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Description

Chapter Three

- associative model,

80 bias,

- 105 centered moving average,
- 95 control chart,
- 103 correlation,

101 cycle,

- 82 Delphi method,

81 error,

- 78 exponential smoothing,
- 87 forecast,
- 74 irregular variation,
- 82 judgmental forecasts,

- 98 linear trend equation,
- 90 mean absolute deviation (MAD),
- 78 mean absolute percent error (MAPE),
- 79 mean squared error (MSE),
- 78 moving average,
- 84 naive forecast,
- 82 predictor variables,
- 98 random variations,
- 82 regression,
- seasonal relative,
- 94 seasonal variations,
- 93 seasonality,
- 82 standard error of estimate,
- 100 time series,
- 82 time-series forecasts,
- 80 tracking signal,

105 trend,

- 82 trend-adjusted exponential smoothing,
- 92 weighted average,

SOLVED PROBLEMS

Given the following data: Period

1 2 3 4 5

- 60 65 55 58 64

The appropriate naive approach

- 50 (most recent),

Plot the data to see if there is a pattern

Variations around an average (i

- no trend or cycles)

Therefore,

the most recent value of the series becomes the next forecast: 64

- 55 58 64 59 3 c

20(55)

30(58)

- 50(64) 60

Use the latest values

Start with period 2

and then use exponential smoothing for successive forecasts

60 65 55

- 40(55 62) 59

40(58 59

2) 58

40(64 58

72) 60

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Forecast

- 40(65 60) 62
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Chapter Three

You also can obtain the forecasts and a plot using an Excel template,

- as shown:
- e cel www
- com/stevenson11e

Apple’s Citrus Fruit Farm ships boxed fruit anywhere in the world

Using the following information,

a manager wants to forecast shipments for the first four months of next year

Seasonal Relative

Month Jan

Seasonal Relative

- e cel www
- com/stevenson11e

The monthly forecast equation being used is: Ft 402 3t where t0 January of last year Ft Forecast of shipments for month t a

Determine trend amounts for the first four months of next year: January,

- 402 402 402 402

3( 24 ) 3( 25) 3( 26 ) 3( 27)

- 474 477 480 483

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Seasonal Relative

2) 568

8 477(1

3) 620

1 480(1

3) 624

0 483(1

1) 531

- 11/19/10 9:15:58 PM

- 116 Problem 3

and verify visually that a linear trend line is appropriate

- 1 2 3 4 5 6 7 8 9
- 44 52 50 54 55 55 60 56 62

A plot of the data indicates that a linear trend line is appropriate:

- 65 Trend line
- 60 55 50 45

Period Period,

Demand,

- 1 2 3 4 5 6 7 8 9
- 44 52 50 54 55 55 60 56 62 488
- b a

nty ty n t 2 ( t ) 2

ty 44 104 150 216 275 330 420 448 558 2,545

- with n 9,
- t 45 and t2 285
- 545) 45( 488) 1
- 75 9( 285) 45(45)
- y b t 488 1
- 75( 45) 45
- the trend equation is Ft 45

- 75(10) 62
- 97 F11 45
- 75(11) 64
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Confirming Pages

Chapter Three

Seasonal relatives

Obtain estimates of quarter relatives for these data using the centered moving average method:

- 1 2 3 4 1 2 3 4 1 2 3 4 1
- 14 18 35 46 28 36 60 71 45 54 84 88 58
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a four-period moving average),

the “centered value” will not correspond to an actual data point

the center of 4 is between the second and third data points

a second set of moving averages must be computed using the MA4 values

- the first MA4 value is 28

between quarter 2 and quarter 3)

When the average of the first two MA4 values is taken (i

- it lines up with the 35 and,
- with quarter 3

whenever an even-numbered moving average is used as a centered moving average (e

- a second moving average,
- a two-period moving average,

is used to achieve correspondence with periods

Quarter: Demand:

Solution

- 11/19/10 9:16:03 PM

Confirming Pages

Multiplying each by 4

- 037 will standardize the relatives,
- making their total equal 4

- quarter 2,
- quarter 3,
- quarter 4,

A large midwestern retailer has developed a graph that summarizes the effect of advertising expenditures on sales volume

determine an equation of the form y a bx that describes this relationship

The linear equation has the form y a bx,

where a is the value of y when x 0 (i

where the line intersects the y axis) and b is the slope of the line (the amount by which y changes for a one-unit change in x)

a 1 and b (3 1)/(10 0)

- so y a bx becomes y 1

[Note: (3 1) is the change in y,

and (10 0) is the change in x

Problem 6

The owner of a small hardware store has noted a sales pattern for window locks that seems to parallel the number of break-ins reported each week in the newspaper

The data are: Sales: Break-ins:

- linear or nonlinear,
- is appropriate

Estimate average sales when the number of break-ins is five

Solution

The graph supports a linear relationship

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Forecasting

Note: Be careful to enter the values for the variable you want to predict as y values

In this problem,

the objective is to predict sales,

so the sales values are entered in the y column

The equation is yc 7

129 4

- e cel www
- com/stevenson11e

129 4

- 275(5) 28

Accuracy of forecasts

The manager of a large manufacturer of industrial pumps must choose between two alternative forecasting techniques

Using MAD as a criterion,

which technique has the better performance record

- ? FORECAST Demand

Technique 1

- 1 2 3 4 5 6
- 492 470 485 493 498 492
- 488 484 480 490 497 493
- 495 482 478 488 492 493

- (See computations that follow
- ) Month

- 1 2 3 4 5 6
- 492 470 485 493 498 492
- 488 484 480 490 497 493
- 4 14 5 3 1 1 2
- 4 14 5 3 1 1 28
- 495 482 478 488 492 493
- 3 12 7 5 6 1 2
- 3 12 7 5 6 1 34

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Confirming Pages

Technique 1 is superior in this comparison because its MAD is smaller,

although six observations would generally be too few on which to base a realistic comparison

prepare a naive forecast for periods 2 through 10

Then determine each forecast error,

and use those values to obtain 2s control limits

can you conclude that the forecasts are in control

- ? Period: Demand:

For a naive forecast,

each period's demand becomes the forecast for the next period

the forecasts and errors are: Period

Forecast

- 1 2 3 4 5 6 7 8 9 10
- 118 117 120 119 126 122 117 123 121 124

— 118 117 120 119 126 122 117 123 121

- — 1 3 1 7 4 5 6 2 3 6
- — 1 9 1 49 16 25 36 4 9 150

Error 2 n 1

150 4

33 9 1

- ( n Number of errors)

The control limits are 2(4

33) 8

Demand turned out to be 125,

for an error of 125 124 1

- the error is 5
- this is within the limits,

so you cannot conclude the forecast is not working properly

With more values—at least five or six—you could plot the errors to see whether you could detect any patterns suggesting the presence of nonrandomness

What are the main advantages that quantitative techniques for forecasting have over qualitative techniques

? What limitations do quantitative techniques have

What are some of the consequences of poor forecasts

- ? Explain

List the specific weaknesses of each of these approaches to developing a forecast: a

What factors would you consider in deciding whether to use wide or narrow control limits for forecasts

Contrast the use of MAD and MSE in evaluating forecasts

How does the number of periods in a moving average affect the responsiveness of the forecast

What factors enter into the choice of a value for the smoothing constant in exponential smoothing

? Support your answer with actual data

Explain how using a centered moving average with a length equal to the length of a season eliminates seasonality from a time series

Contrast the terms sales and demand

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Explain how flexibility in production systems relates to the forecast horizon and forecast accuracy

How is forecasting in the context of a supply chain different from forecasting for just a single organization

? List possible supply chain benefits and discuss potential difficulties in doing supply chain forecasting

Which type of forecasting approach,

- qualitative or quantitative,
- is better

Choose the type of forecasting technique (survey,

Delphi,

- averaging,
- seasonal,

or associative) that would be most appropriate for predicting a

Demand for vacations on the moon

Explain the trade-off between responsiveness and stability in a forecasting system that uses timeseries data

How has technology had an impact on forecasting

It has been said that forecasting using exponential smoothing is like driving a car by looking in the rear-view mirror

What are the conditions that would have to exist for driving a car that are analogous to the assumptions made when using exponential smoothing

or a patent idea needs funding,

venture capitalists or investment bankers will want to see a business plan that includes forecast information related to a profit and loss statement

What type of forecasting information do you suppose would be required

Omar has heard from some of his customers that they will probably cut back on order sizes in the next quarter

The company he works for has been reducing its sales force due to falling demand and he worries that he could be next if his sales begin to fall off

Believing that he may be able to convince his customers not to cut back on orders,

he turns in an optimistic forecast of his next quarter sales to his manager

Give three examples of unethical conduct involving forecasting and the ethical principle each violates

CRITICAL THINKING EXERCISES

A commercial bakery has recorded sales (in dozens) for three products,

- as shown below:

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- 30 34 32 34 35 30 34 36 29 31 35 31 37 34 33
- 18 17 19 19 22 23 23 25 24 26 27 28 29 31 33
- 45 26 27 23 22 48 29 20 14 18 47 26 27 24 22
- 11/19/10 9:16:14 PM

Confirming Pages

Hint: Plot each data set

National Scan,

sells radio frequency inventory tags

Monthly sales for a seven-month period were as follows:

Sales (000 units)

May Jun

- 19 18 15 20 18 22 20

(2) A five-month moving average

(3) Exponential smoothing with a smoothing constant equal to

assuming a March forecast of 19(000)

- (4) The naive approach
- (5) A weighted average using
- 60 for August,
- 30 for July,
- 10 for June

? (Hint: Refer to your plot from part a

What does use of the term sales rather than demand presume

- actual usage was 89
- 6 percent of capacity

1 is used

Prepare a forecast for September

prepare a forecast for October usage

An electrical contractor’s records during the last five weeks indicate the number of job requests: Week: Requests:

Exponential smoothing with

Use 20 for week 2 forecast

A cosmetics manufacturer’s marketing department has developed a linear trend equation that can be used to predict annual sales of its popular Hand & Foot Cream

Are annual sales increasing or decreasing

- ? By how much

From the following graph,

determine the equation of the linear trend line for time-share sales for Glib Marketing,

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Confirming Pages

Chapter Three

Annual Sales,

- 600 500 Sales (units)
- 400 300 200 100 0

5 6 Year

Freight car loadings over a 12-year period at a busy port are as follows: Week

the loading volume will reach that level in approximately what week

Obtain the linear trend equation for the following data on new checking accounts at Fair Savings Bank and use it to predict expected new checking accounts for periods 16 through 19

Use trend-adjusted smoothing with

3 and

- 2 to smooth the new account data in part a

What is the forecast for period 16

After plotting demand for four periods,

an emergency room manager has concluded that a trendadjusted exponential smoothing model is appropriate to predict future demand

The initial estimate of trend is based on the net change of 30 for the three periods from 1 to 4,

- for an average of 10 units

5 and

- and TAF of 250 for period 5

Obtain forecasts for periods 6 through 10

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February,

- and March of next year

She uses the following equation to estimate the trend component of monthly demand: Ft 70 5t,

where t 0 in June of last year

- 10 for January,
- 02 for February,
- 95 for March

The following equation summarizes the trend portion of quarterly sales of condominiums over a long cycle

prepare a forecast of sales for each quarter of next year (not this year),

and the first quarter of the year following that

Ft 40 6

- 5t 2t 2 where Ft Unit sales t 0 at the first quarter of last year Quarter

Relative

1 2 3 4

A tourist center is open on weekends (Friday,

- and Sunday)

The owner-manager hopes to improve scheduling of part-time employees by determining seasonal relatives for each of these days

Data on recent traffic at the center have been tabulated and are shown in the following table: WEEK

- 149 250 166
- 154 255 162
- 152 260 171
- 150 268 173
- 159 273 176
- 163 276 183

Develop seasonal relatives for the shop using the SA method (see Example 8B)

Explain why the results of the two methods correlate the way they do

The manager of a fashionable restaurant open Wednesday through Saturday says that the restaurant does about 35 percent of its business on Friday night,

- 30 percent on Saturday night,

and 20 percent on Thursday night

- 1 2 3 4 5 6 7 8 9
- 405 410 420 415 412 420 424 433 438
- 10 11 12 13 14 15 16 17 18
- 440 446 451 455 464 466 474 476 482

Use an appropriate technique to develop a forecast for the expected number of passengers for the next three weeks

Obtain estimates of daily relatives for the number of customers at a restaurant for the evening meal,

- given the following data

(Hint: Use a seven-day moving average

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Number Served

Number Served

- 1 2 3 4 5 6 7 8 9 10 11 12 13 14
- 80 75 78 95 130 136 40 82 77 80 94 131 137 42
- 15 16 17 18 19 20 21 22 23 24 25 26 27 28
- 84 78 83 96 135 140 44 87 82 88 99 144 144 48

A pharmacist has been monitoring sales of a certain over-the-counter pain reliever

1 36 10 48

2 38 11 52

3 42 12 55

4 44 13 54

5 48 14 56

6 49 15 57

Which method would you suggest using to predict future sales—a linear trend equation or trendadjusted exponential smoothing

would that knowledge cause you any concern

- ? Explain

Assume that the data refer to demand rather than sales

an initial trend estimate of 2,

- and

develop forecasts for days 9 through 16

What is the MSE for the eight forecasts for which there are actual data

for the past year are shown in the following table,

along with monthly indexes (seasonal relatives),

which are supplied to the dealer by the regional distributor

Month Jan

May Jun

- 640 648 630 761 735 850
- 765 805 840 828 840 800

Plot the data

Plot the deseasonalized data on the same graph as the original data

Assuming no proactive approach on the part of management,

discuss (no calculations necessary) how you would forecast sales for the first three months of the next year

What action might management consider based on your findings in part b

What sales would you predict for the first quarter of next year

? Quarter relatives are SR1 1

- and SR4 1

Quarter Sales

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Confirming Pages

Chapter Three Forecasting 19

Compute seasonal relatives for this quarterly data

Which set of relatives is better

- ? YEAR Quarter

1 2 3 4

- 11 20 29 38
- 14 23 32 41
- 17 26 35 44

An analyst must decide between two different forecasting techniques for weekly sales of roller blades: a linear trend equation and the naive approach

The linear trend equation is Ft 124 2t,

and it was developed using data from periods 1 through 10

Based on data for periods 11 through 20 as shown in the table,

which of these two methods has the greater accuracy if MAD and MSE are used

- 11 12 13 14 15 16 17 18 19 20
- 147 148 151 145 155 152 155 157 160 165

Two different forecasting techniques (F1 and F2) were used to forecast demand for cases of bottled water

- 1 2 3 4 5 6 7 8
- 68 75 70 74 69 72 80 78
- 66 68 72 71 72 70 71 74
- 66 68 70 72 74 76 78 80

Compute MAD for each set of forecasts

Given your results,

which forecast appears to be more accurate

- ? Explain

Compute the MSE for each set of forecasts

which forecast appears to be more accurate

either MAD or MSE would be employed to compute forecast errors

Compute MAPE for each data set

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Chapter Three

Two independent methods of forecasting based on judgment and experience have been prepared each month for the past 10 months

- 1 2 3 4 5 6 7 8 9 10
- 770 789 794 780 768 772 760 775 786 790
- 771 785 790 784 770 768 761 771 784 788
- 769 787 792 798 774 770 759 775 788 788

Compute the MSE and MAD for each forecast

- ? Explain

Compute each of the following

- (1) MSE,

(2) MAD,

- (3) tracking signal at month 10,
- and (4) 2s control limits

How do the naive results compare with the other two forecasts

Long-Life Insurance has developed a linear model that it uses to determine the amount of term life insurance a family of four should have,

based on the current age of the head of the household

- 1x where y Insurance needed ($000) x Current age of head of household a

Use the equation to determine the amount of term life insurance to recommend for a family of four if the head of the household is 30 years old

Timely Transport provides local delivery service for a number of downtown and suburban businesses

Delivery charges are based on distance and weight involved for each delivery: 10 cents per pound and 15 cents per mile

there is a $10 handling fee per parcel

Develop an expression that summarizes delivery charges

Determine the delivery charge for transporting a 40-pound parcel 26 miles

Experimenting with prices produced the following data: Average Number Sold per Day,

- 200 190 188 180 170 162 160

- y 155 156 148 140 133

Plot the data and a regression line on the same graph

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Confirming Pages

The following data were collected during a study of consumer buying patterns: Observation

- 1 2 3 4 5 6 7
- 15 25 40 32 51 47 30
- 74 80 84 81 96 95 83
- 8 9 10 11 12 13
- 18 14 15 22 24 33
- 78 70 72 85 88 90

What percentage of the variation is explained by the regression line

? Use the equation determined in part b to predict the expected value of y for x 41

Lovely Lawns,

intends to use sales of lawn fertilizer to predict lawn mower sales

The pertinent data are:

Fertilizer Sales (tons)

- 1 2 3 4 5 6 7
- 10 8 11 12 12 9 8

Number of Mowers Sold (six-week lag)

- 8 9 10 11 12 13 14
- 7 10 6 11 8 10 9

- ? Explain

given fertilizer sales six weeks earlier of 2 tons

The manager of a travel agency has been using a seasonally adjusted forecast to predict demand for packaged tours

Predicted

- 1 2 3 4 5 6 7 8 9 10 11 12 13 14
- 129 194 156 91 85 132 126 126 95 149 98 85 137 134
- 124 200 150 94 80 140 128 124 100 150 94 80 140 128

Compute MAD for the fifth period,

then update it period by period using exponential smoothing with

Compute a tracking signal for periods 5 through 14 using the initial and updated MADs

- what can you conclude
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Confirming Pages

Chapter Three

Forecasting

Compute a tracking signal for the 10th month for each forecast using the cumulative error for months 1 to 10

- ? Explain

The classified department of a monthly magazine has used a combination of quantitative and qualitative methods to forecast sales of advertising space

Results over a 20-month period are as follows: Month

- 1 2 3 4 5 6 7 8 9 10
- 8 2 4 7 9 5 0 3 9 4
- 11 12 13 14 15 16 17 18 19 20
- 1 6 8 4 1 2 4 8 5 1

Compute a tracking signal for months 11 through 20

and then update it for each month using exponential smoothing with

- ? Assume limits of 4

Using the first half of the data,

construct a control chart with 2s limits

What can you conclude

Plot the last 10 errors on the control chart

? What is the implication of this

A textbook publishing company has compiled data on total annual sales of its business texts for the preceding nine years: Year: Sales (000):

forecast textbook sales for each of the next five years

Is the forecast performing adequately

- ? Explain

A manager has just received an evaluation from an analyst on two potential forecasting alternatives

saying that they should be equally effective

1 37 36 36

2 39 38 37

3 37 40 38

4 39 42 38

5 45 46 41

6 49 46 52

7 47 46 47

8 49 48 48

9 51 52 52

- 10 54 55 53

What information can you add to enhance the analysis

Over the past eight periods,

demand has been as follows: Period,

- t: Demand:

- ? Explain

Quarter relatives are SR1

- and SR4 1

demand has been as follows: Period,

- t: Demand:

Is the forecast performing adequately

- ? Explain
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the company distributes these and similar items to office supply stores and computer stores as replacement parts for printers and desktop copiers

the company makes about 20 different items

The two markets (the major manufacturer and the replacement market) require somewhat different handling

For example,

replacement products must be packaged individually whereas products are shipped in bulk to the major manufacturer

the operations manager decides which items to produce and the batch size,

based on orders and the amounts in inventory

The products that have the fewest amounts in inventory get the highest priority

and the company has experienced being overstocked on some items and out of others

although the operations manager thinks that this might be a temporary condition

the manager has decided to undertake a number of changes

One change is to introduce more formal forecasting procedures in order to improve production planning and inventory management

the manager wants to begin forecasting for two products

These products are important for several reasons

they account for a disproportionately large share of the company’s profits

the manager believes that one of these products will become increasingly important to future growth

- and third,

the other product has experienced periodic outof-stock instances

The manager has compiled data on product demand for the two products from order records for the previous 14 weeks

These are shown in the following table

Product 1

- 1 2 3 4 5 6 7 8 9 10 11 12 13 14
- 50 54 57 60 64 67 90* 76 79 82 85 87 92 96
- 40 38 41 46 42 41 41 47 42 43 42 49 43 44

*Unusual order due to flooding of customer's warehouse

Questions 1

Briefly explain why you chose the methods you used

- (Hint: For product 2,
- a simple approach,

possibly some sort of naive/ intuitive approach,

would be preferable to a technical approach in view of the manager’s disdain of more technical methods

Managing partner Freddie Mack is getting ready to prepare financial and personnel hiring (or layoff) plans for the coming year

which seems to show oscillating demand for the three categories of services over the past eight quarters:

1 2 3 4

- 60 45 100 75
- 95 85 92 65
- 93 90 110 90

1 2 3 4

- 72 51 112 85
- 85 75 85 50
- 102 75 110 100

Examine the demand that this company has experienced for the three categories of service it offers over the preceding two years

Assuming nothing changes in terms of advertising or promotion,

and competition doesn’t change,

predict demand for the services the company offers for the next four quarters

Nonetheless,

you should be able to make reasonably good,

approximate intuitive estimates of demand

What general observations can you make regarding demand

? Should Freddie have any concerns

- ? Explain
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