Assignment 2

Month Sales (1000)Feb 19Mar 18Apr 15May 20Jun 18Jul 22Aug 20

Given the following data

(a) Plot the data(b) Forecast for Sep. using linear

regression(c) Forecast for Sep. using 5 period

moving average(d) Forecast for Sep. using

exponential smoothing. Alpha is .2 and forecast for march was 19

(e) Forecast for Sep. using Naïve method

(f) Compute MAD for all

(a) Plot the Data

Month Sales (1000)1 Feb 192 Mar 183 Apr 154 May 205 Jun 186 Jul 227 Aug 20

Monthly Sales

0

5

10

15

20

25

0 2 4 6 8

Month

Sa

le (

10

00

)

Monthly Sales

(b-1)Forecast for Sep Using Regression

Linear Trend Equation, Regression, Lest Square Method are alternative names for the same method.

X Y1 192 183 154 205 186 227 20

Linear Regression

X Y XY X^21 19 19 12 18 36 43 15 45 94 20 80 165 18 90 256 22 132 367 20 140 49

Linear Regression

X Y XY X^21 19 19 12 18 36 43 15 45 94 20 80 165 18 90 256 22 132 367 20 140 4928 132 542 140

SumX SumY SumXY SumX2

b0 and b1

28 132 542 140SumX SumY SumXY SumX2

nXX

nYXXYb

/)(

/)(221

b1= 0.500b0= 16.8571y = 16.8571 + .5 xX Value Y Value 8 20.86

XbYb 10

b0 and b1 and R^2 Using excel

SUMMARY OUTPUT

Regression Statistics Forecast using simple regressionMultiple R 0.492518281R Square 0.242574257Adjusted R Square 0.091089109Standard Error 2.090796157Observations 7

ANOVAdf SS MS F Significance F

Regression 1 7 7 1.60130719 0.261481287Residual 5 21.85714286 4.371428571Total 6 28.85714286

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%Intercept 16.85714286 1.767045268 9.539734585 0.000214193 12.31480839 21.39947732X Variable 1 0.5 0.395123334 1.265427671 0.261481287 -0.515696865 1.515696865

(b-2)Forecast for Sep Using 5 Period Moving Averaget At

1 192 183 154 205 186 227 20

F8 =MA7= (A7+A6+A5+A4+A3)/5 = (20+22+18+20+15)/5

F8 =MA7= 19

(b-2)Forecast Using 5 Period Moving Average for All Periods

t At MAt Ft1 192 183 154 205 18 186 22 18.6 187 20 19 18.6

19

Moving Average

(b-3)Forecast for Sep Using Exponential Smoothing α =.2 and F(Mar) = 19

t At1 192 183 154 205 186 227 20

March is period 2

F3 = (1-α)F2 + α A2

F3 = (.8)19+ .2(18)

F3 = 18.8

(b-3)Forecast for Sep Using α =.2 and F(Mar) = 19

Using the same formula, we compute F4, F5, F6, F7, and finally F8 which is the demand for Sep.

At Ft1 192 18 193 15 18.804 20 18.045 18 18.436 22 18.357 20 19.08

19.26

(b-4)Forecast for Sep Using Naïve Method

F(t +1) =AtF8 =A7 F8 = 20

Forecast for all periods using Naïve Method

t At Ft1 192 18 193 15 184 20 155 18 206 22 187 20 22

20

(c) Which Technique ? When comparing several methods using MAD, we need to use the same time horizon for all methods. We need to have actual as well as forecasts for all methods for all periods of MAD computationsHere we have Actual for periods 1 to 7; that is 8 periodsRegression for periods 1 to infinityTherefore, if regression was the only method under consideration, then I could have computed MAD over 8 periods.However, we have Five period moving average forecasts for periods 6 and 7; that is 2 periodsTherefore, to compare all these methods, we can compute MAD only over 2 periods.But 2 periods is too short, so we forget moving averages. We have Naïve method forecasts for periods 2 to 7; That is 6 periodsExponential Smoothing for periods 2 to 7; That is 6 periodsWe can compare NM, ES, and Reg over 6 periods.We may also ignore period 2 because in exponential smoothing forecast for period 2 is just the same as actual demand for period 1.Here we compare NM, ES, and Reg over a 5 period time horizon.From period 3 to period 7

(c) Which Technique ?

Period Actual Naïve MethodExponential S Regression NM ES Reg

3 15 18 18.80 18.36 3 3.80 3.364 20 15 18.04 18.86 5 1.96 1.145 18 20 18.43 19.36 2 0.43 1.366 22 18 18.35 19.86 4 3.65 2.147 20 22 19.08 20.36 2 0.92 0.36

When comparing several methods using MAD, we need to do it over the same time horizon for all methods.Here we have moving average for 2 periods

(c) Which Technique ?

Period Actual Naïve MethodExponential S Regression NM ES Reg

3 15 18 18.80 18.36 3 3.80 3.364 20 15 18.04 18.86 5 1.96 1.145 18 20 18.43 19.36 2 0.43 1.366 22 18 18.35 19.86 4 3.65 2.147 20 22 19.08 20.36 2 0.92 0.36

(c) Which Technique ?

Period Actual Naïve MethodExponential S Regression NM ES Reg

3 15 18 18.80 18.36 3 3.80 3.364 20 15 18.04 18.86 5 1.96 1.145 18 20 18.43 19.36 2 0.43 1.366 22 18 18.35 19.86 4 3.65 2.147 20 22 19.08 20.36 2 0.92 0.36

MAD 3.2 2.15 1.67

Worst Best

However, we need to keep all methods, because we need more actual data.A MAD computed just 5 periods is not a reliable measure.It is better to have all methods for say 10-20 more periods, and then identify the best method

F(t+1) = Ft + (At-Ft)

Assignment 2: Problem 2(a)

Exponential smoothing is being used to forecast demand. The previous forecast of 66 turned out to be 5 units larger than actual demand. The next forecast is 65. Compute ?

65 = 66 + (-5)

5 = 1

= 0.2

66 +565 - 5

The 5-period moving average in month 6 was 150 units. Actual demand in month 7 is 180 units. What is 6 period moving average in month 7?

Assignment 2: Problem 1

MA56 = (A6+A5+A4+A3+A2)/5

MA67 = (A7+A6+A5+A4+A3+A2)/6

MA56 = (A6+A5+A4+A3+A2)/5 = 150

A6+A5+A4+A3+A2 = 750

A7 = 180

MA67 = (A7+A6+A5+A4+A3+A2)/6

MA68 = (180+750)/6 = 155