Question

The observed sales for January, February, March and April are 113, 122, 130 and 116, respectively. Assuming the sales forecast of 115 for January, what is the sales forecast for May with exponential smoothing method with alpha = 0.5?

a. 110.
b. 115.
c. 120.
d. 125.

Answer 1

The sale forecast for May is
`i= 120.56`

Explanation:

From the question we are told that

The value of
`\alpha = 0.5`

Month January February March April

Observed sales a= 113 b= 122 c= 130 d= 116

The sales forecast for January is
`e = 115`

Generally the sales forecast for February is mathematically represented as

`f = \alpha * a + [1- \alpha * ( e)]`

=>
`f = 0.5 * 113 + [(1- 0.5) * (115)]`

=>
`f =114`

Generally the sales forecast for March is mathematically represented as

`g = \alpha * b + [(1- \alpha) * ( f)]`

=>
`g = 0.5 * 122 + [(1- 0.5) * ( 118.5)]`

=>
`g = 120.25`

Generally the sales forecast for April is mathematically represented as

`h= \alpha * c + [(1- \alpha) * ( g )]`

=>
`h= 0.5 * 130 + [(1- 0.5) * ( 120.25 )]`

=>
`h= 125.125`

Generally the sales forecast for April is mathematically represented as

`i= \alpha * d + [(1- \alpha) * ( h )]`

=>
`i= 0.5 * 116 + [(1- 0.5) * ( 125.125 )]`

=>
`i= 120.56`