Question

she e A O AoCE A Cd Aaßbo AabCc T H Rp E Question 4 (20%) Historical demand for a product is Demand January February 11 March 12 15 April May June 12 16 15 a) Using a weighted moving average with weights of 0.60, 0.30 and 0.10, find the July forecast b) Using a simple three-month moving average, find the July forecast. c) Using single exponential smoothing with a 0.2 and a June forecast 13, find the July forecast. Make whatever assumptions you wish. d) Using the regression equation analysis, calculate the regression equation for the preceding demand data.

Answer 1

Solution:

Given demands –

Month	Demand
January (D1=)	12
February (D2=)	11
March (D3=)	15
April (D4=)	12
May (D5=)	16
June (D6=)	15

(a)         Weighted Moving Average:

              Given weights = 0.60, 0.30 and 0.10

              July Forecast will be as follows:

              F₇           =            (0.60 * D₆)          +            (0.30 * D₅)          +              (0.10 * D₄)

                             =            (0.60 * 15)          +            (0.30 * 16)          +              (0.10 * 12)

                             =            9            +            4.8         +            1.2

                             =            15

(b)         Simple three-month moving average (n=3):

              July Forecast will be as follows:

              F₇           =            ( D₄ + D₅ + D₆ ) / 3

                            =            ( 12 + 16 + 15 ) / 3

                            =            43 / 3

                             =            14.33

(c)          Single Exponential Smoothing:

              Given    -             α            =            0.2

                             and       June forecast     F₆           =            13

              F₇           =            F₆           +            α ( D₆ – F₆ )

                             =            13          +            0.2 ( 15 – 13 )

                             =            13          +            (0.2 * 2)

                             =            13.4

(d)       Regression Equation Analysis:

           

	Month (X)	Demand (Y)	X.Y	X-Square
	1	12	12	1
	2	11	22	4
	3	15	45	9
	4	12	48	16
	5	16	80	25
	6	15	90	36
Total	21	81	297	91
Average	3.5	13.5	49.5	15.167

n=6

Equation Y = a + bX

Slope

b= X.Y-n.X.YX2-n.X2 $wHNRAX9JNsIFwAAAABJRU5ErkJggg==$

b = ( 297 – (6 * 3.5 * 13.5) ) / ( 91 – (6 * 3.5² ) )

b = 13.5 / 17.5

b = 27/35

b = 0.7714

Intercept

a= Y-b.X

a = 13.5 – ( (27/35) * 3.5 )

a = 13.5 – 2.7

a = 10.8

Regression equation

Y = a + b.X

Y = 10.8 + (27/35).X

Y = 10.8 + 0.7714 X   ANSWER