3.forecastingclass

Demand Forecasting• Introduction

• Demand Forecasting Techniques– Qualitative Forecasting Methods

– Quantitative Forecasting Models

• Forecast Error

• Case: Yankee Fork and Hoe Company

• Designing a Demand Forecasting System for PPC

Forecasting Effective planning requires matching

product requirements of customers with the capacity of operations

Forecasting: Predicting future events, such as, customer demand

Demand forecast is generally daily/weekly/monthly/quarterly figure for each product/product group in a geographic region

Patterns of Demand /Components of Demand

Component of demand include:

1) Horizontal/Permanent/Base Demand

2)Trends

3)Cycle

4) Seasonal

5) Promotional

6) Irregular or Random fluctuation (noise)

Patterns of Demand /Components of Demand

• Horizontal/Permanent/Base- data cluster about a horizontal line.

• Trends are noted by a gradual upward or downward sloping line.

• Cycle is a data pattern (up or down movement) that may cover several years before it repeats itself.

• Seasonality is a data pattern (periodic oscillation in demand) that repeats itself over the period of one year or less.

• Promotional: Demand swing initiated by a firm’s marketing initiatives such as advertising, deals or promotions (known to the firm so need not be forecast)

• Random fluctuation (noise) results from random variation or unexplained causes.

Patterns of Demand: BaseQ

uant

ity

Time

(a) Horizontal/Base: It represents long term average after the remaining components have been removed. Data cluster about a horizontal line.

Patterns of Demand: TrendQ

uant

ity

Time

(b) Trend: Long term shift in periodic sales. Data consistently increase or decrease.

Patterns of Demand: SeasonalQ

uant

ity

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

Months(c) Seasonal: Recurring upward/downward trend repeated within a year.

Year 1

Patterns of Demand: SeasonalQ

uant

ity

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

Months

Year 1

Year 2

(c) Seasonal: Data consistently show peaks and valleys.

Patterns of Demand: CyclicalQ

uant

ity

| | | | | |1 2 3 4 5 6

Years(c) Cyclical: Data reveal gradual increases and

decreases over extended periods.

Forecasting Techniques Forecasting is both an art & a science. The

science part deals with mathematical models, whereas the art part deals with judgment, experience and intuition. Thus, two broad methods

Qualitative methods (subjective) Based on subjective methods

Quantitative methods (objective) Based on mathematical formulas

Forecasting Techniques Qualitative Methods (subjective)• experts’ intuition, experience, opinions• not repeatable by others.• Used when

– little or no historical data available– Unstable environment during forecast horizon– Forecast has long time horizon

• Methods Available– Jury of executive opinion– Sales force composite– Delphi method– Consumer market survey

Qualitative Methods

Jury of Executive Opinion

Given sales data and other reports, a group of high-level executives give their estimates of future demand. These estimates are summarized

Main disadvantages-

– Top level executives are not close to the customers

– Power struggles occur among executives

Qualitative Methods

Sales Force Composite

Each salesperson provides an estimate of sales for his/her territory, and then the results are aggregated for all territories. This approach is often called the grass roots approach because salespeople are close to customers.

Main disadvantages-– Overestimate for fear of losing job/territory– Underestimate to have the quota set at a low level

and reap good bonuses

Qualitative Methods

Delphi Method

A coordinator asks a group of outside experts to estimate future demand. A statistical summary of their responses is prepared and sent back to the experts who can then revise their estimates if they choose to do so. The purpose is to reach consensus. Names of the participants are not revealed.

Main disadvantages– lengthy process

Qualitative Methods

Market Research

A systematic approach to determine consumer interest in a product or service by creating and testing hypotheses through data-gathering surveys.

Disadvantage

– Poor response rate

Forecasting Techniques

Quantitative methods (objective)• mathematical models of relationships between variables,

repeatable method

• Types of quantitative models

1. Time series methods: analyze the pattern in past demand to project demand in future period

2. Causal model: Forecast by Regression/Causal methods estimates sales on the basis of values of other independent factors.

Quantitative models: Time series models

• A time series is a set of numbers where the order or sequence of the numbers is important, e.g., historical demand

• Analysis of the time series identifies patterns

• Once the patterns are identified, they can be used to develop a forecast

Components of Demand in Time Series

• Permanent (Base) component, B• Trend, T• Seasonal, S• Cyclic, C• Promotion, P• Random, et

• ExamplesYt = (B + T) + S + et , additiveYt = (B + T) x S + et , multiplicative

Seasonal Patterns

Period

Dem

and

(a) Multiplicative pattern

| | | | | | | | | | | | | | | |0 2 4 5 8 10 12 14 16

Quantitative Method: Time-Series Methods

• Naive approach

• Moving averages

• Exponential smoothing

• Trend projection (linear regression)

• Seasonal influences

• Combined seasonal and trend

Time-series methodNaive forecasting

The forecast for the next period equals the demand for the current period. The naïve forecast can take into account a demand trend - the forecast is increased with the number with which it missed the last time. The advantages of the naive forecasts are its simplicity and low cost.

Example - If demand for Wednesday was 35 people, then forecast for Thursday is 35 people. If 42 on Thursday, then 42 is the forecast for Friday. With trend it will be 49.

Simple Moving Average, SMA(n)

Ft+1 = [Dt + Dt-1 + ... + Dt-n+1 ]/n

• Small n, more responsive to changes in data

• Large n, more stable forecasts over time

• n is typically between 3 & 10

Time-Series MethodsSimple Moving Averages

Week

450 —

430 —

410 —

390 —

370 —

| | | | | |0 5 10 15 20 25 30

Actual patientarrivals

Patie

nt a

rriv

als



Week

450 —

430 —

410 —

390 —

370 —

| | | | | |0 5 10 15 20 25 30

PatientWeek Arrivals

1 4002 3803 411

F4 = 411 + 380 + 4003

= 397Patie

nt a

rriv

als


Week

450 —

430 —

410 —

390 —

370 —

| | | | | |0 5 10 15 20 25 30


3-week MAforecast

6-week MAforecast

Patie

nt a

rriv

als

Weighted Moving Average, WMA(n)

Moving averages are unresponsive/sluggish to change, to partially overcome this we use weighted average

Ft+1 = w1 Dt + w2 Dt-1 + ... + wn Dt-n+1

One method to assign weights (not the only method):

• w1 > w2 > ... > wn > 0, weights sum to 1

• Sum-of-digits weights

S= 1+2+...+n

w1 = n/S, w2 = (n-1)/S, ……, wn = 1/S

Time-Series MethodsWeighted Moving Average

450 —

430 —

410 —

390 —

370 —

Week

| | | | | |0 5 10 15 20 25 30


3-week MAforecast

6-week MAforecastWeighted Moving Average

Assigned weightst 0.70

t-1 0.20t-2 0.10

F4 = 0.70(411) + 0.20(380) +0.10(400) =403.7

Patie

nt a

rriv

als

Simple Exponential Smoothing, SES (α)

• To overcome the drawback of large data requirements of moving averages, SES implicitly considers previous points. It is a sophisticated weighted moving average technique.

Ft+1 = Ft +α( Dt - Ft)Ft+1 = α Dt + α (1− α) Dt-1 + α (1− α)2 Dt-2 +……

+(1− α) t F0 • smoothing constant 0 ≤ α ≤ 1• Dt - Ft = forecasting error in period t• Larger α values make forecast more responsive• If α=1, naive model• In practice, 0.05 ≤ α ≤ 0.30

Weights & Initial Forecasts

• w1 =α, w2 =α(1- α ), w3 =α(1- α )2 ...• Initial forecast required

– use actual value at initial period

F1 = D1

– use average of some initial actual values

F1 = [D1 + D2 + D3 ]/3

Time-Series MethodsExponential Smoothing

450 —

430 —

410 —

390 —

370 —

Week

| | | | | |0 5 10 15 20 25 30

Exponential Smoothingα = 0.10

Ft +1 = Ft + α (Dt – Ft )

Patie

nt a

rriv

als


450 —

430 —

410 —

390 —

370 —

Week

| | | | | |0 5 10 15 20 25 30


F4 = 0.10(411) + 0.90(390)

F3 = (400 + 380)/2D3 = 411

Ft +1 = Ft + α (Dt – Ft )

Patie

nt a

rriv

als


450 —

430 —

410 —

390 —

370 —

Week

| | | | | |0 5 10 15 20 25 30

F4 = 392.1


F3 = (400 + 380)/2D3 = 411

Ft +1 = Ft + α (Dt – Ft )

Patie

nt a

rriv

als


Week

450 —

430 —

410 —

390 —

370 —

| | | | | |0 5 10 15 20 25 30

F4 = 392.1D4 = 415


F4 = 392.1 F5 = 394.4

Ft +1 = Ft + α (Dt – Ft )

Patie

nt a

rriv

als


450 —

430 —

410 —

390 —

370 —Patie

nt a

rriv

als

Week

| | | | | |0 5 10 15 20 25 30

Exponential smoothing

α = 0.10


450 —

430 —

410 —

390 —

370 —Patie

nt a

rriv

als

Week

| | | | | |0 5 10 15 20 25 30

3-week MAforecast

6-week MAforecast

Exponential smoothing

α = 0.10

Time-Series MethodsTrend-Adjusted Exponential Smoothing

A = average; T = Trend

α =smoothing constant for average;

β = smoothing constant for trend

At = α Dt + (1-α) (At-1 + Tt-1)

Tt = β (At – At-1) + (1- β) Tt-1

Ft+1 = At + Tt


| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80 —

70 —

60 —

50 —

40 —

30 —

Patie

nt a

rriv

als

Week

A1 = 0.2(27) + 0.80(28 + 3)T1 = 0.2(30.2 - 28) + 0.80(3)

Medanalysis, Inc.Demand for blood analysis

A0 = 28 patients T0 = 3 patientsα = 0.20 β = 0.20

At = α Dt + (1 – α)(At-1 + Tt-1)Tt = β (At – At-1) + (1 – β)Tt-1


| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80 —

70 —

60 —

50 —

40 —

30 —

Patie

nt a

rriv

als

Week

A1 = 30.2T1 = 2.8


A0 = 28 patients T0 = 3 patientsα = 0.20 β = 0.20

At = α Dt + (1 – α)(At-1 + Tt-1)Tt = β (At – At-1) + (1 – β)Tt-1

Forecast2 = 30.2 + 2.8 = 33


| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80 —

70 —

60 —

50 —

40 —

30 —

Patie

nt a

rriv

als

Week


A2 = 30.2 D2 = 44 T1 = 2.8α = 0.20 β = 0.20

At = α Dt + (1 – α)(At-1 + Tt-1)Tt = β (At – At-1) + (1 - β)Tt-1

A2 = 0.2(44) + 0.80(30.2 + 2.8)T2 = 0.2(35.2 - 30.2) + 0.80(2.8)


| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80 —

70 —

60 —

50 —

40 —

30 —

Patie

nt a

rriv

als

Week


A2 = 30.2 D2 = 44 T1 = 2.8α = 0.20 β = 0.20

At = α Dt + (1 – α)(At-1 + Tt-1)Tt = β (At – At-1) + (1 - β)Tt-1

A2 = 35.2T2 = 3.2

Forecast = 35.2 + 3.2 = 38.4


| | | | | | | | | | | | | | |0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

80 —

70 —

60 —

50 —

40 —

30 —

Patie

nt a

rriv

als

Week

Trend-adjusted forecast

Actual blood test requests

Quarter Year 1 Year 2 Year 3 Year 41 45 70 100 1002 335 370 585 7253 520 590 830 11604 100 170 285 215

Total 1000 1200 1800 2200Average 250 300 450 550

Seasonal Index = Actual Demand

Average Demand

Time-Series MethodsSeasonal Influences

Quarter Year 1 Year 2 Year 3 Year 41 45/250 = 0.18 70/300 = 0.23 100/450 = 0.22 100/550 = 0.182 335/250 = 1.34 370/300 = 1.23 585/450 = 1.30 725/550 = 1.323 520/250 = 2.08 590/300 = 1.97 830/450 = 1.84 1160/550 = 2.114 100/250 = 0.40 170/300 = 0.57 285/450 = 0.63 215/550 = 0.39



Quarter Average Seasonal Index1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20234



Quarter Average Seasonal Index1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.202 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.303 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50



Quarter Average Seasonal Index Forecast1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 1302 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.303 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50

Projected Annual Demand = 2600Average Quarterly Demand = 2600/4 = 650



Quarter Average Seasonal Index Forecast1 (0.18 + 0.23 + 0.22 + 0.18)/4 = 0.20 650(0.20) = 1302 (1.34 + 1.23 + 1.30 + 1.32)/4 = 1.30 650(1.30) = 8453 (2.08 + 1.97 + 1.84 + 2.11)/4 = 2.00 650(2.00) = 13004 (0.40 + 0.57 + 0.63 + 0.39)/4 = 0.50 650(0.50) = 325


Linear Trend and Seasonality

• A more refined method will be discussed

Choosing a MethodFORECAST ACCURACY

FORECAST ACCURACY refers to the difference between forecasts and corresponding actual sales.

Choosing a MethodForecast Error

Measures of Forecast Error

Et = Dt – Ft

Σ|Et |n

ΣEt2

n

CFE = ΣEt

MSE =

MAD = MAPE = Σ[|Et | (100)]/Dt

n

Absolute Error Absolute Percent

Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et

2 |Et| (|Et|/Dt)(100)1 200 225 -25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7

Total –15 5275 195 81.3%



Absolute Error Absolute Percent

Month, Demand, Forecast, Error, Squared, Error, Error, t Dt Ft Et Et

2 |Et| (|Et|/Dt)(100)1 200 225 –25 625 25 12.5% 2 240 220 20 400 20 8.3 3 300 285 15 225 15 5.0 4 270 290 –20 400 20 7.4 5 230 250 –20 400 20 8.7 6 260 240 20 400 20 7.7 7 210 250 –40 1600 40 19.0 8 275 240 35 1225 35 12.7

Total –15 5275 195 81.3%

MSE = = 659.45275

8

CFE = – 15

Measures of Error

MAD = = 24.41958

MAPE = = 10.2%81.3%

8

E = = – 1.875– 15 8

Linear Trend With Seasonality

• Carpet example

• Apply linear trend model

• 1st & 2nd quarter errors positive

• 3rd & 4th quarter errors negative

• Seasonality present

• Multiplicative model

Dt = [a + bt] cs + et

a + bt = 135.7 + 12.2 t = linear trend component

cs = quarterly seasonal factor

Linear trend applied to carpet dataDt Ft

t Yr Qtr Act. Fcst. Errors Error2

1 1 1 160 147.9 +12.1 146.42 1 2 170 160.1 +9.9 98.03 1 3 140 172.3 -32.3 1043.34 1 4 150 184.5 -34.5 1190.35 2 1 230 196.7 +33.3 1108.96 2 2 240 108.9 +31.1 967.27 2 3 180 221.1 -41.1 1689.28 2 4 200 233.3 -33.3 1108.99 3 1 310 245.5 +64.5 4160.310 3 2 310 257.5 +52.3 2735.311 3 3 230 269.9 -39.9 1592.012 3 4 260 282.1 -22.1 488.4

MAD = 33.9 MSE = 1360.7

Carpet Data & Trend Line1 2 170 160.1 9.9 981 3 140 172.3 -32.3 1043.31 4 150 184.5 -34.5 1190.32 1 230 196.7 33.3 1108.92 2 240 108.9 31.1 967.22 3 180 221.1 -41.1 1689.22 4 200 233.3 -33.3 1108.93 1 320 245.5 64.5 4160.33 2 310 257.5 52.3 2735.33 3 230 269.9 -39.9 15923 4 260 282.1 -22.1 488.4

MAD = 33.9 MSE = 1360.7Carpet Fcst

160 147.9170 160.1140 172.3150 184.5230 196.7240 208.9180 221.1200 233.3320 245.5310 257.7230 269.9260 282.1

120

170

220

270

320

370Sa

les

Time

Carpet

Constructing Model1. Compute 4-period moving averages,

e.g., average quarters 1-4, then quarters 2-5

2. Compute centered moving averages (CMA),

[avg for 1-4 + avg for 2-5]/2

3. Compute seasonal ratios

4. = Actual/CMA = Col(1)/Col(3)

5. Estimate cs = average of seasonal ratios for season s

6. Deseasonalize data = Actual/ cs

7. Estimate “a” & “b” for deseasonalized data

8. Forecast = deseasonalized forecast x cs for quarter

(1) (2) (3) (4) (5) (6)t Yr Qtr Act. MA CMA SI cs Deseas.1 1 1 160 1.191 134

2 1 2 170 1.153 147155.0

3 1 3 140 163.75 0.855* 0.830* 169172.5

4 1 4 150 181.25 0.828 0.826 182190.0

5 2 1 230 195.00 1.179 1.191 193200.0

6 2 2 240 506.25 1.164 1.153 208212.5

7 2 3 180 222.50 0.809* 0.830 217232.5

8 2 4 200 241.25 0.829 0.826 242250.0

9 3 1 310 256.25 1.210 1.191 260262.5

10 3 2 310 270.00 1.148 1.153 269277.5

11 3 3 230 0.830 277

12 3 4 260 0.826 315

Computing Termsc1 = (1.179 + 1.210)/2 = 1.195 x [4/4.011] = 1.191

c2 = (1.164 + 1.148)/2 = 1.156 x [4/4.011] = 1.153

c3 = (0.855 + 0.809)/2 = 0.832 x [4/4.011] = 0.830

c4 = (0.828 + 0.829)/2 = 0.828 x [4/4.011] = 0.826

Totals 4.011 4.000

Use deseasonalized data to compute a & b

b = 15.4, a = 117.6

Ft = [117.6 + 15.4 t] cs

Ft = [117.6 + 15.4 (6)] 1.153 = 242

Dt Ftt Yr Qtr Act. Fcst Error Error2

1 1 1 160 158 +2 42 1 2 170 171 -1 13 1 3 140 136 +4 164 1 4 150 148 +2 45 2 1 230 232 -2 46 2 2 240 242 -2 47 2 3 180 187 -7 498 2 4 200 199 +1 19 3 1 310 305 +5 2510 3 2 310 313 -3 911 3 3 230 238 -8 6412 3 4 260 250 +10 100

MAD = 3.9 MSE = 23.4

Case: Yankee Fork and Hoe Company

Forecasting Techniques: Causal/Regression Model

Forecast by Regression/Causal methods estimates sales on the basis of values of other independent factors. Use historical data on independent variables, such as promotional campaigns, economic conditions and competitors actions to predict demand

Quantitative Approach: Causal

Method/Regression Model(Linear Regression)

Dep

ende

nt v

aria

ble

Independent variableX

Y

Actualvalueof Y

Estimate ofY fromregressionequation

Value of X usedto estimate Y

Deviation,or error

{

Regressionequation:Y = a + bX

Causal MethodsLinear Regression

Sales AdvertisingMonth (000 units) (000 $)

1 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0

a = – 8.137b = 109.23r = 0.98r2 = 0.96


Sales AdvertisingMonth (000 units) (000 $)

1 264 2.52 116 1.33 165 1.44 101 1.05 209 2.0

a = – 8.137b = 109.23r = 0.98r2 = 0.96

| | | |1.0 1.5 2.0 2.5

Advertising (thousands of dollars)

300 —

250 —

200 —

150 —

100 —

50 Y = – 8.137 + 109.23X

Sale

s (th

ousa

nds

of u

nits

)

Forecast for Month 6X = $1750, Y = 183.015, or 183,015 units

a = Y – bX b = ΣXY – nXYΣX 2 – n(X )2

Sales, Y Advertising, XMonth (000 units) (000 $) XY X 2 Y 2

1 264 2.5 660.0 6.25 69,6962 116 1.3 150.8 1.69 13,4563 165 1.4 231.0 1.96 27,2254 101 1.0 101.0 1.00 10,2015 209 2.0 418.0 4.00 43,681

Total 855 8.2 1560.8 14.90 164,259Y = 171 X = 1.64

Causal MethodsLinear Regression (formula)


a = Y – bX b = 1560.8 – 5(1.64)(171)

14.90 – 5(1.64)2


1 264 2.5 660.0 6.25 69,6962 116 1.3 150.8 1.69 13,4563 165 1.4 231.0 1.96 27,2254 101 1.0 101.0 1.00 10,2015 209 2.0 418.0 4.00 43,681

Total 855 8.2 1560.8 14.90 164,259Y = 171 X = 1.64



1 264 2.5 660.0 6.25 69,6962 116 1.3 150.8 1.69 13,4563 165 1.4 231.0 1.96 27,2254 101 1.0 101.0 1.00 10,2015 209 2.0 418.0 4.00 43,681

Total 855 8.2 1560.8 14.90 164,259Y = 171 X = 1.64

nΣXY – ΣX ΣY

[nΣX 2 – (ΣX) 2][nΣY 2 – (ΣY) 2]r =

Coefficient of Correlation (r)• The coefficient of correlation, r, explains the relative

importance of the relationship between x and y.

• The sign of r shows the direction of the relationship.

• The absolute value of r shows the strength of the relationship.

• The sign of r is always the same as the sign of b.

• r can take on any value between –1 and +1.

Coefficient of Correlation (r)

• Meanings of several values of r:

-1 a perfect negative relationship (as x goes up, ygoes down by one unit, and vice versa)

+1 a perfect positive relationship (as x goes up, ygoes up by one unit, and vice versa)

0 no relationship exists between x and y

+0.3 a weak positive relationship

-0.8 a strong negative relationship

Time Frame (How far to forecast?) Short-range, medium-range, long-range

Appropriate Variable to Forecast, Units of measure (What to forecast?)

Forecasting Technique (How to forecast?) Purpose of forecast and decisions from it Time and effort required Data availability

Designing a Demand Forecasting System: some considerations

Examples of Production Resource Forecasts

LongRange

MediumRange

ShortRange

Years

Months

Days,Weeks

Product Lines,Factory Capacities

ForecastHorizon

TimeSpan

Item BeingForecasted

Unit ofMeasure

Product Groups,Depart. Capacities

Specific Products,Machine Capacities

Dollars,Tons

Units,Pounds

Units,Hours

Demand Forecast ApplicationsTime Horizon

Medium Term Long TermShort Term (3 months– (more than

Application (0–3 months) 2 years) 2 years)

Forecast quantity Individual Total sales Total salesproducts or Groups or familiesservices of products or

servicesDecision area Inventory Staff planning Facility location

management Production CapacityFinal assembly planning planning

scheduling Master production ProcessWorkforce scheduling management

scheduling PurchasingMaster production Distribution

schedulingForecasting Time series Causal Causal

technique Causal Judgment JudgmentJudgment

3.forecastingclass

Documents