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Chapter 3: Workload Assessment (Forecasting)

TRUE/FALSE

1. It is possible to forecast the number of patients in a hospital but such demand analysis cannot be used to determine how to set the agenda for the entire organization. This is especially true of planning work schedules.

ANS: F REF: Introduction to Chapter 3

2. A good forecast strategy is not being reactive to what must happen. Instead, an effort is made to modify the forecast. This is known as proactive planning.

ANS: T REF: Introduction to Chapter 3

3. Forecasting is not a term readily associated with gambling games for which the probabilities of specific events are established. Ask the manager of Wynn Las Vegas or the Venetian-Macao about next year’s occupancy. The manager will call upon a forecast sales demand volume.

ANS: T REF: 3.1

4. In every sales forecasting situation, volatility of demand will determine if a good forecast can be made. A good forecast is usually based upon finding a pattern that is likely to persist.

ANS: T REF: 3.1

5. Sales patterns are becoming more stable with increasing information being available.

ANS: F REF: 3.1

6. Strategists are often less affected by forecasts than one might suppose. The reason is summed up in number 2 above. We might also say that brilliant strategists create the future.

ANS: T REF: Open to discussion

7. As new products move through life cycle stages, it becomes evident why P/OM must be comfortable with forecasting future developments.

ANS: T REF: 3.9.3 and Figure 3.10

8. Strategies for the introduction of new products and for replacement of existing products must be formulated with the fact in mind that operations managers’ time and talents are limited resources.

ANS: T REF: Open for discussion

9. After market growth stops, share equilibrium occurs. Finally, the product starts to lose its demand volume and it may either be restaged or terminated. Nothing should be done until the fall off is significant. Then, the old is withdrawn to be replaced by a new version.

ANS: F REF: 3.9.2

10. The cycle of the new product is similar to that of the one that is replaced in that it goes through introduction, growth, maturation, and decline.

ANS: T REF: 3.9.2 and Figure 3.10

11. Marketing is responsible for the intelligent management of the production transformation process which changes in various ways according to the life cycle stage.

ANS: F REF: 3.9

12. The trick (to forecasting life cycle stages) is to estimate how fast demand will increase overtime, and for how long a period growth will continue.

ANS: T REF: 3.9.3

13. Businesspeople often use their sense of what is happening to reach decisions that might be better made if someone had kept a record of what had taken place already. In other words, often some empirical analysis can be helpful.

ANS: T REF: 3.1

14. Stable patterns that persist for a short period of time make company forecasters confident that a credible job of forecasting can be done.

ANS: F REF: 3.1

15. In the time series analysis, external causes are brought into the picture.

ANS: F REF: 3.2

16. Many decisions require believable forecasts before they can be made.

ANS: T REF: 3.2

17. The historical forecast is not based on the assumption that what happened last year will happen again.

ANS: F REF: 3.3.4

18. Historical forecasting is never applied to daily or weekly sales; only on a semiannual, quarterly, or monthly basis.

ANS: F REF: 3.3.4

19. Forecasting cannot be done without mathematics.

ANS: F REF: 3.1

20. Random variations occur in time series. The various causes of such random fluctuations are often logical but not predictable. Nevertheless, forecasts can be prepared even when there is an associated trend and/or seasonal variability.

ANS: T REF: 3.2

21. How far to go back in calculating moving averages depends on the recency of events that tend to determine the future. “Very recent” requires including more values; “not so recent” requires using only a few values.

ANS: F REF: 3.3.1

22. When the direction and magnitude of the trend is inconclusive and the pattern is not consistent, then the fewer the number of periods in the set, the better.

ANS: F REF: 3.3.1

23. With moving averages, reacting to fluctuations rapidly—which means tracking them faster—is less likely to occur if the number of values in the average (n) is large.

ANS: T REF: 3.3.1

24. In the weighted moving average, the biggest weights are assigned to the most recent events when there is a continuing trend.

ANS: T REF: 3.3.2

25. Weighted moving averages cannot track strong trends more accurately than unweighted moving averages.

ANS: F REF: 3.3.2

26. When using regression analysis the simplest assumption that is generally made first is that the relationship between the correlate pairs is nonlinear.

ANS: F REF: 3.4

27. During linear regression analysis, when outcomes are to be forecast, the knowledge that one time series leads another is valuable information. That lead in time may be due to a causal link.

ANS: T REF: 3.5

28. A causal factor common to both x and y which operates as an unknown link may be responsible for whatever relationship is found.

ANS: T REF: 3.5

29. When considering a regression analysis, if nonlinear relations appear to exist, there are strong methods for dealing with such analyses.

ANS: T REF: 3.4

30. Usually, better forecasts can be obtained if both data and experience are pooled.

ANS: T REF: 3.8

31. When actual demand results are known, the various forecasting methods are evaluated again, and the one that is least successful is chosen to make the prediction for the next period.

ANS: F REF: 3.8

32. Formal methods can be used to evaluate how well different forecasting techniques are doing.

ANS: T REF: 3.6

33. Not all forecasting errors are based on comparing the actual demand for a time period with the forecast demand for that same period.

ANS: F REF: 3.6

34. The only forecasting error that can occur is when actual demand is greater than forecasting.

ANS: F REF: 3.6

35. Absolute measures are signified by open brackets (see below) which mean that positive and negative errors are not treated the same way. [pic]

ANS: F REF: 3.6

36. A most commonly used method calculates Mean Absolute Deviation (MAD) of the error terms. To determine MAD, divide the sum of the absolute measures of the errors by the number of observations.

ANS: T REF: 3.6

37. MAD is simply the sum of all the error terms and is useful when overestimation errors cancel out underestimation errors.

ANS: F REF: 3.6

38. The Delphi Method is a forecasting method that relies on expert estimation of future events.

ANS: T REF: 3.7

39. The Delphi manager is anonymous since that person does all the calculations and the promotions. The experts are known and their forecasts are promoted by the Delphi manager to bring convergence to the group as rapidly as possible.

ANS: F REF: 3.7

40. MAD is often called a conservative estimate of error. In fact, absolute measures of error count over and under-errors as errors to be added together. Without the absolute, plus errors cancel minus errors.

ANS: T REF: 3-6

41. Strategic thinking and planning to realize objectives involves teamwork.

ANS: T REF: Summary

42. Throughout the company, the planning function marches to the drumbeat of product life cycle stages. Operations managers need to be aware of timing and the stages required by development schedules.

ANS: T REF: 3.9

43. Active participation of P/OM is characterized by doing just what is asked and nothing more. P/OM lives by conformance to quality standards for its products. Why should that criterion be different for organizational performance?

ANS: F REF: Open for discussion

44. If a moving average trend is gradual, either up or down, and if fluctuations around the average are common, then having fewer periods of time in the set is better than having too many.

ANS: F REF: 3.3.1

45. To make forecasts more responsive to most recent actual occurrences, use weighted moving averages.

ANS: T REF: 3.3.2

46. The coefficient of determination is the square of the correlation coefficient.

ANS: T REF: 3.5

47. Time series data also can reflect erratic bursts called impulses.

ANS: T REF: 3.2

48. Increased competition has led to higher levels of market volatility. Nevertheless, for most product categories, there is still opportunity to benefit from mature product life cycle stages.

ANS: T REF: 3.9.4

49. To compete in the global market, companies must deal with different time zones around the world.

ANS: T REF: Open for discussion

50. Syzygy is a Greek word for conjunction. In business, various forces sometimes line up in this way causing larger than normal amplitudes in time series values. We have gotten so used to the term “a perfect storm” that we had better be prepared to discuss forecasting it and dealing with it.

ANS: T REF: Open for discussion

51. The terms strategy and tactics have military origins. Both terms are deeply involved with forecasting.

ANS: T REF: Open for discussion

52. @RISK uses Monte Carlo simulation to answer “what-if” questions and allows planners and decision makers to take into account all possible outcomes of any particular course of action. Palisade is the software company that has installed @RISK in many companies all over the world.

ANS: T REF: Open for discussion (Google @RISK and look for )

53. Exponential smoothing (ES) method is a forecasting method. Like the weighted moving average (WMA) method, it calculates an average demand. It is a simpler method, requiring fewer calculations than WMA.

ANS: T REF: 3.3.3

54. It is never beneficial for forecasters in an organization to pool or share their forecasts and information.

ANS: F REF: 3.8

55. The Delphi forecasting method relies on the opinions of experts who are totally unbiased and whose estimates of future events are almost always correct.

ANS: F REF: 3.7

56. The participants in a Delphi Forecast are rewarded by the Delphi manager for agreeing with each other.

ANS: F REF: 3.7 (We hope this is false, but worry that a biased manager could influence results.)

57. When actual demand is significantly less than the forecast, there is a substantial forecasting underestimate.

ANS: F REF: 3.6

MULTIPLE CHOICE

1. _____ is the comprehensive and overall planning for the organization’s future.

|a. |Adaptation |c. |Profit maximization |

|b. |Conversion |d. |Strategy |

ANS: D REF: Introduction to Chapter 3

2. Strategy entails broad-based, cooperative goal setting followed by planning to achieve this goal by:

|a. |modifying the forecast. |

|b. |influencing what the future might bring. |

|c. |rejecting the forecast as inevitable truth. |

|d. |all of the above |

ANS: D REF: Introduction to Chapter 3

3. Data in a time series may consist of:

|a. |random variations |c. |decreasing trend values |

|b. |increasing trend values |d. |all of the above |

ANS: D REF: 3.2

4. Legitimate categories of time series include:

|a. |step functions |c. |a and b |

|b. |impulse functions |d. |strategic functions |

ANS: C REF: 3.2

5. The evolution of both new and existing products follows a pattern that is called:

|a. |life cycles |c. |syzygistic alignment |

|b. |synergistic cycles |d. |lunar cycle |

ANS: A REF: 3.9.3

6. Major techniques for time series analysis include:

|a. |mobile averages |c. |exponential smoothing |

|b. |average harmonics |d. |seasonal smoothing |

ANS: C REF: 3.3

7. No forecast can be made using moving averages until:

|a. |there are n observations |c. |there are n-1 observations |

|b. |there are n+1 observations |d. |there are n2 observations |

ANS: A REF: 3.3.1

8. All products and all services go through the following stages:

|a. |introduction, growth, maturity, decline. |

|b. |introduction, maturity, decline. |

|c. |introduction, decline. |

|d. |growth, decline. |

ANS: A REF: 3.9

9. Much time and talent is needed to conceptualize the product, design its specifics, organize the process for making it, cost it out, pilot test it, and so forth. When the product is accepted, it is released for production and marketing. All of this takes place in the _____ stage.

|a. |growth |c. |introduction |

|b. |maturity |d. |decline |

ANS: C REF: 3.9.1

10. _____ is responsible for using different pricing, advertising, and promotion activities during appropriate life cycle stages.

|a. |management |c. |marketing |

|b. |operations management |d. |management information technology |

ANS: C REF: 3.9

11. _____ describe future events and their probabilities of occurrence.

|a. |growth plans |c. |demand analytics |

|b. |forecasts |d. |statistical phenomena |

ANS: B REF: Introduction to Chapter 3

12. Marketing models for predicting sales (lacking a contract) deal with levels of uncertainty that make forecasts of _____ difficult, but not irrational.

|a. |demand volumes |c. |revenues |

|b. |market shares |d. |all of the above |

ANS: D REF: 3.1

13. _____ and _____ are sales that move around the globe in response to currency fluctuations that are increasingly unstable.

|a. |Inputs; outputs |c. |Time; extrapolation |

|b. |Exports; imports |d. |Methods; forecasting |

ANS: B REF: 3.1

14. _____ is a stream of numbers that represent different values over time.

|a. |Extrapolation |c. |Time series |

|b. |Time series analysis |d. |Cycle time |

ANS: C REF: 3.2

15. _____ is the process of moving from observed data to the projected values of future points.

|a. |Time series |c. |Cycle time |

|b. |Extrapolation |d. |Time series analysis |

ANS: B REF: 3.2

16. Extrapolations of time series can be based on

|a. |cyclical wave patterns. |

|b. |trend lines. |

|c. |step functions. |

|d. |combinations of any or all of these patterns. |

ANS: D REF: 3.2

17. _____ are the basic pallet for the development of forecasting models.

|a. |Cycles |c. |Steps |

|b. |Trends |d. |all of the above |

ANS: D REF: 3.2

18. _____ deals with using knowledge about cycles, trends, and averages to forecast future events.

|a. |Time analysis |c. |Time series analysis |

|b. |Time series |d. |Series analysis |

ANS: C REF: 3.3

19. If the time series shows a linear trend, there is a(n) _____ of the numbers.

|a. |constant rate of change |c. |estimated rate of change |

|b. |historical forecast rate of change |d. |seasonal rate of change |

ANS: A REF: 3.2

20. When they work,_____ allow P/OM to excel at capacity planning and production scheduling for mature manufactured products and services.

|a. |forecasting systems |c. |historical cycles |

|b. |seasonal cycles |d. |semiannual forecasting methods |

ANS: C REF: 3.3.4

21. Assume that in 2013 the quarterly demands were 10, 30, 20, and 40. This gives a yearly demand of 100 units. Further, assume that in 2014 the annual demand is expected to increase to 120 units. Then, the model for the second quarter (2nd Q) forecast adjustments would be

|a. |120(35/100) = 42. |c. |120(20/120) = 20. |

|b. |120(30/100) = 36. |d. |120(40/150) = 32. |

ANS: B REF: 3.3.4

22. Assume that in 2013 the quarterly demands were 10, 30, 20, and 40. This gives a yearly demand of 100 units. Further, assume that in 2014 the annual demand is expected to increase to 120 units. Then, the first quarter (1st Q) forecast adjustments would be

|a. |120(40/100) = 48. |c. |120(10/100) = 12. |

|b. |120(20/100) = 24. |d. |all of the above |

ANS: C REF: 3.3.4

23. Assume that in 2013 the quarterly demands were 10, 30, 20, and 40. This would give a yearly demand of 100 units. Further, assume that in 2014 the annual demand is expected to increase to 130 units. Then, the model for the second quarter (2nd Q) forecast adjustments would be

|a. |130(30/100) = 39. |c. |10(130/100) = 13. |

|b. |100(40/100) = 40. |d. |40(100/130) = 30.77. |

ANS: A REF: 3.3.4

24. Exponential smoothing forecasts the demand for a given period t by combining the forecast______ and the actual demand of the previous period t-1.

|a. |of the next period t+1 |c. |of the first period t=1 |

|b. |of the previous period t-1 |d. |of the Nth period t=N |

ANS: B REF: 3.3.3

25. A way to make forecasts more responsive to the most recent actual occurrences is to use

|a. |exponential smoothing with alpha being very small. |

|b. |moving averages for trends. |

|c. |weighted moving averages. |

|d. |the Delphi method. |

ANS: C REF: 3.3.3

26. The method that is useful when trying to establish a relationship between two sets of time series numbers is _____.

|a. |the Delphi method |c. |regression analysis |

|b. |the weighted moving average |d. |exponential smoothing |

ANS: C REF: 3.4

27. When last year’s monthly sales are used to predict next year’s monthly sales values, the method is based on using_____ to forecast.

|a. |exponential smoothing |c. |weighted moving averages |

|b. |past history |d. |regression analysis |

ANS: D REF: 3.3.4

28. Linear regression is based on the assumption of ________.

|a. |straight-line equations |c. |average values |

|b. |any form of relationship |d. |regression equations |

ANS: C REF: 3.4

29. In regression analysis X is the independent variable and Y is the dependent variable which means that X could be_____ and Y could be_________.

|a. |Umbrellas bought, rain |c. |Study hours, grades |

|b. |Rain, umbrellas bought |d. |Grades, study hours |

ANS: B and C PTS: 2 REF: 3.4

30. _____ is a forecasting method that relies on expert estimation of future events occurring.

|a. |Weighted moving average |c. |Delphi method |

|b. |Time series analysis |d. |Exponential smoothing |

ANS: C REF: 3.7

31. The _____ is meant to put all participants on an equal footing with respect to getting their ideas heard.

|a. |exponential smoothing |c. |Delphi method |

|b. |weighted moving average |d. |regression analysis |

ANS: C REF: 3.7

32. The forecasting error that can occur is that the

|a. |actual demand is greater than the forecast. |

|b. |actual demand is less than the forecast. |

|c. |both a and b |

|d. |neither a nor b |

ANS: C REF: 3.6

33. To calculate MAD take the _____ of the_______ measures of the errors and divide that sum by the number of observations.

|a. |Sum, absolute |c. |Product, absolute |

|b. |Quotient, sign-valued |d. |Sum, plus and minus |

ANS: A REF: 3.6

34. Using Table 3.12, what is the sum of all the error terms without using absolute values?

|a. |171 |c. |171-127 = 44 |

|b. |127 |d. |-127 |

ANS: B REF: 3.6

35. It is always true that the sum of a set of absolute values will be _____ than the sum of the same series of numbers without absolute values.

|a. |Greater |c. |Less |

|b. |Equal to or greater |d. |Better |

ANS: B REF: 3.6

36. Today, sales patterns are becoming _____ stable with _____ competition and information.

|a. |less; decreasing |c. |more; decreasing, |

|b. |less; increasing |d. |more; increasing |

ANS: B REF: 3.1

37. Product life cycles have been speeding up, which means that growth has to occur _____.

|a. |neither slower nor faster |c. |slower |

|b. |at historical average levels |d. |faster |

ANS: D REF: 3.9.3

38. The first stage of the life cycle is

|a. |growth. |c. |maturity. |

|b. |introduction. |d. |decline. |

ANS: B REF: 3.9.3

39. In the _____ stage of the life cycle, equilibrium is reached.

|a. |introduction |c. |maturity |

|b. |growth |d. |decline |

ANS: C REF: 3.9.3

40. _____ is responsible for using different pricing, advertising, and promotion activities during appropriate life cycle stages.

|a. |Accounting |c. |Production |

|b. |Finance |d. |Marketing |

ANS: D REF: 3.9

41. When the new product or service stops growing its market share, it is considered mature. This means that its volume is _____ at the_______for that brand.

|a. |Stabilized, saturation level |c. |Destabilized, saturation level |

|b. |Stabilized, equilibrium level |d. |Restabilized, fatuation level |

ANS: A REF: 3.9.2

42. When actual demand is greater than the forecast, there is a forecasting _____.

|a. |overestimate |c. |both a and b |

|b. |underestimate |d. |neither a nor b |

ANS: B REF: 3.6

SHORT ANSWER

1. Why should we maintain a history of forecasting errors? In line with that question, should we care about who are the good estimators and who are bad ones?

ANS:

Keep historical records about hits and misses on forecasts, predictions and estimates. Companies can gain major advantages by finding out which team members are good estimators in general, and in specific situations. For example, some people are good at estimating next month’s sales but not good at estimating the cost of buying and making something. Each has value as long as we don’t get them confused in their challenges.

PTS: 1 REF: 3.6

2. What is a strategy? Why are strategies required?

ANS:

Successful strategies are required for the organization’s effective pursuit of its clearly defined goals. Strategy is the comprehensive and overall planning for the organization’s future. It has to be product-oriented and marketing-aware in order to take the customer and the competition into account, and process-oriented and P/OM oriented to deliver the product that customers want. It needs to be systems-oriented to coordinate marketing and P/OM. In direct answer to the text, a good strategy modifies forecasts to influence what the future holds in store.

REF: Introduction to Chapter 3

3. In what situations should moving averages be used to extrapolate next events?

ANS:

Moving averages should be used to extrapolate next events if there are no discernible cyclical patterns and if the system appears to be generating a series of values such that the last set of values provides the best estimate of what will be the next value. If these occur, there is “momentum” which can be a vital indicator. Momentum has magnitude and direction. The continuity of magnitude and direction are both reflected by the time series movements.

REF: 3.3.1

4. Why should several readings be preferred over a single reading in forecasting?

ANS:

Forecasting requires an understanding of the momentum of the system. The reason not to use just a single reading is that several readings provide information from different perspectives about a trend over time. Several readings provide a trend line that captures rates of change along the trajectory. Pooling information usually (but not always) increases the probabilities of reducing forecasting error.

REF: 3.8

5. When is regression analysis recommended?

ANS:

Regression analysis is useful when trying to establish a relationship between two sets of numbers that are individual time series. It is straightforward when that relationship between the numbers or correlate pairs is linear. When outcomes are to be forecast, the knowledge that one times series leads (or lags) another can be valuable information.

REF: 3.4

6. How does the trial and error method relate to successful pooling of information for combining multiple forecasts?

ANS:

Methods for pooling information to provide stronger forecasts are recommended and should be explored. It is critical that all parties share their forecasts as much as possible and try to find ways to combine them. Usually stronger forecasts can be obtained if both data and experience are pooled. Experience may have to do with weightings applied or the number of observations used. One of the keys to success in combining forecasts is trial and error. For example, different weighting systems are applied to past forecasts for which actual results are already known. Averaging of forecast results is also used to predict demand.

REF: 3.8

7. Could one of the experts be a computer when applying the Delphi Method of forecasting?

ANS: Increasingly, computers will be used by experts to form their own opinions. It is quite possible to program an artificially intelligent computer to provide expert estimation of future events without human intervention. Consider the fact that Watson (the IBM expert computer) beat the best contenders at the game of Jeopardy. In 2011, Watson beat human experts to win the first prize of $1 million. In February, 2013, IBM assigned Watson the task of diagnosing and prescribing (a type of forecasting) for lung cancer treatments for Memorial-Sloan Kettering Cancer Center.

REF: 3.7

8. What is the mean squared error (MSE) and how is it calculated? How is it different from the MAD?

ANS:

The mean square error is calculated by squaring all the error terms obtained from forecasting and then adding them together. Then, the sum is divided by the number of observations. Since both positive and negative errors are squared, the positive and negative errors don’t cancel each other out. The MSE does magnify large errors. The MAD (mean absolute deviation) is the sum of the absolute measures of the errors divided by the number of observations. Here too, positive and negative errors do not cancel out. Because MAD treats all errors linearly, it is a more conservative measure than MSE.

PTS: 2 REF: 3.6

This Q&A introduces material not covered in the text. Students can learn what is required by googling “mean squared error” and using Wikipedia plus other explanations.

9. Why is it important to maintain a history of all forecasting errors?

ANS:

A history of all forecasting errors should be maintained for all personnel that are making the forecasts, predictions, and estimates. Some individuals are good at forecasting and others are not. Some people are better at forecasting under certain circumstances. Companies gain a major advantage by finding out who can make good estimates, and under what circumstances. Bad forecasters can be shifted to other activities. When a record is not kept, all such advantage potentials are lost. Further, training certain candidates may be effective. There is evidence that is possible to make a good forecaster even better. Certain types of forecasting errors are correctable leading to the conversion of a bad forecaster into an exceptionally good forecaster.

REF: 3.6

10. What is the history of time series analysis and why is it important?

ANS:

Time series analysis has a rich history that clearly shows TSA evolving out of the practical efforts of bankers and financiers to understand cycles, trends, and averages in order to better forecast future events. The history of at least 350 years is compelling because it encompasses such diverse streams of data as prices for wheat, sunspot activity, tidal movements, population growth, disease epidemics, stock prices, cost of gasoline, trade deficits, business failures, and the list goes on and on. Learning about the history of statisticians working to derive intelligence from sequences of information is a fascinating and rewarding subject for further study by those who want to forecast the future.

REF: All sections devoted to forecasting

This Q&A introduces material not covered in the text. Students can learn what is required by looking at a book such as “Statistical Visions in Time: A History of Time Series Analysis, 1662-1938.” This work by Judy L. Klein is a classic even though it was first published by Cambridge University Press in December of 2008.

PROBLEM

1. Use the moving average forecasting method with n = 2 to develop a forecast for May.

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

Forecast for May = (50 + 60)/2 = 55 (which is the average of the forecast for the prior two months of March and April.

REF: 3.3.1

2. Use the moving average forecasting method with n = 3 to develop a forecast for May.

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

Forecast for May = (50 + 50 + 60)/3 = 53.3333 (which is the average of the forecast for the prior Three months of February, March and April.

REF: 3.3.1

3. Use the moving average forecasting method with n = 4 to develop a forecast for May.

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

Forecast for May = (40 + 50 + 50 + 60)/4 = 50 (which is the average of the forecast for the prior four months of January, February, March and April.

REF: 3.3.1

4. What have we been able to learn from problems 1, 2, and 3?

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

The two month moving average projected more than March and less than April. That is reasonable if the driving forces are immediate and not long-term.

The three month moving average projected more caution to earlier results. So it diminished the forecast from 55 to 53.3333. That makes sense because both March and February were 50 and only April jumped ahead to 60.

The four month moving average showed a lot more caution. After all, January was only 40 and this moving average is saying let January play a part in reaching a conclusion. Therefore, the forecast has been reduced from 55 (n=2) to 50 (n=4).

This simple example provides an intuitive example of how forecasts can be optimistic (accelerating) short-term and become cautious (decelerating) or even pessimistic longer-term.

REF: 3.3.1

5. Employ weights of 0.5, 0.25 and 0.25 to obtain a 3-month weighted moving average for May. Calculate the error term if the actual demand in May is 65.

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

Forecast for May = .5(60) + .25 (50) + .25(50) = 55.

The error term is positive ten (+10) calculated by Actual - Forecast = 65 - 55.

REF: 3.6

6. Employ weights of 0.4, 0.3, 0.2, 0.1, to obtain a 4-month weighted moving average for May. Calculate the error term if the actual demand in May is 65.

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

Forecast for May = .4(60) + .3(50) + .2 (50) + .1(40) = 53.

The error term is positive twelve (+12) calculated by Actual - Forecast = 65 - 53.

REF: 3.6

7. With respect to the same table (below) what did we learn from Problems 5 and 6?

|Month |Actual |Forecast |

|January |40 | |

|February |50 | |

|March |50 | |

|April |60 | |

|May | | |

|June | | |

ANS:

We learned that the forecast error is increased (from +10 to +12) by letting January have a say in this forecast. In other words, January’s low value of 40 introduces a force for lowering the forecast, even though it is clear that momentum is building over the four months for higher values. Specifically, the error term increases when we include January. It goes from positive ten (+10) calculated by Actual - Forecast = 65 – 55 to positive twelve (+12) calculated by Actual - Forecast = 65 – 53. It would be more informative if we had been given data from prior months as well as the times series of forecasts.

REF: 3.6

8. Employ weights of 0.4, 0.3, and 0.3 to obtain a weighted moving average for April, May and June. Calculate the error terms.

|Month |Actual |Forecast |

|January |10 | |

|February |12 | |

|March |16 | |

|April |16 | |

|May |18 | |

|June |20 | |

ANS:

Forecast for April = .4(16) + .3 (12) + .3(10) = 13.0

Forecast for May = .4(16) + .3 (16) + .3(12) = 14.8

Forecast for June = .4(18) + .3 (16) + .3(16) = 16.8

The error term for April is + 3.0, computed as (16 - 13).

The error term for May is + 3.2, computed as (18 - 14.8).

The error term for June is + 3.2, computed as (20 - 16.8).

REF: 3.6

9. Given the following data, compute the MAD.

|Month |Actual |Forecast |Deviation |

|January |100 |120 | |

|February |120 |100 | |

|March |160 |140 | |

|April |160 |140 | |

|May |180 |200 | |

|June |200 |180 | |

ANS:

Given the following data, compute the MAD.

|Month |Actual |Forecast |Absolute Deviation |

|January |100 |120 |20 |

|February |120 |100 |20 |

|March |160 |140 |20 |

|April |160 |140 |20 |

|May |180 |200 |20 |

|June |200 |180 |20 |

MAD = (20 + 20 + 20 + 20 + 20 + 20)/6 = 20.

REF: 3.6

10. Given the following data, calculate the forecast for June using the moving average method with n = 3.

|Month |Actual |Forecast |

|January |100 | |

|February |120 | |

|March |160 | |

|April |160 | |

|May |180 | |

|June | | |

ANS:

Moving Average for June (180 + 160 + 160)/3 = 166.67

11. Continuing with the data from Problem 8, calculate a weighted moving average forecast for June using weights of 0.5, 0.3, and 0.2. Assume the actual demand for June was 200 units. Comparing Problem 8 with Problem 9, which method produced the best results?

|Month |Actual |Forecast |

|January |100 | |

|February |120 | |

|March |160 | |

|April |160 | |

|May |180 | |

|June |200 | |

ANS:

Weighted Moving Average Forecast for June = .5(180) + .3(160) + .2(160) = 170.

Moving Average for June (180 + 160 + 160)/3 = 166.67

|Month |Actual |Forecast |

|January |100 | |

|February |120 | |

|March |160 | |

|April |160 | |

|May |180 | |

|June |200 |170 or 166.67 |

Given an actual demand of 200 units in June, the weighted moving average produced a better (closer) forecast but both methods underestimated demand.

REF: 3.6

12. The data in the table below illustrates the forecast using Exponential Smoothing Method. Calculate the MAD value for the months of July through December. A value of alpha = 0.2 was used.

|Month |Actual |Forecast |

|July | 95 |100.62 |

|August |115 | 99.5 |

|September |120 | 102.6 |

|October | 90 | 106.08 |

|November |105 | 102.86 |

|December |110 | 103.29 |

ANS: SUM [(95 - 100.62) + (115 – 99.5) + (120 – 102.6) + (90 – 106.08) + (105 – 102.86) + (110 – 103.29)] = 63.45

13. The data in the table below illustrates the Exponential Smoothing Method. A value of alpha = 0.2 was used. Change the value of alpha from 0.2 to 0.4. Calculate the MAD value for the months of July through December. Then, compare the results obtained in Problem 12 with those obtained with Problem 13. Use forecast

|Month |Actual |Forecast (alpha = 0.2) |Forecast (alpha = 0.4) |

|July | 95 |100.62 |100.62 |

|August |115 | 99.5 | |

|September |120 | 102.6 | |

|October | 90 | 106.08 | |

|November |105 | 102.86 | |

|December |110 | 103.29 | |

ANS:

SUM [(95 - 102) + (115 – 99.9) + (120 – 104.43) + (90 – 109.1) + (105 – 103.37) + (110 – 103.86)] = 64.54

Since MAD is larger with alpha = 0.4, we prefer alpha = 0.2. Using the same logic, we could test alpha values of 0.195 for example. Through trial and error we might find the optimal value of alpha.

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