Forecasting

CHAPTER

3

Forecasting

Manajemen Transportasi & Logistik Manajemen Transportasi & Logistik Manajemen Transportasi & Logistik Manajemen Transportasi & Logistik

Forecasting

Rahmi Yuniarti,ST.,MT Anni Rahimah, SAB,MAB

FIA - Prodi Bisnis Internasional Universitas Brawijaya

Manajemen Permintaan Manajemen Permintaan

2

Order Pesanan

Ramalan Permintaan Manajemen

Permintaan

Pengelolaan Order Pesanan Pengelolaan Order Pesanan

3

Permintaan

Penawaran

Negosiasi

Kesepakatan Perjanjian

FORECAST:

• A statement about the future value of a variable of interest such as demand.

• Forecasts affect decisions and activities throughout an organization

What is Forecasting?

What is Forecasting?

• Accounting, finance

• Human resources

• Marketing

• MIS

• Operations

• Product / service design

Accounting Cost/profit estimates

Finance Cash flow and funding

Human Resources Hiring/recruiting/training

Uses of Forecasts Uses of Forecasts

Marketing Pricing, promotion, strategy

MIS IT/IS systems, services

Operations Schedules, MRP, workloads Product/service design New products and services

Peramalan Permintaan Peramalan Permintaan

6

• Assumes causal system past ==> future

• Forecasts rarely perfect because of randomness

Forecasts more accurate for

Common in all forecasts Common in all forecasts

• Forecasts more accurate for groups vs. individuals

• Forecast accuracy decreases as time horizon increases

I see that you will

get an A this semester.

Steps in the Forecasting Process Steps in the Forecasting Process

“The forecast”

Step 1 Determine purpose of forecast Step 2 Establish a time horizon

Step 3 Select a forecasting technique Step 4 Gather and analyze data

Step 5 Prepare the forecast

Step 6 Monitor the forecast

Forecasting Models Forecasting Models

Forecasting Techniques

Qualitative

Models Time Series

Methods Delphi

Method Jury of Executive

Opinion

Naive Moving Average

Causal Methods

Sales Force Composite Consumer Market

Survey

Weighted Moving Average

Exponential Smoothing Trend Analysis

Seasonality Analysis Simple

Regression Analysis

Multiple Regression

Analysis

Multiplicative Decomposition

Model Differences Model Differences

• Qualitative – incorporates judgmental & subjective factors into forecast.

• Time-Series – attempts to predict the future by using historical data.

• Causal – incorporates factors that may influence

• Causal – incorporates factors that may influence the quantity being forecasted into the model

Qualitative Forecasting Models Qualitative Forecasting Models

• Delphi method

• Iterative group process allows experts to make forecasts

• Participants:

• decision makers: 5 -10 experts who make the forecast

• staff personnel: assist by preparing, distributing, collecting, and summarizing a series of questionnaires and survey results

summarizing a series of questionnaires and survey results

• respondents: group with valued judgments who provide input to decision makers

Qualitative Forecasting Models Qualitative Forecasting Models

(cont) (cont)

• Jury of executive opinion

• Opinions of a small group of high level managers, often in combination with statistical models.

• Result is a group estimate.

• Sales force composite

• Each salesperson estimates sales in his region.

• Each salesperson estimates sales in his region.

• Forecasts are reviewed to ensure realistic.

• Combined at higher levels to reach an overall forecast.

• Consumer market survey.

• Solicits input from customers and potential customers regarding future purchases.

• Used for forecasts and product design & planning

Metode Peramalan Deret Waktu Metode Peramalan Deret Waktu

(Time Series Methods) (Time Series Methods)

• Teknik peramalan yang menggunakan data-data historis penjualan beberapa waktu terakhir dan

mengekstrapolasinya untuk meramalkan penjualan di masa depan

• Peramalan deret waktu mengasumsikan pola

kecenderungan pemasaran akan berlanjut di masa depan.

13

kecenderungan pemasaran akan berlanjut di masa depan.

• Sebenarnya pendekatan ini cukup naif, karena

mengabaikan gejolak kondisi pasar dan persaingan

Langkah

Langkah--langkah Peramalan Deret Waktulangkah Peramalan Deret Waktu

• Kumpulkan data historis penjualan

• Petakan dalam diagram pencar (scatter diagram)

• Periksa pola perubahan permintaan

• Identifikasi faktor pola perubahan permintaan

• Pilih metode peramalan yang sesuai

14

• Pilih metode peramalan yang sesuai

• Hitung ukuran kesalahan peramalan

• Lakukan peramalan untuk satu atau beberapa periode mendatang

TTrend , Seasonalityrend , Seasonality Analysis Analysis

• Trend - long-term movement in data

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

Time Series

Time Series Methods Methods

year’s duration

• Seasonality - short-term regular variations in data

• Random variations - caused by chance

Pola Kecenderungan Data Historis Penjualan Pola Kecenderungan Data Historis Penjualan

Forecast Error Forecast Error

• Bias - The arithmetic sum of the errors

• Mean Square Error - Similar to simple sample variance

t

t F

A Error

Forecast = −

T F

A MSE

t t

T

/ ) (

/T

| error forecast

|

2 T

1 t

2

−

=

=

∑

∑

=

• MAD - Mean Absolute Deviation

• MAPE – Mean Absolute Percentage Error

T F

A

MAD _{t t}

T

t

/

|

| /T

| error forecast

|

1

T

1 t

−

=

= ∑ ∑

= =

T A

F A

MAPE _{t t t}

T

t

/ ] /

| [|

100

1

−

= ∑

=

T F

A_{t t}

t

/ ) (

1

−

= ∑

=

Example Example

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

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= 9,50

MAPE= 1,28

Controlling the Forecast 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

Controlling the forecast Controlling the forecast

Quantitative Forecasting Models Quantitative Forecasting Models

• Time Series Method

• Naïve

• Whatever happened recently will happen again this time

(same time period)

F

_t

= Y

_t −1

• The model is simple and flexible

• Provides a baseline to measure other models

• Attempts to capture seasonal factors at the expense of

ignoring trend

data Monthly

:

data Quarterly

:

12 4

−

−

=

=

t t

t t

Y F

Y F

Naive Forecasts Naive Forecasts

Uh, give me a minute....

We sold 250 wheels last week.... Now, next week we should sell....

we should sell....

The forecast for any period equals the previous period’s actual value.

Naïve Forecast Naïve Forecast

Wallace Garden Supply

Forecasting

Period

Actual Value

Naïve

Forecast Error

Absolute Error

Percent Error

Squared Error

January 10 N/A

February 12 10 2 2 16,67% 4,0

March 16 12 4 4 25,00% 16,0

Storage Shed Sales

April 13 16 -3 3 23,08% 9,0

May 17 13 4 4 23,53% 16,0

June 19 17 2 2 10,53% 4,0

July 15 19 -4 4 26,67% 16,0

August 20 15 5 5 25,00% 25,0

September 22 20 2 2 9,09% 4,0

October 19 22 -3 3 15,79% 9,0

November 21 19 2 2 9,52% 4,0

December 19 21 -2 2 10,53% 4,0

0,818 3 17,76% 10,091

BIAS MAD MAPE MSE

Naïve Forecast Graph Naïve Forecast Graph

Wallace Garden - Naive Forecast

20 25

0 5 10 15

February March April May June July August September October November December

Period

Sheds Actual Value

Naïve Forecast

• Simple to use

• Virtually no cost

• Quick and easy to prepare

• Easily understandable

Naive Forecasts Naive Forecasts

• Easily understandable

• Can be a standard for accuracy

• Cannot provide high accuracy

Techniques for Averaging Techniques for Averaging

• Moving average

• Weighted moving average

• Exponential smoothingExponential smoothing

Moving Averages Moving Averages

• Moving average – A technique that averages a number of recent actual values, updated as new values become available.

MA

_n

=

A

_i

i = 1

∑

n

• The demand for wheels in a wheel store in the past 5 weeks were as follows. Compute a three-period

moving average forecast for demand in week 6.

83 80 85 90 94

MA

_n

=

n

Moving average & Actual demand Moving average & Actual demand

Moving Averages Moving Averages

Wallace Garden Supply

Forecasting

Period

Actual

Value Three-Month Moving Averages

January 10

Storage Shed Sales

January 10

February 12

March 16

April 13 10 + 12 + 16 / 3 = 12.67

May 17 12 + 16 + 13 / 3 = 13.67

June 19 16 + 13 + 17 / 3 = 15.33

July 15 13 + 17 + 19 / 3 = 16.33

August 20 17 + 19 + 15 / 3 = 17.00

September 22 19 + 15 + 20 / 3 = 18.00

October 19 15 + 20 + 22 / 3 = 19.00

November 21 20 + 22 + 19 / 3 = 20.33

December 19 22 + 19 + 21 / 3 = 20.67

Moving Averages Forecast Moving Averages Forecast

Wallace Garden Supply

Forecasting 3 period moving average

Input Data Forecast Error Analysis

Period Actual Value Forecast Error

Absolute error

Squared error

Absolute

% error

Month 1 10

Actual Value - Forecast

Month 1 10

Month 2 12

Month 3 16

Month 4 13 12,667 0,333 0,333 0,111 2,56%

Month 5 17 13,667 3,333 3,333 11,111 19,61%

Month 6 19 15,333 3,667 3,667 13,444 19,30%

Month 7 15 16,333 -1,333 1,333 1,778 8,89%

Month 8 20 17,000 3,000 3,000 9,000 15,00%

Month 9 22 18,000 4,000 4,000 16,000 18,18%

Month 10 19 19,000 0,000 0,000 0,000 0,00%

Month 11 21 20,333 0,667 0,667 0,444 3,17%

Month 12 19 20,667 -1,667 1,667 2,778 8,77%

Average 12,000 2,000 6,074 10,61%

Next period 19,667 BIAS MAD MSE MAPE

Moving Averages Graph Moving Averages Graph

Three Period Moving Average

20 25

0 5 10 15

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

Tim e

Value Actual Value

Forecast

Moving Averages Moving Averages

• Weighted moving average – More recent values in a series are given more weight in computing the

forecast.

Assumes data from some periods are more important than data from other periods (e.g. earlier periods).

Use weights to place more emphasis on some periods and less on Use weights to place more emphasis on some periods and less on others.

Example:

• For the previous demand data, compute a weighted average forecast using a weight of .40 for the most recent period, .30 for the next most recent, .20 for the next and .10 for the next.

• If the actual demand for week 6 is 91, forecast demand for week 7 using the same weights.

Weighted Moving Average Weighted Moving Average

Wallace Garden Supply

Forecasting

Period

Actual

Value Weights Three-Month Weighted Moving Averages

January 10 0,222

February 12 0,593

March 16 0,185

Storage Shed Sales

March 16 0,185

April 13 2,2 + 7,1 + 3 / 1 = 12,298

May 17 2,7 + 9,5 + 2,4 / 1 = 14,556

June 19 3,5 + 7,7 + 3,2 / 1 = 14,407

July 15 2,9 + 10 + 3,5 / 1 = 16,484

August 20 3,8 + 11 + 2,8 / 1 = 17,814

September 22 4,2 + 8,9 + 3,7 / 1 = 16,815

October 19 3,3 + 12 + 4,1 / 1 = 19,262

November 21 4,4 + 13 + 3,5 / 1 = 21,000

December 19 4,9 + 11 + 3,9 / 1 = 20,036

Next period 20,185

Sum of weights = 1,000

Weighted Moving Average Weighted Moving Average

Wallace Garden Supply

Forecasting 3 period weighted moving average

Input Data Forecast Error Analysis

Period Actual value Weights Forecast Error

Absolute error

Squared error

Absolute

% error

Month 1 10 0.222

Month 2 12 0.593

Month 2 12 0.593

Month 3 16 0.185

Month 4 13 12.298 0.702 0.702 0.492 5.40%

Month 5 17 14.556 2.444 2.444 5.971 14.37%

Month 6 19 14.407 4.593 4.593 21.093 24.17%

Month 7 15 16.484 -1.484 1.484 2.202 9.89%

Month 8 20 17.814 2.186 2.186 4.776 10.93%

Month 9 22 16.815 5.185 5.185 26.889 23.57%

Month 10 19 19.262 -0.262 0.262 0.069 1.38%

Month 11 21 21.000 0.000 0.000 0.000 0.00%

Month 12 19 20.036 -1.036 1.036 1.074 5.45%

Average 1.988 6.952 6.952 10.57%

Next period 20.185 BIAS MAD MSE MAPE

Sum of weights = 1.000

Exponential Smoothing Exponential Smoothing

• ES didefinisikan sebagai:

Keterangan:

F_t+1 = Ramalan untuk periode berikutnya D = Demand aktual pada periode t

t t

t D F

F ₊₁ = α + (1−α)

D_t = Demand aktual pada periode t

F_t = Peramalan yg ditentukan sebelumnya untuk periode t α = Faktor bobot

α besar, smoothing yg dilakukan kecil

α kecil, smoothing yg dilakukan semakin besar α optimum akan meminimumkan MSE, MAPE

Exponential Smoothing Exponential Smoothing

• Weighted averaging method based on previous forecast plus a percentage of the forecast error

F

_t

= F

_t-1

+ α (A

_t-1

- F

_t-1

)

forecast plus a percentage of the forecast error

• A-F is the error term, α is the % feedback

Exponential Smoothing Data Exponential Smoothing Data

Wallace Garden Supply

Forecasting

Exponential Smoothing Period

Actual

Value F_t α A_t F_t F_t+1

Storage Shed Sales

t α _{t t t+1}

January 10 10 0,1

February 12 10 + 0,1 *( 10 - 10 ) = 10,000

March 16 10 + 0,1 *( 12 - 10 ) = 10,200

April 13 10 + 0,1 *( 16 - 10 ) = 10,780

May 17 11 + 0,1 *( 13 - 11 ) = 11,002

June 19 11 + 0,1 *( 17 - 11 ) = 11,602

July 15 12 + 0,1 *( 19 - 12 ) = 12,342

August 20 12 + 0,1 *( 15 - 12 ) = 12,607

September 22 13 + 0,1 *( 20 - 13 ) = 13,347

October 19 13 + 0,1 *( 22 - 13 ) = 14,212

November 21 14 + 0,1 *( 19 - 14 ) = 14,691

December 19 15 + 0,1 *( 21 - 15 ) = 15,322

Exponential Smoothing Exponential Smoothing

Wallace Garden Supply

Forecasting Exponential smoothing

Input Data Forecast Error Analysis Period Actual value Forecast Error

Absolute error

Squared error

Absolute

% error

Month 1 10 10.000

Month 2 12 10.000 2.000 2.000 4.000 16.67%

Month 3 16 10.838 5.162 5.162 26.649 32.26%

Month 4 13 13.000 0.000 0.000 0.000 0.00%

Month 5 17 13.000 4.000 4.000 16.000 23.53%

Month 6 19 14.675 4.325 4.325 18.702 22.76%

Month 7 15 16.487 -1.487 1.487 2.211 9.91%

Month 8 20 15.864 4.136 4.136 17.106 20.68%

Month 9 22 17.596 4.404 4.404 19.391 20.02%

Month 10 19 19.441 -0.441 0.441 0.194 2.32%

Month 11 21 19.256 1.744 1.744 3.041 8.30%

Month 12 19 19.987 -0.987 0.987 0.973 5.19%

Average 2.608 9.842 14.70%

Alpha 0.419 MAD MSE MAPE

Next period 19.573

Exponential Smoothing Exponential Smoothing

Exponential Smoothing

15 20 25

Sheds Actual value

Forecast

0 5 10

January

February

March

April

May

June July

Aug ust

Sep tember

October Novem

ber

Decem ber

Sheds

Forecast

Techniques for Trend Techniques for Trend

• Develop an equation that will suitably describe trend, when trend is present.

• The trend component may be linear or nonlinear

• The trend component may be linear or nonlinear

• We focus on linear trends

Common Nonlinear Trends Common Nonlinear Trends

Parabolic

Exponential

Growth

Linear Trend Equation Linear Trend Equation

• F = Forecast for period t

F_t = a + bt

0 1 2 3 4 5 t

F_t

• F_t = Forecast for period t

• t = Specified number of time periods

• a = Value of F_t at t = 0

• b = Slope of the line

0 1 2 3 4 5 t

Example Example

• Sales for over the last 5 weeks are shown below:

Week: 1 2 3 4 5 Sales: 150 157 162 166 177

• Plot the data and visually check to see if a linear trend line is appropriate.

• Determine the equation of the trend line

• Predict sales for weeks 6 and 7.

Line chart Line chart

Sales

160 165 170 175 180

Sales

135 140 145 150 155 160

1 2 3 4 5

Week

Sales

Sales

Calculating a and b Calculating a and b

b = n (ty) - t y n t2 - ( t)2

∑

∑

∑

∑

∑

a = y - b t n

∑

∑

Linear Trend Equation Example Linear Trend Equation Example

t y

Week t² Sales ty

1 1 150 150

2 4 157 314

3 9 162 486

4 16 166 664

5 25 177 885

Σ t = 15 Σ t² = 55 Σ y = 812 Σ ty = 2499 (Σ t)² = 225

Linear Trend Calculation Linear Trend Calculation

b = 5 (2499) - 15(812)

5(55) - 225 = 12495-12180

275 -225 = 6.3

y = 143.5 + 6.3t

a = 812 - 6.3(15)

5 = 143.5

Linear Trend plot Linear Trend plot

165 170 175 180

Actual data Linear equation

135 140 145 150 155 160 165

1 2 3 4 5