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Description

Confirming Pages

Chapter Three

KEY TERMS

80 bias,

101 cycle,

81 error,

Forecasting least squares line,

105 trend,

SOLVED PROBLEMS

Problem 1

Forecasts based on averages

Given the following data: Period

Number of Complaints

1 2 3 4 5

Prepare a forecast for period 6 using each of these approaches: a

The appropriate naive approach

A three-period moving average

A weighted average using weights of

Exponential smoothing with a smoothing constant of

Solution Step by step

Plot the data to see if there is a pattern

Variations around an average (i

Therefore,

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

20(55) 

30(58) 

Use the latest values

Start with period 2

Use the data in period 1 as the forecast for period 2,

and then use exponential smoothing for successive forecasts

Number of Complaints

60 65 55

40(58  59

2)  58

40(64  58

72)  60

Forecast

Calculations [The previous value of the series is used as the starting forecast

Confirming Pages

Chapter Three

Forecasting

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

Using seasonal relatives

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

Problem 2

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,

February,

FJan FFeb FMar FApr

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

Solution

Multiply each monthly trend by the corresponding seasonal relative for that month

Month Jan

Seasonal Relative

Forecast

2)  568

8 477(1

3)  620

1 480(1

3)  624

0 483(1

1)  531

Confirming Pages

Chapter Three

Forecasting

Linear trend line

Plot the data on a graph,

and verify visually that a linear trend line is appropriate

Develop a linear trend equation for the following data

Then use the equation to predict the next two values of the series

Solution

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

Period Period,

Demand,

nty  ty n t 2  (  t ) 2

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

From Table 3

The next two forecasts are: F10  45

Confirming Pages

Chapter Three

Forecasting

You also can use an Excel template to obtain the coefficients and a plot

Simply replace the existing data in the template with your data

Seasonal relatives

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

Quarter

Demand/MA2

Note that each season has an even number of data points

When an even-numbered moving average is used (in this case,

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

To correct for this,

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

The MA2 values are centered between the MA4 and “line up” with actual data points

For example,

It is centered between 18 and 35 (i

between quarter 2 and quarter 3)

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

MA2) and centered,

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

is used to achieve correspondence with periods

This procedure is not needed when the number of periods in the centered moving average is odd

Quarter: Demand:

Problem 4

Solution

Confirming Pages

Chapter Three

Forecasting

QUARTER

Average for the quarter:

The sum of these relatives is 4

Multiplying each by 4

The resulting relatives are quarter 1,

Regression line

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

Using the graph,

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

Sales ($ millions)

Problem 5

Advertising ($ thousands)

Solution

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)

Accordingly,

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

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

and (10  0) is the change in x

Problem 6

Regression analysis

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:

Plot the data to determine which type of equation,

Obtain a regression equation for the data

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

Solution

Number of break-ins

The graph supports a linear relationship

Confirming Pages

Chapter Three

Forecasting

You can obtain the regression coefficients using the appropriate Excel template

Simply replace the existing data for x and y with your data

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

For x  5,

129  4

Accuracy of forecasts

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

Both techniques have been used to prepare forecasts for a sixmonth period

Using MAD as a criterion,

which technique has the better performance record

Technique 1

Technique 2

Check that each forecast has an average error of approximately zero

Technique 1

Technique 2

MAD 2 

Problem 7

Solution

Confirming Pages

Chapter Three

Forecasting

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

Problem 8

Control chart

Given the demand data that follow,

prepare a naive forecast for periods 2 through 10

Then determine each forecast error,

and use those values to obtain 2s control limits

If demand in the next two periods turns out to be 125 and 130,

can you conclude that the forecasts are in control

Solution

For a naive forecast,

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

the forecasts and errors are: Period

Forecast

— 118 117 120 119 126 122 117 123 121

Error 2  n 1

150  4

33 9 1

The control limits are 2(4

33)  8

The forecast for period 11 was 124

Demand turned out to be 125,

for an error of 125  124  1

This is within the limits of 8

If the next demand is 130 and the naive forecast is 125 (based on the period 11 demand of 125),

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

DISCUSSION AND REVIEW QUESTIONS

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

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

Consumer surveys

Salesforce composite

Committee of managers or executives

Briefly describe the Delphi technique

What are its main benefits and weaknesses

What is the purpose of establishing control limits for forecast errors

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

What advantages as a forecasting tool does exponential smoothing have over moving averages

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

How accurate is your local five-day weather forecast

? 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

Confirming Pages

Chapter Three

Forecasting

Contrast the reactive and proactive approaches to forecasting

Give several examples of types of organizations or situations in which each type is used

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,

Suppose a software producer is about to release a new version of its popular software

What information do you think it would take into account in forecasting initial sales

Choose the type of forecasting technique (survey,

Delphi,

or associative) that would be most appropriate for predicting a

Demand for Mother’s Day greeting cards

Popularity of a new television series

Demand for vacations on the moon

The impact a price increase of 10 percent would have on sales of orange marmalade

Demand for toothpaste in a particular supermarket

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

Who needs to be involved in preparing forecasts

How has technology had an impact on forecasting

TAKING STOCK

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

What capability would an organization have to have to not need forecasts

When a new business is started,

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

Discuss how you would manage a poor forecast

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

What are the pros and cons of doing that

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,

PROBLEMS

Day 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Blueberry Muffins

Cinnamon Buns

Cupcakes

Confirming Pages

Chapter Three Forecasting a

Predict orders for the following day for each of the products using an appropriate naive method

Hint: Plot each data set

What should the use of sales data instead of demand imply

National Scan,

sells radio frequency inventory tags

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

Sales (000 units)

May Jun

Plot the monthly data on a sheet of graph paper

Forecast September sales volume using each of the following: (1) A linear trend equation

(2) A five-month moving average

(3) Exponential smoothing with a smoothing constant equal to

assuming a March forecast of 19(000)

Which method seems least appropriate

? (Hint: Refer to your plot from part a

What does use of the term sales rather than demand presume

A dry cleaner uses exponential smoothing to forecast equipment usage at its main plant

August usage was forecasted to be 88 percent of capacity

A smoothing constant of

1 is used

Prepare a forecast for September

Assuming actual September usage of 92 percent,

prepare a forecast for October usage

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

Predict the number of requests for week 6 using each of these methods: a

A four-period moving average

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

Ft  80  15t where Ft  Annual sales (000 bottles) t  0 corresponds to 1990 a

Are annual sales increasing or decreasing

Predict annual sales for the year 2006 using the equation

From the following graph,

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

Confirming Pages

Chapter Three

Forecasting

Annual Sales,

Glib Sales,

5 6 Year

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

Determine a linear trend line for expected freight car loadings

Use the trend equation to predict expected loadings for weeks 20 and 21

The manager intends to install new equipment when the volume exceeds 800 loadings per week

Assuming the current trend continues,

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

New Accounts

New Accounts

New Accounts

Use trend-adjusted smoothing with  

3 and  

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,

Use  

5 and  

Obtain forecasts for periods 6 through 10

Confirming Pages

Chapter Three Forecasting 10

A manager of a store that sells and installs spas wants to prepare a forecast for January,

February,

Her forecasts are a combination of trend and seasonality

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

where t  0 in June of last year

Seasonal relatives are 1

What demands should she predict

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

Sales also exhibit seasonal variations

Using the information given,

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

Relative

1 2 3 4

A tourist center is open on weekends (Friday,

Saturday,

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

Friday Saturday Sunday

Develop seasonal relatives for the shop using the centered moving average method

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,

and 20 percent on Thursday night

What seasonal relatives would describe this situation

Air travel on Mountain Airlines for the past 18 weeks was: Week

Passengers

Passengers

Explain why an averaging technique would not be appropriate for forecasting

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,

Use the centered moving average method

(Hint: Use a seven-day moving average

Use the SA method

Confirming Pages

Chapter Three

Number Served

Number Served

Forecasting

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

Daily sales during the last 15 days were Day: Number sold: Day: Number sold:

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

If you learn that on some days the store ran out of the specific pain reliever,

would that knowledge cause you any concern

Assume that the data refer to demand rather than sales

Using trend-adjusted smoothing with an initial forecast of 50 for week 8,

an initial trend estimate of 2,

develop forecasts for days 9 through 16

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

New car sales for a dealer in Cook County,

Illinois,

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

Units Sold

Units Sold

Plot the data

Does there seem to be a trend

Deseasonalize car sales

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

Comment on the two graphs

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

The following table shows a tool and die company’s quarterly sales for the current year

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

? Quarter relatives are SR1  1

Quarter Sales

Confirming Pages

Chapter Three Forecasting 19

Compute seasonal relatives for this quarterly data

Use the SA method

Use the centered moving average method

Which set of relatives is better

1 2 3 4

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

Units Sold

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

Actual demand and the two sets of forecasts are as follows: PREDICTED DEMAND Period

Compute MAD for each set of forecasts

Given your results,

which forecast appears to be more accurate

Compute the MSE for each set of forecasts

Given your results,

which forecast appears to be more accurate

In practice,

either MAD or MSE would be employed to compute forecast errors

What factors might lead a manager to choose one rather than the other

Compute MAPE for each data set

Which forecast appears to be more accurate

Confirming Pages

Chapter Three

Forecasting

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

The forecasts and actual sales are as follows: Month

Forecast 1

Forecast 2

Compute the MSE and MAD for each forecast

Does either forecast seem superior

Compute MAPE for each forecast

Prepare a naive forecast for periods 2 through 11 using the given sales data

Compute each of the following

(2) MAD,

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

The equation is: y  150 

Plot the relationship on a graph

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

The manager of a seafood restaurant was asked to establish a pricing policy on lobster dinners

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

Average Number Sold per Day,

Plot the data and a regression line on the same graph

Determine the correlation coefficient and interpret it

Confirming Pages

Chapter Three Forecasting 26

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

Observation

Plot the data

Obtain a linear regression line for the data

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 store manager estimates a probable six-week lag between fertilizer sales and mower sales

The pertinent data are:

Fertilizer Sales (tons)

Number of Mowers Sold (six-week lag)

Fertilizer Sales (tons)

Number of Mowers Sold (six-week lag)

Determine the correlation between the two variables

Does it appear that a relationship between these variables will yield good predictions

Obtain a linear regression line for the data

Predict expected lawn mower sales for the first week in August,

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

The actual and predicted values are as follows: Period

Predicted

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

If limits of 4 are used,

Confirming Pages

Chapter Three

Forecasting

Refer to the data in problem 22

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

Use action limits of 4

Is there bias present

Compute 2s control limits for each forecast

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

Compute a tracking signal for months 11 through 20

Compute an initial value of MAD for month 11,

and then update it for each month using exponential smoothing with  

What can you conclude

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

Are the errors random

? 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):

Using an appropriate model,

forecast textbook sales for each of the next five years

Prepare a control chart for the forecast errors using the original data

Use 2s limits

Suppose actual sales for the next five years turn out as follows: Year: Sales (000):

Is the forecast performing adequately

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

The analyst is indifferent between the two alternatives,

saying that they should be equally effective

Period: Data: Alt

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

What would cause the analyst to reach this conclusion

What information can you add to enhance the analysis

A manager uses this equation to predict demand for landscaping services: Ft  10  5t

Over the past eight periods,

demand has been as follows: Period,

Is the forecast performing adequately

A manager uses a trend equation plus quarterly relatives to predict demand

Quarter relatives are SR1 

SR3  1

The trend equation is: Ft  10  5t

Over the past nine quarters,

demand has been as follows: Period,

Is the forecast performing adequately

Confirming Pages

M&L Manufacturing

M&L Manufacturing makes various components for printers and copiers

In addition to supplying these items to a major manufacturer,

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

In all,

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 company does not use forecasts for production planning

Instead,

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

Demand is uneven,

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

Being understocked has occasionally created tensions with the managers of retail outlets

Another problem is that prices of raw materials have been creeping up,

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

Because of competitive pressures and falling profits,

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

With that in mind,

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

Second,

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

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

Product 2

*Unusual order due to flooding of customer's warehouse

Questions 1

What are some of the potential benefits of a more formalized approach to forecasting

Prepare a weekly forecast for the next four weeks for each product

Briefly explain why you chose the methods you used

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

Highline Financial Services,

Highline Financial Services provides three categories of service to its clients

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

He is a bit perplexed by the following printout he obtained,

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

SERVICE Year

Quarter

1 2 3 4

SERVICE Year

Quarter

1 2 3 4

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

Note that there are not enough data to develop seasonal relatives

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