Forecasting:

Forecasting is the art and science of predicting future events. It may involve taking historical data and projecting them into the future with some sort of mathematical model. It may be subjective or intuitive prediction. Or it may involve a combination of these-that is a mathematical model adjusted by a manager’s good judgment.

Types of Forecast:

Economic Forecast: Planning indicators valuable in helping organization prepare medium-to-long range forecasts.

Technological forecasts: Long term forecasts concerned with the rates of technological progress.

Demand forecasts: Projections of a company’s sales for each time period in the planning horizon.

Forecasting Time Horizons:

1. Short-range forecast : This forecast has a time span of up to 1 year but is generally less than 3 months. It is used for planning, purchasing, job scheduling, workforce levels, job assignments and production.

2. Medium-range forecast : A medium-range forecast generally spans from 3 months to 3 years. It is useful in sales planning, production planning and budgeting and analyzing various operating plans.

3. Long- range forecast : Generally 3 years more in time spans, long –range forecasts are used in planning for new products, capital expenditures, facility expansion, research and development.

Examples: Forecast in Business Organization,

Accounting: New product/process cost estimates, profit projections.

Finance: Timing and amount of finding/borrowing needs.

Human resources: Hiring activities, including recruitment, interviewing, training and counseling.

Marketing: Pricing and promotion, gl0bal competition strategies.

MIS: New/revised information system, internet services.

Operation: Schedules, work assignments and workload, project management.

Product or service design: Revision if current features, design of new products and services.

Step in the forecasting process:

1. Determine the purpose of the forecast .How will it be used and when will it be needed?

2. Select the items to be forecasted.3. Establish a time horizon. The forecast must indicate a time interval,

keeping in mind that accuracy decreases as the time horizons increases.

4. Select the forecasting model.5. Gather and analyze relevant data.6. Make the forecast.7. Monitor the forecast. A forecast has to be monitored to determine

whether it is performing in a satisfactory manner. If it is not, reexamine the method, assumption, validity of data, and so on; modify as needed, and prepare a revised forecast.

Forecasting Approach:

Qualitative or subjective forecasts incorporate such factors as the decision maker’s intuition, emotions, personal experience, and value system in reaching a forecast.

Quantitative forecasts that employ one or more mathematical models that rely on historical data and/or causal variables to forecast demand.

Overview of Qualitative method:

1. Jury of executive opinion: A forecasting technique that takes the opinion of a small group of high-level managers and results in a group estimate of demand.

2. Delphi method: A forecasting technique using a group process that allows experts to make forecasts. There are three different types of participants in the Delphi method: decision makers staff personnel, and respondents. Decision makers usually consist of a group of 5 to 10 experts who will be making the actual forecast. Staff personnel assist decision makers by preparing, distributing, collecting and summarizing a series of questionnaires and survey results. The respondents are a group of people, often located in the different places, whose judgment are valued. This group provides inputs to the decision makers before the forecast is made.

3. Sales force opinions: The sales or the customer service staff is often a good source of information because of their direct contact with consumers. Sales force composite is a forecasting technique based on salespersons estimates of expected sales.

4. Consumer market survey: A forecasting method that solicits input from customers or potential customers regarding future purchasing plans.

Measuring Forecast Error:

Forecast error is the difference between the actual value and value that was predicted for a given period. If Ft denotes the forecast in period t, and At denotes the actual demand in period t, the forecast error is defined as-

Forecast error= Actual demand – Forecast demand

= At - Ft

Three commonly used measures for summarizing historical errors are the mean absolute deviation (MAD), the mean squared error (MSE) and the mean absolute percent error.

Mean Absolute Deviation (MAD):

MAD is the average absolute forecast error.

MAD= ∑ ¿ ACTUALi−Forecast i∨¿n¿ =∑ ¿( Ai−F i¿)∨

¿n¿¿ = ∑ Di

n

Mean squared error: The average of the squared differences between the forecasted and observed values.

MSE = ∑ ¿¿¿

Mean Absolute Percent Error (MAPE): The average of the absolute differences between the forecast and absolute values, expressed as a percent of actual values.

MAPE = 100∑i=1n

|Actuali−Foecasti|/ Actuali

n

Overview of Quantitative Methods:

Time series forecasts: A forecasting technique that uses a series of past data points to make a forecast.

1. Moving averages2. Naïve approach 3. Exponential smoothing 4. Trend projection.

Associative Model: Forecasting technique that was explanatory variables to predict future demand.

1. Linear regression

Moving Average:

A moving average forecast uses a number of the most recent actual data values in generating a forecast. The moving average forecast can be computed using the following equation.

Ft= MAn = ∑i=1n

A t−i

n

Where, i= an index that corresponds to time period.

n= Number of period (data points) in the moving average.

AI=Actual value in period t-i.

MA= Moving average.

Ft= Forecast for time period.

Weighted Moving Average:

A moving average with most recent demand values adjusted with weights. A weighted average may be expressed mathematically as-

WMAn = ∑ (weight for period i )(Demand∈period i)

∑Weight

=∑ wi Di=∑w i A i

Where actual value Ai=Di and w i the weight of period i, between 0 and 100 percent.

∑ wi=1 .

Note: Moving average is useful if we can assume that market demand will stay fairly steady over time.

Problem (1.1): A manufacturing has monthly demand for one of its production as follows:

Month Demand February 520 March 490 April 550 May 580 June 600 July 420 August 510 September 610

a) Develop a three period moving average forecast and a three period weight moving average forecast with weight of 0.50, 0.30, 0.20 for the most recent demand values, in that order.

b) Calculate MAD for each forecast, and indicate which would seem to be most accurate.

Solution:

Step-1: Compute the 3 month moving average using the formula

MA= ∑I =13

Di

3

For many, the moving average forecast is-

MA3= 520+490+5503 ¿520

Step-2: Compute the 3 month weighted moving average using the formula-

WMA3= ∑ wi Di

For many, the weighted moving average forecast is-

WMA3 = 0.50×550+0.30×490+0.20×520=526

The value for both moving average forecast are shown in the table:

Month (1) Demand(2) MA3(3) WMA3(4) Absolute for MAD(MA3)[2-3]

Absolute for MAD(WMA3) [2-4]

February 520 - - - -March 490 - - - -April 550 - - - -May 580 ¿¿ 526 60 54June 600 490+550+580

3=540 553 60 47

July 420 550+580+6003

=576.67 584 156.67 164

August 510 580+600+4203

=533.33 506 23.33 4

September 610 600+420+5103

=510 501 110 109

October 420+510+6103

=513.33 542

535 532.22 535.33

Step3: Compute the MAD Value for both forecasts:

MAD = ∑ ¿ Dt−F t∨¿n

¿ Or∑ ( Actual demand−Forecast)n

Moving average MAD =60+60+156.67+23.33+1105=82.0

Weighted Moving average MAD= ∑ Actual demand−Weightedn

=54+47+164+4+109

5

= 75.6

The MAD value for the 3 month moving average is 82.0 and the MAD value for the 3 month weighted moving average is 75.6, indicating that there is not much difference in accuracy between the two forecast, the weight moving average is slightly better.

Problem (2.1):

A large manufacturer uses exponential smoothing to forecast demand for a piece of pollution control equipment. It appears that an increasing trend is present.

Math (t) Actual Demand(At) 1 12 2 17 3 20 4 19 5 24 6 21 7 31 8 28 9 36 10 ?

Smoothing constants are assigned the value of ∝=0.2 and β=0.4. Assume that the initial forecast for month 1 (F1) was 11 units and the trend over the period (T1) was 2 units.

Month Actual Demand Smoothed forecast (Ft)

Smoothed Trend (Tt)

Forecasting including trend(FITt)

1 12 11 2 13 2 17 12.8 1.92 14.72 3 20 15.18 2.10 17.28 4 19 17.82 2.32 20.14 5 24 19.91 2.23 22.14 6 21 22.51 2.38 24.89 7 31 24.11 2.07 26.18 8 28 27.14 2.45 29.59 9 36 29.28 2.32 31.60 10 - 32.48 2.68 35.16

Exponential Smoothing with trend Adjustment:

Exponential smoothing is a weighted averaging method based on previous forecast plus a percentage of the forecast error.

With trend adjusted exponential smoothing, estimates for both the average and the trend are smoothed. This procedure requires two smoothing constants, ∝ for the average and β for the trend. The computational procedure is-

Step1: Compute Ft, the exponential smoothed forecast for period t, by using equation

Ft= ∝( At−1)+(1−∝)(F t−1+T t−1)

I.e. Ft = ∝ ( Actual demand last period )+(1−∝ ) ( Forecast last period+Trend estimate last period )

Where, 0≤∝≤1

Step 2: Computed the smoothed trend, Tt, using equation-

T t=β ( F t−F t−1 )+(1−β )T t−1

i.e. T t=β ( Forecast this period−Forecast last period )+¿

(1−β ) (Trend estimate last period )

Step 3: Calculate forecast including trend,FIT t , by the formula

FIT t=F t+T t

Problem (1-2): The monthly sales for Telco batteries, inc. were as follows.

Monthly: Jan Feb Mar Apr may June July Aug Sep Oct Nov Dec

Sales: 20 21 15 14 13 16 17 18 20 20 21 23

a. Plot the monthly sales data on a sheet of a graph paper.

b. Forecast journey sales using each of the following-

1. A 3month moving average

2. A 3 month weighted moving average using .2, .3, .5 with the heaviest weights applied to the most recent month.

3. Exponential smoothing using an ∝=0.3 and a September forecast of 18.

4. A trend projection.

c. With the data given, which method allow you to forecast next march’s sales?

Exponential smoothing:

Exponential smoothing is a weighted moving average forecasting technique in which data points are weighted by an exponential function.

Smoothing constant is the weighted factor used in an exponential smoothing forecast; a number between 0 to 1, the equation is-

F t=F t−1+∝( At−1−Ft−1)

Where,

F t=new forecast

F t−1=¿ Previous forecast

=smoothing constant (0≤∝≤1)

At−1=previous periods actual demand.

Problem (1-1):

The data for sales in 2001 to 2005 are as follows:

Year: 2001 2002 2003 2004 2005 2006

Sales: 450 495 518 563 584 ?

Using exponential smoothing with a weight of∝=0.30 develops forecasting for 2002 to 2006 if initial forecast for 2001 is 410.

Solution:

year sales Forecast2001 450 4102002 495 410+.3(450-410)=4222003 518 422+.3(495-422)=443.92004 563 433.9+.3(518-443.9)=466.12005 584 466.1+.3(563-466.1)=495.22006 - 495.2+.3(584-495.2)=521.8

Problem (2.2):

Income at the law firm of Smith and Wesson for the period February to July was as

follows:

Month: February March April May June July

Income (in$ thousands): 70.0 68.5 64.8 71.7 71.3 72.8

Forecast for February is $65000 and the initial trend adjustment is 0. The smoothing

constants selected are ∝=0.1and β=0.2

Here ,∝=0.1∧β=0.2

MonthActual Income

$

Smoothed

forecast(F t)

$

smoothed trend

(T t)

$

Forecast

including(FIT ¿¿ t)¿

trend $

February 70.0 65000 0 65000

March 68.5 58507 1298.6 59805.6

April 64.8 53831.89 103.86 53935.75

May 71.7 48548.65 973.56 49522.21

June 71.3 44577.15 15.45 44592.6

July 72.8 40140.47 874.98 41015.45

Step1: Compute Ft, the exponential smoothed forecast for period t, by using equation

Ft= ∝( At−1)+(1−∝)(F t−1+T t−1)

I.e. Ft = ∝ ( Actual demand last period )+(1−∝ ) ( Forecast last period+Trend estimate last period )

March =0 .1(70) + (1-0.1) (65000+0) = 58507

April =0.1(68.5) + (1-0.1) (58507+1298.6) = 53831.89

May =0.1(64.8) + (1-0.1) (53831.89+103.86) = 48548.65

June =0.1(71.7) + (1-0.1) (48548.65+973.56) = 44577.15

July =0.1(71.3) + (1-0.1) (44577.15+15.45) = 40140.47

Where, 0≤∝≤1

Step 2: Computed the smoothed trend, Tt, using equation-

T t=β ( F t−F t−1 )+(1−β )T t−1

i.e. T t=β ( Forecast this period−Forecast last period )+¿

(1−β ) (Trend estimate last period )

March = 0.2(58507-65000) + (1-0.2)0 =1298.6

April = 0.2(53831.89-58507) + (1-0.2)1298.6 = 103.86

MAY = 0.2(48548.65-53831.89) + (1-0.2)103.86 = 973.56

June = 0.2(44577.15-48548.65) + (1-0.2)973.56 = 15.45

July = 0.2(40140.47-44577.15) + (1-0.2)15.45 = 874.98

Step 3: Calculate forecast including trend,FIT t , by the formula−¿

FIT t=F t+T t

February = (65000+0) = 65000

March = (58507+1298.6) = 59805.6

April = (53831.89+103.86) = 53935.75

May = (48548.65+973.56) = 49522.21

June = (44577.15+15.45) = 44592.6

July = (40140.47+874.98) =41015.45