topic 2 -forecasting

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Operat ionsManagement

Top ic 2 – Forecast ing



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What is Forecasting?

Process of predicting afuture event

Can be any orcombination of:

Mathematical model

Intuitive

Hmm… you

gonna get an for

this subject



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Short-range forecast Up to 1 year but generally less than 3 months

used for planning purchasing, job scheduling,workforce levels, job assignments, production levels.

Medium-range forecast Generally spans from 3 months to 3 years

useful for sales planning, production planning andbudgeting, cash budgeting, and analyzing variousoperating plans.

Long-range forecast Generally 3 years or more

used in planning for new products, capitalexpenditures, facility location or expansion, and

R&D

Forecasting Time Horizons



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Types of Forecasts

Economic forecasts Address business cycle – inflation rate, money

supply, housing starts, etc.

Technological forecasts

Predict rate of technological progress

Impacts development of new products

Demand forecasts

Predict sales of existing products and services

We can also forecast the economy or the technology.

But for OM, demand forecasting the most relevant.

The forecast is the only estimate of demand until actual

demand becomes known.



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Importance of Forecasting

Human Resources – Hiring, training, laying offworkers

Capacity – Capacity shortages can result inundependable delivery, loss of customers,loss of market share

Supply Chain Management – Good supplierrelations and price advantage



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Seven Steps in Forecasting

1. Determine the use of the forecast

2. Select the items to be forecasted

3. Determine the time horizon of theforecast

4. Select the forecasting model(s)

5. Gather the data6. Make the forecast

7. Validate and implement results



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The Realities!

Forecasts are seldom perfect

Most techn iques assume anunder ly ing stabi l ity in the system

Product fam i ly and agg regated

forecasts are more accu rate than

indiv idual produc t forecasts



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Forecasting Approaches

Qualitative (subjective)

Forecast incorporates the decision maker’sintuition, emotion, personal experiences, and

value system in reaching a forecast.

Quantitative

Forecast use a variety of mathematical models/

techniques that rely on historical data and/orcausal variables to forecast demand.



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Forecasting Approaches

Used when situation is ‘stable’ and

historical data exist Existing products

Current technology

e.g., forecasting sales of color televisions

Quantitative Methods



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Qualitative methods

1. Jury of executive opinion – uses the opinion of a

small group of high level managers to form a group estimate

of demand.

2. Delphi method – using a group process that allowsexperts to make forecasts.

3. Sales force composite – based on salesperson’s

estimates of expected sales.

4. Consumer market survey – solicits inputs from

customers or potential customers regarding future

purchasing plans.



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Quantitative Methods

1. Naive approach

2. Moving averages3. Weighted Moving

Averages

4. Exponentialsmoothing

5. Trend projection

6. Linear regression

Time-SeriesModels

Associative Model



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uses a series of past data points to make aforecast. It is based on a sequence of evenly

spaced (weekly, monthly, quarterly, etc) data

points.

Predict on the assumption that the future is afunction of the past.

Forecast based only on past values, no other

variables important Look what happened over a period of time and use

a series of past data to make a forecast.

For example: to predict the sales of lawn mowers,

use the past sales to make the forecasts.

Time Series Models



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Components of Demand

D e m a

n d f o r p r o d u c t o r

s e r v i c e

| | | |

1 2 3 4

Year

Average demand

over four years

Seasonal peaks

Trendcomponent

Actualdemand

Randomvariation

Figure 4.1

Product demand charted over 4 years witha Growth Trend and Seasonality added:



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Persistent, overall upward or

downward pattern

Changes due to population,technology, age, culture, etc.

Typically several years duration

Trend Component



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Regular pattern of up and down

fluctuations

Due to weather, customs, etc.

Occurs within a single year

Seasonal Component

Number ofPeriod Length Seasons

Week Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12

Year Week 52



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Erratic, unsystematic, ‘residual’

fluctuations

Due to random variation or unforeseenevents

Short duration and

nonrepeating

Random Component

M T W T F



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Naive Approach

Assumes demand in nextperiod is the same as

demand in most recent period e.g., If January sales were 68, then

February sales will be 68

Sometimes cost effective and efficient

Can be good starting point



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Moving average

Weighted moving average

Exponential smoothing

Techniques for Averaging



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Moving Average Method

Moving average =∑ demand in previous n periods

n

A forecasting method that uses an average of the ‘n’ most recent

periods of data to forecast the next period. Useful if we can assume

that market demands will stay fairly steady over time.

e.g. a 4-month moving average is found by summing the demand during

the past 4 months and dividing by 4. This practice tends to smooth out

short term irregularities in the data series.

Where n is the number of periods in the moving average.

The above is used as an estimate of the next period’s demand



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Moving Average Example

Storage shed sales at a Garden Supply shop are as shown in the following

Table.

Example 1:

Calculate the 3-month

moving average forecast.



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January 10

February 12 March 13

Apr i l 16

May 19

June 23Ju ly 26

Actual 3-MonthMonth Shed Sales Movin g Average

(12 + 13 + 16)/3 = 13 2 /3

(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1 /3


10

12 13

(10 + 12 + 13)/3 = 11 2 /3



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e.g. the forecast for December is 20.7

The forecast for coming January is

(18+16+14)/3=16.0



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Graph of Moving Average

| | | | | | | | | | | |

J F M A M J J A S O N D

S h e

d

S a

l e s

30 –

28 –

26 –

24 –

22 –

20 –

18 –

16 –

14 – 12 –

10 –

Actual

Sales

MovingAverageForecast



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Weighted Moving Average

Weightedmoving average =

∑ (weight for per iod n ) x (demand in period n )

∑ weights

When a detectable trend or pattern is present, weights can be used to place

more emphasis on recent values. This makes forecasting techniques more

responsive to changes because more recent periods may be more heavily

weighted.



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Weighted Moving Average Ex:

Example 2 The shop in Example 1 decides to forecast storage shed sales by weighting the past 3 months as

follows:

Period Weight applied

Last month 3

2 months ago 2

3 months ago 1

_____________________________

Solution:

∑ (weights) = 6

Based on the weightings above, the forecast for any month

[(3 x Sales last month) + (2 x Sales 2 months ago) + (1 x Sales 3 months ago)]

= -------------------------------------------------------------------------------------------------∑ (weights)



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January 10

February 12

March 13

Apr i l 16May 19

June 23

Ju ly 26

Actual 3-Month Weigh ted

Month Shed Sales Movin g Average

[(3 x 16) + (2 x 13) + (12)]/6 = 141 /3

[(3 x 19) + (2 x 16) + (13)]/6 = 17

[(3 x 23) + (2 x 19) + (16)]/6 = 201 /2

Weighted Moving Average

10

12

13

[(3 x 13) + (2 x 12) + (10)]/6 = 121

/6

Weights Appl ied Per iod

3 Last month

2 Two months ago

1 Three mon ths ago

6 Sum of weights



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Weighted Moving Average Ex:

Note that in this situation more heavily weighting the latest month provides a much more

accurate projection.

Note also that moving averages are effective in smoothing out sudden fluctuations in the

demand pattern to provide stable estimates.



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Moving Average AndWeighted Moving Average

Note from the graph that both moving averages lag the actual demand. The

weighted moving average, however reacts more quickly to changes in

demand.



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Increasing n smooths the forecast but makes

it less sensitive to real changes in the data.

Cannot pick up trends very well. Because

they are averages, they will always stay

within past levels and will not predict

changes to either higher or lower levels.

Require extensive historical of past data.

Potential Problems With

Moving Average



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Exponential Smoothing

Is a weighted moving average forecasting technique

in which data points are weighted by an exponential

function. This technique involves little record keeping of past

data.

Easy to use.



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Exponential Smoothing

New forecast = Last period’s forecast

+ (Last period’s actual demand

– Last period’s forecast )

F t = F t – 1 + (A t – 1 - F t – 1)

where F t = new fo recast

F t – 1 = previous fo recast

= smooth ing (or weight ing)

constant (0 ≤ ≤ 1)

Remember This!!!!!!!!Basic exponential smoothing formula:



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Exponential Smoothing Example

Example 3

In January, a car dealer predicted February demand for 142 Ford Mustangs. Actual

February demand was 153. Using a smoothing constant chosen by management of α =0.20, forecast the March demand using the exponential smoothing model.

Solution:

Substituting into the formula above,

New forecast (for March demand),

FMac

= FFeb

+ α (AFeb

– FFeb

)

= 142 + 0.20 (153 – 142)

= 144.2

Therefore the March demand forecast for Ford Mustang is 144.



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Measuring Forecast Error

Forecast error (or Deviation) = Actual demand – Forecast demand= At - Ft.

Several measures in use:

•Mean absolute deviation (MAD)

•Mean squared error (MSE)

•Mean absolute percent error (MAPE)

∑ | Actual - Forecast |

MAD = ------------------------------

n

∑ (Forecast error)

2

MSE = ------------------------

n

n

100 ∑ | Actual i - Forecast i | / Actual i

MAPE = -------i=1--------------------------------------------

n



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Forecast Error Example:



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Exponential Smoothing Example

2Demand for the last four months was:

Predict demand for July using each of these methods:

(A)

1) A 3-period moving average

2) exponential smoothing with alpha equal to .20 (use naïve to

begin).

(B)

3) If the naive approach had been used to predict demand for April

through June, what would MAD have been for those months?



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Exponential Smoothing Example 2

Month Demand Forecast

March 6 -

April 8 6May 10 6 + 0.2(8 – 6) = 6.4

June 8 6.4 + 0.2(10 – 6.4) = 7.12

7.12 + 0.2(8 – 7.12) = 7.296

A) 1. (8+10+8)/3 = 8.33 (July Forecast)

2. Use naïve to begin

B)

Month March April May JuneDemand 6 8 10 8

Naïve - 6 8 10

Error - +2 +2 -2

MAD 6/3 = 2.0



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Moving Average

Weekly sales of ten-grain bread at the local organic food market are in the

table below. Based on this data, forecast week 9 using a five-week moving

average.

Other Examples

Week 1 2 3 4 5 6 7 8

Sales 415 389 420 382 410 432 405 421

(382+410+432+405+421)= 410.0



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Exponential Smoothing & MAD Jim's department at a local department store has tracked the sales of a product

over the last ten weeks. Forecast demand using exponential smoothing with

an alpha of 0.4, and an initial forecast of 28.0. Calculate MAD.

Other Examples

Period Demand1 24

2 23

3 26

4 36

5 26

6 30

7 32

8 26

9 25

10 28



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Period Demand Forecast Error Absolute

1 24 28.00

2 23 26.40 -3.40 3.40

3 26 25.04 0.96 0.96

4 36 25.42 10.58 10.58 5 26 29.65 -3.65 3.65

6 30 28.19 1.81 1.81

7 32 28.92 3.08 3.08

8 26 30.15 -4.15 4.15

9 25

28.49 -3.49 3.49 10 28 27.09 0.91 0.91

Total 2.64 32.03

Average 0.29 3.56

Bias MAD

Other Examples – Exponential Smoothing



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Other ExamplesProblems: Forecasting



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QUIZ 1

The docking rate of ships at the Northport varies monthly and the operationsmanager is attempting to test the use of exponential smoothing to determine the

effectiveness of the technique in forecasting. He begins the analysis in the

month of January and continues for an additional 5 months. The initial forecast

for January is 320. Actual data for the past 6 month are as follows:

The operation manager has decided on 2 values for a i.e. = 0.1 and a = 0.4.

Which of these alpha values will be more accurate? Explain why?

topic 2 -forecasting

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