples Predict the next number in the pattern:
a) 3.7, , , , , y = 3.7
b) 2.5, , , , , y = x
c) 5.0, 7.5, 6.0, 4.5, 7.0, 9.5, 8.0, 6.5,
y = x + ci
c1 = 0; c2 = 2; c3 = 0; c4 = -2; etc

4. Outline Types of Forecasts. Eight Steps in the Forecasting System.
Time-Series Forecasting:
Moving Averages.
Exponential Smoothing.
Trend Projection.
Associative Forecasting: Regression.
Monitoring and Controlling Forecasts.
Forecasting in the Service Sector.

5. What is Forecasting? Art and science of predicting future events.
Underlying basis of all business decisions.
Production & Inventory.
Personnel & Facilities.
Focus on forecasting demand.
Sales will be $200 Million!

6. Types of Forecasts by Time Horizon
Short-range forecast: Usually < 3 months.
Job scheduling, worker assignments.
Medium-range forecast: 3 months to 3 years.
Sales & production planning, budgeting.
Long-range forecast: > 3 years.
New product planning, facility location.
At this point, it may be useful to point out the “time horizons” considered by different industries. For example, some colleges and universities look 30 to fifty years ahead, industries engaged in long distance transportation (steam ship, railroad) or provision of basic power (electrical and gas utilities, etc.) also look far ahead (20 to 100 years). Ask them to give examples of industries having much shorter long-range horizons.

7. Short- vs. Long-term Forecasting
Medium & Long range forecasts:
Long range for design of system.
Deal with comprehensive issues.
Support management decisions regarding planning.
Short-term forecasts:
To plan detailed use of system.
Usually use quantitative techniques.
More accurate than longer-term forecasts.
At this point it may be helpful to discuss the actual variables one might wish to forecast in the various time periods.

8. Forecasting During the Life Cycle
Hard to forecast - Often use qualitative models.
Need long-range forecasts.
Introduction
Growth
Maturity
Decline
Sales
Forecasting critical, for future magnitude and growth rate.
Long-range forecasts still important.
Easier to forecast.
Use quantitative models.
Hard to forecast, but forecasting is less important.
Time

9. Eight Steps in Forecasting
Determine the use of the forecast.
Select the item(s) to be forecast.
Determine the time horizon of the forecast.
Select the forecasting model(s).
Gather the data.
Make the forecast.
Validate and implement results.
Monitor forecasts and adjust when needed.
A point to be made here is that one requires a forecasting “plan,” not merely the selection of a particular forecasting methodology.

10. Realities of Forecasting
Assumes future will be like the past (causal factors will be the same).
Forecasts are imperfect.
Forecasts for groups of product are more accurate than forecasts for individual products.
Accuracy decreases with length of forecast.
This slide provides a framework for discussing some of the inherent difficulties in developing reliable forecasts. You may wish to include in this discussion the difficulties posed by attempting forecast in a continuously, and rapidly changing environment where product life-times are measured less often in years and more often in months than ever before.
One might wish to emphasize the inherent difficulties in developing reliable forecasts.

11. Forecasting Approaches
Qualitative Methods
Quantitative Methods
Used when little data or time exist.
New products & technology.
Long time horizon.
Major changes expected.
Involves intuition, experience.
Example: forecasting for e-commerce sales.
Used when situation is ‘stable’ & data exist.
Existing products & current technology.
Major changes not expected.
Involves mathematical techniques.
Example: forecasting sales of color televisions.
This slide distinguishes between Quantitative and Qualitative forecasting. If you accept the argument that the future is one of perpetual, and perhaps significant change, you may wish to ask students to consider whether quantitative forecasting will ever be sufficient in the future - or will we always need to employ qualitative forecasting also. (Consider Tupperware’s ‘jury of executive opinion.’)

12. Overview of Qualitative Methods
Jury of executive opinion.
Combine opinions from executives.
Sales force composite.
Aggregate estimates from salespersons.
Delphi method.
Query experts interatively.
Consumer market survey.
Survey current and potential customers.
This slide outlines several qualitative methods of forecasting. Ask students to give examples of occasions when each might be appropriate.
The next several slides elaborate on these qualitative methods.

13. Jury of Executive Opinion
Seek opinions/estimates from small group of high-level managers working together.
Combines managerial experience with statistical models.
Relatively quick.
‘Group-think’.
Leader may dominate.
Ask your students to consider other potential disadvantages. (Politics?)

14. Sales Force Composite Each salesperson projects their sales.
Aggregate projections at district & national levels.
Sales rep’s know customers.
Must not reward inaccurate forecasts.
May over- or under-forecast to acquire more resources.
Sales
You might ask your students to consider what problems might occur when trying to use this method to predict sales of a potential new product.

15. Delphi Method Iterative group process. 3 types of people:
Decision makers.
Staff.
Respondents.
Reduces ‘group-think’.
Takes time.
Respondents
Staff
(Make forecast)
(Provide input to decision makers)
Decision Makers
(Administer)
You might ask your students to consider whether there are special examples where this technique is required. ( Questions of technology transfer or assessment, for example; or other questions where information from many different disciplines is required.)

16. Consumer Market Survey
How many hours will you use the Internet next week?
Ask customers about purchasing plans.
Relatively simple.
What consumers say, and what they actually do are often different.
You might discuss some of the difficulties with this technique. Certainly there is the issue that what consumers say is often not what they do. There are other problems such as that consumers sometime wish to please the surveyor; and for unusual, future, products, consumers may have a very imperfect frame of reference within which to consider the question.

17. Quantitative Forecasting Methods
Time Series
Associative
Models
Models
A point you may wish to make here is that only in the case of linear regression are we assuming that we know “why” something happened. General time-series models are based exclusively on “what” happened in the past; not at all on “why.” Does operating in a time of drastic change imply limitations on our ability to use time series models?
Moving
Exponential
Trend
Linear
Average
Smoothing
Projection
Regression

18. What is a Time Series? Set of evenly spaced numerical data.
From observing response variable at regular time periods.
Forecast based only on past values.
Assumes that factors influencing past will continue influence in future.
Example:
Year:
Sales:
This and subsequent slide frame a discussion on time series - and introduce the various components.

19. Time Series Components
Trend
Seasonal
Cyclical
Random

20. Product Demand over 4 Years
Demand for product or service
This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?
Year 1
Year 2
Year 3
Year 4

21. Product Demand over 4 Years
Trend component
Seasonal peaks
Random variation
Cyclic component
Actual demand line
Demand for product or service
This slide illustrates a typical demand curve. You might ask students why it is important to know more than simply the actual demand over time. Why, for example, would one wish to be able to break out a “seasonality” factor?
Year 1
Year 2
Year 3
Year 4

22. Trend Component Persistent, overall upward or downward pattern.
Due to population, technology etc.
Several years duration.
Time

23. Seasonal Component Regular pattern of up & down fluctuations.
Due to weather, customs etc.
Occurs within 1 year.
Quarterly, monthly, weekly, etc.
Time
Demand
Summer

24. Cyclical Component Repeating up & down movements.
Due to interactions of factors influencing economy.
Usually 2-10 years duration.
Year
Demand
Cycle

25. Random Component Erratic, unsystematic, ‘residual’ fluctuations.
Due to random variation or unforeseen events.
Union strike
Tornado
Short duration & non-repeating.

26. General Time Series Models
Any value in a time series is a combination of the trend, seasonal, cyclic, and random components.
Multiplicative model: Yi = Ti · Si · Ci · Ri
Additive model: Yi = Ti + Si + Ci + Ri
This slide introduces two general forms of time series model. You might provide examples of when one or the other is most appropriate.

27. Naive Approach
Demand in next period is the same as demand in most recent period.
e.g., If May sales were 48, then June sales will be 48.
Sometimes cost effective & efficient.
Usually not good.
This slide introduces the naïve approach. Subsequent slides introduce other methodologies.

28.  Moving Average Method MA is a series of arithmetic means.
Used if little or no trend.
Used often for smoothing. MA n  
Demand in
previous
periods
At this point, you might discuss the impact of the number of periods included in the calculation. The more periods you include, the closer you come to the overall average; the fewer, the closer you come to the value in the previous period. What is the tradeoff?

29. Moving Average Example
You’re manager of a museum store that sells historical replicas. You want to forecast sales (in thousands) for months 4 and 5 using a 3-period moving average.
Month 1 4 Month Month 3 5 Month 4 ? Month 5 ?

30. Moving Average Forecast
Month
Sales
(given)
Moving Average
(n=3) 1 4 NA 2 6 3 5 ?
(4+6+5)/3=5

31. Moving Average Graph Sales Actual Forecast Month 4 5 3 2 1 6
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
Month

32. Actual Demand for Month 4 = 3
Sales
(given)
Moving Average
(n=3) 1 4 NA 2 6 3 5 ?

33. Moving Average Graph Sales Actual Forecast Month 4 5 3 2 1 6
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
Month

34. Forecast for Month 5 Month Sales (given) Moving Average (n=3) 1 4 NA 26 3 5 ?
(6+5+3)/3=4.667

35. Moving Average Graph Sales Actual Forecast Month 4 5 3 2 1 6
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
Month

36. Actual Demand for Month 5 = 7
Sales
(given)
Moving Average
(n=3) 1 4 NA 2 6 3 5 7 ?
4.667

37. Moving Average Graph Sales Actual Forecast Month 4 5 3 2 1 6
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
Month

38. Forecast for Month 6 Month Sales (given) Moving Average (n=3) 1 4 NA 25 7 ?
4.667
(5+3+7)/3=5

39. Moving Average Graph Sales Actual Forecast Month 4 5 3 2 1 6
This slide shows the resulting forecast. Students might be asked to comment on the useful ness of this forecast.
Month

40. Weighted Moving Average Method
Gives more emphasis to recent data.
Weights decrease for older data.
Weights sum to 1.0.
May be based on intuition.
Sum of digits weights: numerators are consecutive.
3/6, 2/6, 1/6
4/10, 3/10, 2/10, 1/10
This slide introduces the “weighted moving average” method. It is probably most important to discuss choice of the weights.
WMA =
Σ [(Weight for period n) x (Demand in period n)]
ΣWeights

41. Weighted Moving Average: 3/6, 2/6, 1/6
Month
Response Y i
Weighted
Moving Average 1 4 NA 2 6 3 5
31/6 = 5.167 ? ? ?

42. Weighted Moving Average: 3/6, 2/6, 1/6
Month
Response Y i
Weighted
Moving Average 1 4 NA 2 6 3 5
31/6 = 5.167 7 ?
25/6 = 4.167
32/6 = 5.333

43. Moving Average Methods
Increasing n makes forecast:
Less sensitive to changes.
Less sensitive to recent data.
Weights control emphasis on recent data.
Do not forecast trend well.
Require historical data.
These points should have been brought out in the example, but can be summarized here.

44. Moving Average Graph Demand Time Actual
This slide illustrates graphically the results of the example forecast.
Time

45. Moving Average Graph Large n Small n Demand Time Actual
This slide illustrates graphically the results of the example forecast.

46. Weighted Moving Average Graph
Time
Demand
Actual
Large weight on recent data
Small weight on recent data
This slide illustrates graphically the results of the example forecast.

47. Exponential Smoothing Method
Form of weighted moving average.
Weights decline exponentially.
Most recent data weighted most.
Requires smoothing constant ().
Usually ranges from 0.05 to 0.5
Should be chosen to give good forecast.
Involves little record keeping of past data.
This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.

48. Exponential Smoothing Equation
Ft = Ft-1 + (At-1 - Ft-1)
Ft = Forecast value for time t
At-1 = Actual value at time t-1
 = Smoothing constant
Need initial forecast Ft-1 to start.
Could be given or use moving average.
You may wish to discuss several points:
- this is just a moving average wherein every point in included in the forecast, but the weights of the points continuously decrease as they extend further back in time.
- the equation actually used to calculate the forecast is convenient for programming on the computer since it requires as data only the actual and forecast values from the previous time point.
- we need a formal process and criteria for choosing the “best” smoothing constant.

49. Exponential Smoothing Example
You want to forecast product demand using exponential smoothing with  = Suppose in the most recent month (month 6) the forecast was 175 and the actual demand was 180.
Month Month 7 ? Month 8 ? Month 9 ? Month 10 ?
This slide begins an exponential smoothing example.

50. Exponential Smoothing - Month 7
Ft = Ft-1 + α (At-1 - Ft-1)
Month
Actual
Forecast, F t 6
180
(Given) 7 ?
( ) = 8 9 10 11 ( α
= .10)

51. Exponential Smoothing - Month 8
Ft = Ft-1 + α (At-1 - Ft-1)
Actual
Forecast, F t ( α
= .10)
180
(Given)
168
( ) = ?
( ) =
Month 6 7 8 9 10 11

52. Exponential Smoothing Solution
Ft = Ft-1 + α (At-1 - Ft-1)
Actual
Forecast, F t
180
(Given)
168
( ) =
159
( ) = ?
( ) =
Month 6 7 8 9 10 11 ( α
= .10)
This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.

53. Exponential Smoothing Solution
Ft = Ft-1 + α (At-1 - Ft-1)
Actual
Forecast, F t ( α
= .10)
180
(Given)
168
( ) =
159
( ) =
175
( ) =
190 ?
( ) =
Month 6 7 8 9 10 11
This slide illustrates the result of the steps used to make the forecast desired in the example. In the PowerPoint presentation, there are additional slides to illustrate the individual steps.
( ) =

54. Exponential Smoothing Graph
Sales
Actual
190
170
Forecast
150
This slide illustrates graphically the results of the example forecast. 6 7 8 9 10 11
Month

55. Exponential Smoothing Methods
Increasing α makes forecast:
More sensitive to changes.
More sensitive to recent data.
α controls emphasis on recent data.
Do not forecast trend well.
Trend adjusted exponential smoothing - p
These points should have been brought out in the example, but can be summarized here.

56. Exponential Smoothing Graph
Time
Demand
Actual
This slide illustrates graphically the results of the example forecast.

57. Exponential Smoothing Graph
Time
Demand
Actual
Large α
Small α
This slide illustrates graphically the results of the example forecast.

58. Forecast Effects of Smoothing Constant 
Ft =  At (1- )At (1- )2At
Weights
Prior Period 
2 periods ago
(1 - )
3 periods ago
(1 - )2
= 0.10
= 0.90
This slide illustrates the decrease in magnitude of the smoothing constant. In the Power Point presentation, the several previous slides show the steps leading to this slide.
10% 9%
8.1%
90% 9%
0.9%

59. To Use a Forecasting Method
Collect historical data.
Moving Average methods:
Select n = number of periods.
For weighted moving average: Select weights.
Exponential Smoothing: Select .
Selections should produce a good forecast!
This slide introduces the exponential smoothing method of time series forecasting. The following slide contains the equations, and an example follows.

60. A Good Forecast A good method has a small error.
Error = Demand - Forecast
MAD = Mean Absolute Deviation:
Average of absolute values of errors.
MSE = Mean Squared Error:
Average of squared errors.
MAPE = Mean Absolute Percentage Error:
Average of absolute value of percentage errors.
This slide indicates one method of selecting .

61. Forecast Error Equations
Mean Absolute Deviation (MAD)
Mean Squared Error (MSE)
This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

62. Forecast Error Equations
Mean Absolute Percentage Error (MAPE)
This slide illustrates the equations for two measures of forecast error. Students might be asked if there is an occasion when one method might be preferred over the other.

63. Forecast Error Example
Actual F1 F2
F1 error
F2 error 20 19 1 18 2 10 15 -5 13 -3 24 22 2 21 3 20 21 -1 18 2
MAD F1 = 9/4 = F2 = 10/4 = 2.5
MSE F1 = 31/4 = F2 = 26/4 = 6.5
MAPE F1 = = 17.1% F2 = = 15.6%
This slide indicates one method of selecting .

64. Which Forecast is Best? MAD F1 = 9/4 = 2.25 F2 = 10/4 = 2.5
MSE F1 = 31/4 = F2 = 26/4 = 6.5
MAPE F1 = = 17.1% F2 = = 15.6%
This slide indicates one method of selecting .