Question

A manager of a store that sells and installs spas wants to prepare a forecast for January, February, and March of next year. Her forecasts are a combination of trend and seasonality. She uses the following equation to estimate the trend component of monthly demand: F_t = 80 + 3t, where t = 0 in June of last year. Seasonal relatives are .87 for January, 1.05 for February, and 1.05 for March. What demands should she predict? (Round your answers to 2 decimal places.)

Month	Forecast
January of the next year
February of the next year
March of the next year

Answer 1

Solution:

The trend equation is given as,

F(t) = 80 + 3t

where, t = 0 in June of last year. Therefore,

t = 1, in July of last year

t = 2, in August of last year

t = 3, in September of last year

t = 4, in October of last year

t = 5, in November of last year

t = 6, in December of last year

t = 7, in January of this year

t = 8, in February of this year

t = 18, in December of this year

t = 19, in January of next year

t = 20, in February of next year

t = 21, in March of next year

Putting the values of t for January to March of next year in the trend equation, we get,

F(t) = 80 + 3t

January of Next year:

F(19) = 80 + (3 x 19)

F(19) = 137

February of Next year:

F(20) = 80 + (3 x 20)

F(20) = 140

March of Next year:

F(21) = 80 + (3 x 21)

F(21) = 143

By multiplying the above trend values with the respective seasonal relative, we will get the demand forecast of each month:

January of next year: Forecast = 137 x 0.87 = 119.19

February of next year: Forecast = 140 x 1.05 = 147.00

March of next year: Forecast = 143 x 1.05 = 150.15