Operations Management - engineer.utcc.ac.th · - Short-range forecast (not more than one year;...

Operations Management UTCC Page 1

Operations Management

School of Engineering

The University of the Thai

Chamber of Commerce

Forecasting

School of Engineering

The University of the Thai Chamber of Commerce

Agenda

• What is forecast?

• Elements of good forecasts

• The necessary steps in preparing a forecast

• Basic forecasting techniques

• How to monitor a forecast

How will demand grow ?Long time frames over which Boeing must plan.

Boeing 737

Boeing 717

Mcdonell-Douglas11

Boeing Long-term capacity decisions

Motto in OM class

• It’s an old story, but an instructive note: Two shoe

salesmen arrive on a primitive island where no one

wears shoes. One cables his head office saying “No

business. Shoes not worn”, the other sends a

different message “Send more shoes. No

competition.”

John F. Kenedy

1. Introduction

• Have you ever forecast??

• How much food and drink will I need for the party?

• Will I get the job?

• Which team will be a world champion in 2014?

To make these forecasts,

• One is current factors or conditions.

• The other is past experience in a similar situation.

1. Introduction

• Forecasting are the basis for budgeting and

planning for capacity, sales, production and

inventory, personnel, purchasing, and more.

• Forecast play an important role in the planning

process.

• Forecasts affect decisions and activities throughout

an organization, in accounting, finance, human

resources, marketing, MIS, as well as operations,

and other parts of an organization.

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads

Product/service design New products and services

2.1 Uses of Forecasts

2. FORECAST:

• There are two methods for forecasting.

– Plan the system (involves long term plan about the types of products and service to offer).

– Plan to use the system (involves short and intermediate term plan such as planning inventory , workforce levels, planning purchasing, budgeting and scheduling).

การออกแบบศนูยก์ระจายสนิคา้ของจงัหวดัพษิณุโลกก

• Assumes causal systempast ==> future

• Forecasts rarely perfect because of randomness

• Forecasts more accurate forgroups vs. individuals

• Forecast accuracy decreases as time horizon increases

I see that you will

get an A this semester.

2.1 Features Common to all Forecasts

Forecasting time horizons

- Short-range forecast (not more than one year; Planning purchasing, Job scheduling, Workforce levels and so on)

- Medium-range forecast ( 3 months to 3 years; Production planning and budgeting, Cash budgeting)

- long-range forecast (more than 3 years; planning for new products, Capital expenditures, Facility location and R&D

The influence of product life cycle (PLC)

1 Introduction

2 Growth

3 Maturity

4 Decline

3. Elements of a Good Forecast

Timely

AccurateReliable

Written

4. Steps in the Forecasting Process

Step 1 Determine purpose of forecast

Step 2 Select the items to be forecasted

Step 3 Establish a time horizon

Step 4 Select a forecasting technique

Step 5 Gather and analyze data

Step 6 Monitor the forecast

“The forecast”

Step 7 Validate and Implement the results

5. Types of Forecasts

• Judgmental - uses subjective inputs

• Time series - uses historical data assuming the future will be like the past

• Associative models or Casual Model – use equation that consists of one or more explanatory variables to predict the future. For example, demand for paint might be related to variables such as the price per gallon and the amount spent on advertising, as well as specific characteristics of the paint.

6. Judgmental Forecasts

• Executive opinions

• Sales force opinions

• Consumer surveys

• Outside opinion

• Delphi method

– Opinions of managers and staffs

– Achieves a consensus forecast

7. Time Series Forecasts

• is a time-ordered sequence of observations taken at

regular intervals.

• The data may be measurements of demand, earnings,

profits, shipments, accidents, output and productivity.

• Trend - long-term movement in data

• Seasonality - short-term regular variations in data

• Cycle – wavelike variations of more than one year’s

duration

• Irregular variations - caused by unusual circumstances

• Random variations - caused by chance (Bird Flu)

7.1 Forecast Variations

Irregular

variatio

Seasonal variations

Cycles

7.2 Naive Forecasts

Uh, give me a minute....

We sold 250 wheels last

week.... Now, next week

we should sell....

The forecast for any period equals

the previous period’s actual value.

• Simple to use

• Virtually no cost

• Quick and easy to prepare

• Data analysis is nonexistent

• Easily understandable

• Cannot provide high accuracy

• Can be a standard for accuracy

7.2 Naïve Forecasts

• Stable time series data

– F(t) = A(t-1)

• Seasonal variations

– F(t) = A(t-n)

• Data with trends

– F(t) = A(t-1) + (A(t-1) – A(t-2))

7.2 Uses for Naïve Forecasts

7.2 Naïve Methods

• Uses a single previous value of a time series as the basis

of a forecast

Period Actual Change from previous value Forecast

t-1 50

t 53 +3

t+1 53+3 = 56

7.3 Techniques for Averaging

• Generate forecasts that reflect recent values of a

time series.

• Work best when a series tends to vary around an

average

– Moving average

– Weighted moving average

– Exponential smoothing

7.3.1 Moving average

• Uses a number of the most recent actual data values in

generating a forecast.

i = an index that corresponds to periods

n = number of periods in the moving average

Ai = actual value in period i

MA = Moving Average

Ft = Forecast for period t

Example 1

• Compute a three period

moving average forecast

given demand for

shopping carts for the last

five periods.

Period Age Demand

1 5 42

2 4 40

3 3 43

4 2 40

5 1 41

33.413

414043F6

3941407

FIf actual demand in period 6

turns out to be 39. What is F7 ?

7.3.2 Weighted Moving Average

• A weighted average is similar to a moving average,

except that it assigns more weight to the most

recent values in a time series.

• For instance, the most recent value might be

assigned a weight of .40, the next most recent value

a weight of .30, the next after that a weight of .20,

and the next after that a weight of .10.

• That weights sum to 1.00, and that the heaviest weights are assigned to the most recent values.

a) Compute weighted average forecast using a weight .4 for the most

recent period, .3 for the next most recent, .2 for the next, and .1 for

the next.

b) If the actual demand for period 6 is 39, forecast demand for period 7

using the same weights as in part a.

Period Demand

2.40)43(1.)40(2.)41(3.)39(4.F.b

0.41)40(1.)43(2.)40(3.)41(4.F.a

Note that if four weights are used, only the four most recent demands are used to prepare the forecast.

• The weighted average is more reflective of the most

recent occurrences.

• The choice of weights is somewhat arbitrary and

generally involves the use of trial and error to find a

suitable weighting scheme.

7.3.3 exponential smoothing

• Exponential smoothing is a sophisticated weighted

averaging method that is still relatively easy to use

and understand. Each new forecast is based on the

previous forecast plus a percentage of the

difference between that forecast and the actual

value of the series at that point.

7.3.3 Exponential Smoothing

Forecast) Previous - (Actual forecast Previous forecast Next

α represents a percentage of the forecast error.

Therefore, each new forecast is equal to the previous forecast plus a

percentage of the previous error.

Suppose the previous forecast was 42 units, actual demand was 40

units, and α = .10. the new forecasts

F = 42 + .10(40-42) = 41.8

Then if the actual demand turns out to be 43, the next forecast would

)FA(FF 1t1t1tt

Ans. 41.92

• An alternate form of formula reveals the weighting of the

previous forecast and the latest actual demand:

• For example:

1t1t1tt

AF)1(F

)FA(FF

1t1t1tt

A1.0F)9.0(F

)FA(10.0FF

F = 42 + .10(40-42) = (0.9)(42) + (.10)(40) = 41.8

Example 2

• The following table illustrates two series of forecasts

for a data set and the resulting error for each

period. One forecast uses α = .10 and one uses α =

.40. The following figure plots the actual data and

both sets of forecasts.

Period Actual Alpha = 0.1 Error Alpha = 0.4 Error

2 40 42 -2.00 42 -2

3 43 41.8 1.20 41.2 1.8

4 40 41.92 -1.92 41.92 -1.92

5 41 41.73 -0.73 41.15 -0.15

6 39 41.66 -2.66 41.09 -2.09

7 46 41.39 4.61 40.25 5.75

8 44 41.85 2.15 42.55 1.45

9 45 42.07 2.93 43.13 1.87

10 38 42.36 -4.36 43.88 -5.88

11 40 41.92 -1.92 41.53 -1.53

12 41.73 40.92

Example 2 - Exponential Smoothing

Picking a Smoothing Constant

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

Period

Actual

• The closer α is to zero, the slower the forecast will be to

adjust to forecast errors. (the greater the smoothing,

emphasis the previous data)

• The closer the value of α is to 1.00, the greater the

responsiveness and the less the smoothing. (emphasis the present data )

tttt AAAAF )1(...)1()1( 3

7.4 Techniques for trend

• Develop an equation that will suitably describe trend

• The trend component may be linear, or it may not.

• Two important techniques that can be used to

develop forecasts

– Trend equation

– Extension of exponential smoothing

7.4 Common Nonlinear Trends

Parabolic

Exponential

Growth

Figure 3.5

7.5 Linear Trend Equation

• Ft = Forecast for period t

• t = Specified number of time periods

• a = Value of Ft at t = 0

• b = Slope of the line

Ft = a + bt

0 1 2 3 4 5 t

7.5 Trend equation

The coefficients of the line, a and b, can be computed from

historical data using these components.

tb-yor n

yttynb

n = number of periods

y = value of the time series

Linear Trend Equation Example

Week t2

Sales ty

1 1 150 150

2 4 157 314

3 9 162 486

4 16 166 664

5 25 177 885

t = 15 t2 = 55 y = 812 ty = 2499

(t)2 = 225

Linear Trend Calculation

y = 143.5 + 6.3t

a =812 - 6.3(15)

b =5 (2499) - 15(812)

5(55) - 225=

12495-12180

275 -225= 6.3

Cell phone sales for a

California-based firm over the

last 10 weeks are shown in the

following table. Plot the data,

and visually check to see if a

linear trend line would be

appropriate. Then determine

the equation of the trend line,

and predict sales for weeks 11

and 12.

Example 3

Week Unit Sales

10 775

a. A plot suggests that a linear trend line would be appropriate:

Example 3

unit sales

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

Week (t) Unit Sales

1 700 700

2 724 1448

3 720 2160

4 728 2912

5 740 3700

6 742 4452

7 758 5306

8 750 6000

9 770 6930

10 775 7750

55 7407 41358

699.40 10

)55(51.7407,7a

51.7825

)55(55)385(10

)407,7)(55()358,41(10b

Example 3

Thus the trend line is

t51.740.699yt

tb-yor n

yttynb

c. Substituting values of t into this equation, the forecasts

for the next two periods are:

Example 3

52.789)12(51.740.699y

01.782)11(51.740.699y

unit sales

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

Example 3

d. For purposes of illustration, the original data, the trend line,

and the two projections (forecasts) are shown on the following

graph.

7.6 Associative Forecasting

• Associative techniques rely on identification of related variables that can be used to predict values of the variable of interest.

• Predictor variables - used to predict values of variable interest

• Regression - technique for fitting a line to a set of points

• Least squares line - minimizes sum of squared deviations around the line

7.7 Linear Model Seems Reasonable

A straight line is fitted to a set of sample points.

0 5 10 15 20 25

Computed

relationship

8. Forecast Accuracy

• Error = actual value - predicted value

• Mean Absolute Deviation (MAD)

– Average absolute error

• Mean Squared Error (MSE)

– Average of squared error

• Mean Absolute Percent Error (MAPE)

– Average absolute percent error

8.1 MAD, MSE, and MAPE

MAD =Actual forecast

MSE =Actual forecast)

MAPE =Actual forecas

/ Actual*100)(

Example 4

Period Actual Forecast (A-F) |A-F| (A-F)^2 (|A-F|/Actual)*100

1 217 215 2 2 4 0.92

2 213 216 -3 3 9 1.41

3 216 215 1 1 1 0.46

4 210 214 -4 4 16 1.90

5 213 211 2 2 4 0.94

6 219 214 5 5 25 2.28

7 216 217 -1 1 1 0.46

8 212 216 -4 4 16 1.89

-2 22 76 10.26

MAD= 2.75

MSE= 10.86

MAPE= 1.28

Example 4: Solution

• MAD = 22/8 = 2.75

• MSE = 76/(8-1) = 10.86

• MAPE = 10.26%/8 = 1.28%

9. Controlling the Forecast

• Control chart

– A visual tool for monitoring forecast errors

– Used to detect non-randomness in errors

• Forecasting errors are in control if

– All errors are within the control limits

– No patterns, such as trends or cycles, are present

9.1 Control Chart

• S =

• UCL :

• LCL :

• MSE = 2

• S =

• UCL :

• LCL :

41.1MSE

82.2MSEz

10. Sources of Forecast errors

• Model may be inadequate

• Irregular variations

• Incorrect use of forecasting technique

11. Tracking Signal or Control Chart

Tracking signal =(Actual-forecast)

•Tracking signal

–Ratio of cumulative error to MAD

Bias – Persistent tendency for forecasts to be

Greater or less than actual values.

12. Choosing a Forecasting Technique

• No single technique works in every situation

• Two most important factors

– Cost

– Accuracy

• Other factors include the availability of:

– Historical data

– Computers

– Time needed to gather and analyze the data

– Forecast horizon

13. Forecast factors, by range of forecast

Factor Short Range Intermediate

Long Range

1. Frequency Often Occasional Infrequent

2. Level of Aggregation Item Product family Total output, type of

product/service

3. Type of model Smoothing,

projection,

regression

Smoothing,

projection,

regression

Managerial judgment

4. Degree of management

involvement

Low Moderate High

5. Cost per forecast Low Moderate high

Problem 1

1. The appropriate naïve approach

2. A three period moving average and five period

3. A weighted average using weights of .50 (most recent), .30, and .20

4. Exponential smoothing with a smoothing constant of .40

Period Number of Complaints

Solution:

1. The values are stable. Therefore, the most recent

value of the series becomes the next forecast: 64

2. MA3 = (55+58+64)/3 = 59

MA5 = (60+65+55+58+64)/5 = 60.4

3. F = .20(55)+.30(58)+.50(64) = 60.4

Solution:

Period Number of

complaints

Forecast calculations

2 65 60

3 55 62 60+.40(65-60) = 62

4 58 59.2 62+.40(55-62) = 59.2

5 64 58.72 59.2 + .40(58-59.2) = 58.72

6 60.83 58.72+.40(64-58.72) = 60.83

Problem 2:

• Plot the data on a graph,

and verify visually that a

linear trend line is

appropriate. Develop a line

trend equation for the

following data. Then use

the equation to predict the

next two value of the

series

Period Demand

Solution 2:

0 2 4 6 8 10 12

Period

Solution 2:

Period (t) Demand (y) Ty

1 44 44

2 52 104

3 50 150

4 54 216

5 55 275

6 55 330

7 60 420

8 56 448

9 62 558

448 2545

Solution 2:

45.47 9

)45(75.1488a

75.1)45(45)285(9

)488)(45()545,2(9b

Thus the trend line is

72.64)11(75.147.45F

97.62)10(75.147.45F

t75.147.45F

tb-yor n

yttynb

Problem 3

• The manager of a large manufacturer of industrial pumps must chose

between two alter active forecasting techniques. Both techniques have

been used to prepare forecasts for a six-month period. Using MAD as

a criterion, which technique has the better performance record?

Forecast

Month Demand Technique 1 Technique 2

1 492 488 495

2 470 484 482

3 485 480 478

4 493 490 488

5 498 497 492

6 492 493 493

Solution 3

Solution 3:

• 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 4:

• Given the demand data that follow, prepare a naïve 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?

Period 1 2 3 4 5 6 7 8 9 10

Demand 118 117 120 119 126 122 117 123 121 124

Solution 4:

Period Demand Forecast Error Error square

1 118 - - -

2 117 118 -1 1

3 120 117 3 9

4 119 120 -1 1

5 126 119 7 49

6 122 126 -4 16

7 117 122 -5 25

8 123 117 6 36

9 121 123 -2 4

10 124 121 3 9

Solution 4:

33.419

errors

n = Number of errors

The control limits are 2(4.33) = +/-8.66

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 +/-8.66. If the next demand

is 130 and the naïve forecast is 125, the error is +5. again, 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 non-randomness.

Problem 5:

5. National mixer Inc. sell can

openers. Monthly sales for

a seven-month period

were as follows:

Month Sales

(000 units)

Feb 19

Mar 18

Apr 15

May 20

Jun 18

Jul 22

Aug 20

Problem 5

a. Plot the monthly data

b. Forecast September sales volume using each of the

following:

a. A linear trend equation.

b. A five-month moving average

c. Exponential smoothing with alpha = 0.20, assuming a March

forecast of 19(000).

d. The naïve approach

e. A weighted average using .60 for August, .30 for July, and .10

for June.

c. Which method seems least appropriate? Why?

Problem 6

6. Freight car loadings over a 12 year period at a busy port are

Week Ton Shipped Week Ton Shipped Week Ton Shipped

1 405 8 433 15 466

2 410 9 438 16 474

3 420 10 440 17 476

4 415 11 446 18 482

5 412 12 451

6 420 13 455

7 424 14 464

Problem 6:

a. Determine a linear trend line for freight car

loadings.

b. Use the trend equation to predict loadings for

weeks 20 and 21.

c. 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

Problem 7:

7. Two different forecasting techniques were used to forecast

demand fore cases of bottled water. Actual demand and the two sets of forecasts are as follows:

Forecast

Period Demand Technique 1 Technique 2

1 68 66 66

2 75 68 68

3 70 72 70

4 74 71 72

5 69 72 74

6 72 70 76

7 80 71 78

8 78 74 80

Problem 7:

a) Compute MAD for set of forecasts. Given your results,

which forecast appears to be more accurate? Explain

b) Compute the MSE for each set of forecasts. Given your

results, which forecast appears to be more accurate?

c) 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?

d) Compute MAPE for each data set. Which forecast appears to be more accurate?

Operations Management - engineer.utcc.ac.th · - Short-range forecast (not more than one year;...

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