opm topic 6 forecast

Operations&ProductionManagement 2/21/2015

ResourcePerson:Dr.MuhammadWasif 1

Operations & Production Management

(OPM)Dr. Muhammad Wasif

Visiting Faculty, IBA.

6 Forecasting

Resource Person : Dr. Muhammad Wasif Operations & Production Management7



Introduction to ForecastingSection 6.1


Forecasting

Resource Person : Dr. Muhammad Wasif Operations & Production Management

Process of predicting a future event

Underlying basis of all business

decisions

Production

Inventory

Personnel

Facilities



Applications of Forecasting


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

Forecasting Time Horizon


Short-range forecast Up to 1 year, generally less than 3 months Purchasing, job scheduling, workforce levels, job

assignments, production levels

Medium-range forecast 3 months to 3 years Sales and production planning, budgeting

Long-range forecast 3+ years New product planning, facility location, research and

development

Long-range forecasting

Medium-range forecasting

Short-range forecasting

Production/operation control



Influence of Product Life Cycle


Introduction and growth require longer forecasts than maturity

and decline

As product passes through life cycle, forecasts are useful in

projecting

Staffing levels (Human Resource Requirements)

Inventory levels (Supply chain management)

Factory capacity

Introduction Growth Maturity Decline

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



Seven Steps in Forecasting


1 Determine the use of the forecast Determine the use of the forecast

2 Select the items to be forecasted Select the items to be forecasted

3 Determine the time horizon of the forecast Determine the time horizon of the forecast

4 Select the forecasting model(s) Select the forecasting model(s)

5 Gather the data Gather the data

6 Make the forecast Make the forecast

7 Validate and implement results Validate and implement results

Forecasts Idealism & Reality


Seldom PerfectSeldom Perfect

Based on AssumptionsBased on Assumptions

Aggregate are more accurate than individualAggregate are more accurate than individual

Accuracy decreases as time horizon increasesAccuracy decreases as time horizon increases

Real

ity

TimelyTimely

ReliableReliable

AccurateAccurate

MeaningfulMeaningful

WrittenWritten

Easy to useEasy to use

Idea

l



Approaches to Forecast


Qualitative Methods

Used when situation is vague and little data exist; for example New

products, New technology

Involves intuition, experience. e.g., forecasting sales on Internet

Quantitative Methods

Used when situation is stable and historical data exist; for example Existing

products, Current technology

Involves mathematical techniques, e.g., forecasting sales of color televisions

Overview of Qualitative Methods


Jury of executive opinion

Involves small group of high-level experts and managers

Combines managerial experience with statistical models

Quick decisions but group think is disadvantage

Delphi method

Iterative group process, continues until consensus is

reached

3 types of participants; Decision makers, Staff,

Respondents



Overview of Qualitative Methods


Sales force composite

Each salesperson projects his or her sales

Combined at district and national levels

Tends to be overly optimistic

Consumer Market Survey

Ask customers about purchasing plans

What consumers say, and what they actually do are often different

Sometimes difficult to answer

Overview of Quantitative Approaches


1. Naive approach

2. Moving averages

3. Exponential smoothing

4. Trend projection

5. Linear regression

time-series models

associative model



Time Series ForecastingSection 6.2


Time Series Forecasting


Set of evenly spaced numerical data

Obtained by observing response variable at regular

time periods

Forecast based only on past values, no other

variables important

Assumes that factors influencing past and present

will continue influence in future





Trend Component

Persistent, overall upward or downward pattern

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

Typically several years duration

Seasonal Component

Regular pattern of up and down fluctuations

Due to weather, customs, etc.

Occurs within a single year

Number ofPeriod Length SeasonsWeek Day 7Month Week 4-4.5Month Day 28-31Year Quarter 4Year Month 12Year Week 52



Cyclical Component

Repeating up and down movements

Affected by business cycle, political, and economic factors

Multiple years duration

Random Component

Erratic, unsystematic, residual fluctuations

Due to random variation or unforeseen events

Short duration and nonrepeating



1- Naive Approach


Assumes demand in next

period 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

Simple to use, Virtually no cost

Cannot provide high accuracy

2- Moving Average Method


MA is a series of arithmetic means

Used if little or no trend

Used often for smoothing

Provides overall impression of data over time

Moving average = demand in previous n periodsn



2- Moving Average Method


January 10February 12March 13April 16May 19June 23July 26

Actual 3-MonthMonth Shed Sales Moving Average

(12 + 13 + 16)/3 = 13 2/3(13 + 16 + 19)/3 = 16(16 + 19 + 23)/3 = 19 1/3

101213

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

2- Weighted Moving Average Method


Used when some trend might be present

Older data usually less important

Weights based on experience and intuition



2- Weighted Moving Average Method


January 10February 12March 13April 16May 19June 23July 26

Actual 3-Month WeightedMonth Shed Sales Moving 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

101213

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

Weights Applied Period3 Last month2 Two months ago1 Three months ago6 Sum of weights

Potential Problems With Moving Average


Increasing n smooths the forecast but makes it less

sensitive to changes

Do not forecast trends well

Require extensive historical data



3 - Exponential Smoothing


Form of weighted moving average

Weights decline exponentially

Most recent data weighted most

Requires smoothing constant ()

Ranges from 0 to 1

Subjectively chosen

Involves little record keeping of past data

3 - Exponential Smoothing


Predicted demand = 142 Ford Mustangs

Actual demand = 153

Smoothing constant a = .20

Ft = Ft1 + (At1 - Ft1)

New forecast = 142 + .2(153 142) = 144.2 144 units



Effect of Smoothing Constants


Weight Assigned toMost 2nd Most 3rd Most 4th Most 5th Most

Recent Recent Recent Recent RecentSmoothing Period Period Period Period PeriodConstant () (1 - ) (1 - )2 (1 - )3 (1 - )4

= .1 .1 .09 .081 .073 .066

= .5 .5 .25 .125 .063 .031

Effect of Smoothing Constants


225

200

175

150 | | | | | | | | |1 2 3 4 5 6 7 8 9

Quarter

Dem

and

= .1

Actual demand

= .5

Chose high values of when underlying average is likely to change

Choose low values of when underlying average is stable



Choosing


The objective is to obtain the most accurate forecast no

matter the technique

We generally do this by selecting the model that gives

us the lowest forecast error

Forecast error = Actual demand - Forecast value

= At - Ft

Common Measures of Error


Mean Absolute Deviation (MAD)

MAD = |Actual - Forecast|

n

Mean Squared Error (MSE)

MSE = (Forecast Errors)2

n



Common Measures of Error


Mean Absolute Percent Error (MAPE)

MAPE =100|Actuali - Forecasti|/Actuali

n

n

i = 1

Comparison of Forecast Error


Rounded Absolute Rounded AbsoluteActual Forecast Deviation Forecast Deviation

Tonnage with for with forQuarter Unloaded = .10 = .10 = .50 = .50

1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62







1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

MAD = |deviations|

n

= 82.45/8 = 10.31For = .10

= 98.62/8 = 12.33For = .50





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

= 1,526.54/8 = 190.82For = .10

= 1,561.91/8 = 195.24For = .50

MSE = (forecast errors)2

n







1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62

= 44.75/8 = 5.59%For = .10

= 54.05/8 = 6.76%For = .50

MAPE =100|deviationi|/actuali

n

n

i = 1





1 180 175 5.00 175 5.002 168 175.5 7.50 177.50 9.503 159 174.75 15.75 172.75 13.754 175 173.18 1.82 165.88 9.125 190 173.36 16.64 170.44 19.566 205 175.02 29.98 180.22 24.787 180 178.02 1.98 192.61 12.618 182 178.22 3.78 186.30 4.30

82.45 98.62MAD 10.31 12.33MSE 190.82 195.24MAPE 5.59% 6.76%





0.2Actial F Dev. F Dev. F Dev. F Dev. F Dev.

1 180 175 5 175 5 175 5 175 5 175 52 168 175.5 7.5 176 8 176.5 8.5 177 9 177.5 9.53 159 174.75 15.75 174.4 15.4 173.95 14.95 173.4 14.4 172.75 13.754 175 173.18 1.82 171.32 3.68 169.465 5.535 167.64 7.36 165.88 9.125 190 173.36 16.64 172.056 17.944 171.1255 18.8745 170.584 19.416 170.44 19.566 205 175.05 29.95 175.6448 29.3552 176.7879 28.21215 178.3504 26.6496 180.22 24.787 180 178.02 1.98 181.5158 1.51584 185.2515 5.251495 189.0102 9.01024 192.61 12.618 182 178.22 3.78 181.2127 0.787328 183.676 1.676047 185.4061 3.406144 186.3 4.3

82.42 81.68237 87.99919 94.24198 98.62MAD 10.3025 10.2103 10.9999 11.78025 12.3275MAPE 5.591537 5.545828 5.992131 6.436648 6.755313

0.3 0.4 0.50.1

Exponential Smoothing with Trend Adjustment


When a trend is present, exponential smoothing must be modified

Forecast including (FITt) = trend

Exponentially Exponentiallysmoothed (Ft) + smoothed (Tt)forecast trend

Ft = (At - 1) + (1 - )(Ft - 1 + Tt - 1)

Tt = (Ft - Ft - 1) + (1 - )Tt - 1Step 1: Compute FtStep 2: Compute TtStep 3: Calculate the forecast FITt = Ft + Tt



Exponential Smoothing with Trend Adjustment Example


ForecastActual Smoothed Smoothed Including

Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 3610




Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 173 204 195 246 217 318 289 3610

F2 = A1 + (1 - )(F1 + T1)F2 = (.2)(12) + (1 - .2)(11 + 2)

= 2.4 + 10.4 = 12.8 units

Step 1: Forecast for Month 2






Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.803 204 195 246 217 318 289 3610

T2 = (F2 - F1) + (1 - )T1T2 = (.4)(12.8 - 11) + (1 - .4)(2)

= .72 + 1.2 = 1.92 units

Step 2: Trend for Month 2




Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.923 204 195 246 217 318 289 3610

FIT2 = F2 + T2FIT2 = 12.8 + 1.92

= 14.72 units

Step 3: Calculate FIT for Month 2






Month(t) Demand (At) Forecast, Ft Trend, Tt Trend, FITt1 12 11 2 13.002 17 12.80 1.92 14.723 204 195 246 217 318 289 3610

15.18 2.10 17.2817.82 2.32 20.1419.91 2.23 22.1422.51 2.38 24.8924.11 2.07 26.1827.14 2.45 29.5929.28 2.32 31.6032.48 2.68 35.16



| | | | | | | | |1 2 3 4 5 6 7 8 9

Time (month)

Prod

uct d

eman

d

35

30

25

20

15

10

5

0

Actual demand (At)

Forecast including trend (FITt)with = .2 and = .4



4 - Trend Projections


Fitting a trend line to historical data points to project

into the medium to long-range

Linear trends can be found using the least squares

technique

y = a + bx^

where y = computed value of the variable to be predicted (dependent variable)

a = y-axis interceptb = slope of the regression linex = the independent variable

^

Linear Regression Method


Time period

Valu

es o

f Dep

ende

nt V

aria

ble

Deviation1(error)

Deviation5

Deviation7

Deviation2

Deviation6

Deviation4

Deviation3

Actual observation (y-value)

Trend line, y = a + bx^

Least squares method minimizes the sum of the squared errors (deviations)



Linear Regression Method


Equations to calculate the regression variables

b =xy - nxyx2 - nx2

y = a + bx^

a = y - bx

Linear Regression Method - Example


b = = = 10.54xy - nxyx2 - nx2

3,063 - (7)(4)(98.86)140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

x = 28 y = 692 x2 = 140 xy = 3,063x = 4 y = 98.86





b = = = 10.54xy - nxyx2 - nx2

3,063 - (7)(4)(98.86)140 - (7)(42)

a = y - bx = 98.86 - 10.54(4) = 56.70

Time Electrical Power Year Period (x) Demand x2 xy

2003 1 74 1 742004 2 79 4 1582005 3 80 9 2402006 4 90 16 3602007 5 105 25 5252008 6 142 36 8522009 7 122 49 854

x = 28 y = 692 x2 = 140 xy = 3,063x = 4 y = 98.86

The trend line is

y = 56.70 + 10.54x^



| | | | | | | | |2003 2004 2005 2006 2007 2008 2009 2010 2011

160 150 140 130 120 110 100 90 80 70 60 50

Year

Pow

er d

eman

d

Trend line,y = 56.70 + 10.54x^



5 - Seasonal Variations In Data


The multiplicative seasonal model can adjust trend

data for seasonal variations in demand



Steps in the process:

1. Find average historical demand for each season

2. Compute the average demand over all seasons

3. Compute a seasonal index for each season

4. Estimate next years total demand

5. Divide this estimate of total demand by the number of seasons, then multiply it by the seasonal index for that season





Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94

Demand Average Average Seasonal Month 2007 2008 2009 2007-2009 Monthly Index

San Diego Hospital



Jan 80 85 105 90 94Feb 70 85 85 80 94Mar 80 93 82 85 94Apr 90 95 115 100 94May 113 125 131 123 94Jun 110 115 120 115 94Jul 100 102 113 105 94Aug 88 102 110 100 94Sept 85 90 95 90 94Oct 77 78 85 80 94Nov 75 72 83 80 94Dec 82 78 80 80 94


0.957

Seasonal index = Average 2007-2009 monthly demand

Average monthly demand

= 90/94 = .957

San Diego Hospital





Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851


San Diego Hospital



Jan 80 85 105 90 94 0.957Feb 70 85 85 80 94 0.851Mar 80 93 82 85 94 0.904Apr 90 95 115 100 94 1.064May 113 125 131 123 94 1.309Jun 110 115 120 115 94 1.223Jul 100 102 113 105 94 1.117Aug 88 102 110 100 94 1.064Sept 85 90 95 90 94 0.957Oct 77 78 85 80 94 0.851Nov 75 72 83 80 94 0.851Dec 82 78 80 80 94 0.851


Expected annual demand = 1,200

Jan x .957 = 961,200

12

Feb x .851 = 851,200

12

Forecast for 2010

San Diego Hospital





140

130

120

110

100

90

80

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

Time

Dem

and

2010 Forecast2009 Demand 2008 Demand2007 Demand

San Diego Hospital

San Diego Hospital




Associative ForecastingSection 6.3


Associative Forecasting


Forecasting an outcome based on predictor variables

using the least squares technique

where computed value of the variable to be predicted (dependent variable)

a = y-axis intercept

b = slope of the regression line

x = the independent variable though to predict the value of the dependent variable

a b x



Associative Forecasting - Example


Sales Local Payroll($ millions), y ($ billions), x

2.0 13.0 32.5 42.0 22.0 13.5 7

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll



Sales, y Payroll, x x2 xy2.0 1 1 2.03.0 3 9 9.02.5 4 16 10.02.0 2 4 4.02.0 1 1 2.03.5 7 49 24.5

y = 15.0 x = 18 x2 = 80 xy = 51.5





y = 1.75 + .25x^ Sales = 1.75 + .25(payroll)

If payroll next year is estimated to be $6 billion, then:

Sales = 1.75 + .25(6)Sales = $3,250,000

4.0

3.0

2.0

1.0

| | | | | | |0 1 2 3 4 5 6 7

Sale

s

Area payroll

3.25

Standard Error of the Estimate


A forecast is just a point estimate of a future value

This point is actually the mean

of a probability distribution



Standard Error of the Estimate


Sy,x = .306

The standard error of the estimate is $306,000 in sales

Monitoring and Controlling Forecasts


Tracking

Measures how well the forecast is predicting actual values

Ratio of running sum of forecast errors (RSFE) to mean absolute deviation (MAD)

Good tracking signal has low values

If forecasts are continually high or low, the forecast has a bias error



Monitoring and Controlling Forecasts


Tracking signal

RSFEMAD=

Tracking signal =

(Actual demand in period i -

Forecast demand in period i)

|Actual - Forecast|/n)

Tracking Signal


Tracking signal

+

0 MADs

Upper control limit

Lower control limit

Time

Signal exceeding limit

Acceptable range



Tracking Signal - Example


CumulativeAbsolute Absolute

Actual Forecast Forecast ForecastQtr Demand Demand Error RSFE Error Error MAD

(AD) (FD) (AD-FD) |RSFE| (CAF) CAF/Qtr

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2

Tracking Signal - Example


CumulativeAbsolute Absolute

Actual Forecast Forecast ForecastQtr Demand Demand Error RSFE Error Error MAD

1 90 100 -10 -10 10 10 10.02 95 100 -5 -15 5 15 7.53 115 100 +15 0 15 30 10.04 100 110 -10 -10 10 40 10.05 125 110 +15 +5 15 55 11.06 140 110 +30 +35 30 85 14.2

TrackingSignal

(RSFE/MAD)-10/10 = -1-15/7.5 = -2

0/10 = 0-10/10 = -1

+5/11 = +0.5+35/14.2 = +2.5

The variation of the tracking signal between -2.0 and +2.5 is within acceptable limits



Miscellaneous ForecastingSection 6.4


Adaptive Forecasting


Its possible to use the computer to continually

monitor forecast error and adjust the values of the a

and b coefficients used in exponential smoothing to

continually minimize forecast error

This technique is called adaptive smoothing



Focus Forecasting


Developed at American Hardware Supply, focus forecasting is

based on two principles:

1. Sophisticated forecasting models are not always better than simple ones

2. There is no single technique that should be used for all products or services

This approach uses historical data to test multiple

forecasting models for individual items

The forecasting model with the lowest error is then used to

forecast the next demand

Forecasting in the Service Sector


Presents unusual challenges

Special need for short term records

Needs differ greatly as function of industry and

product

Holidays and other calendar events

Unusual events



Fast Food Restaurant Forecast


20%

15%

10%

5%

11-12 1-2 3-4 5-6 7-8 9-1012-1 2-3 4-5 6-7 8-9 10-11

(Lunchtime) (Dinnertime)Hour of day

Perc

enta

ge o

f sa

les

FedEx Call Center Forecast


12%

10%

8%

6%

4%

2%

0%

Hour of dayA.M. P.M.

2 4 6 8 10 12 2 4 6 8 10 12




References

Operations Management, 10th Ed., by J. Heizer & B. Render

Operations Management, William J. Stevenson.

Operations Management, 7th Ed., N. Slack, A.B. Jones, R. Johnston.

Cases in Operations Management, S. Chambers, C. Harland, A. Harison, N. Slack.

opm topic 6 forecast

Documents

production planning

muhammad wasifvisiting

technological forecasts

workforce levels

years new product planning

years sales

product passes

forecasting models5