# Question: Consider a monthly series of air conditioner AC sales In

Consider a monthly series of air conditioner (AC) sales. In the discussion of Winters’ method, a monthly seasonality of 0.80 for January, for example, means that during January, AC sales are expected to be 80% of the sales during an average month. An alternative approach to modeling seasonality, called an additive model, is to let the seasonality factor for each month represent how far above average AC sales are during the current month. For instance, if SJan = 50, then AC sales during January are expected to be 50 fewer than AC sales during an average month. Similarly, if SJuly = 90, then AC sales during July are expected to be 90 more than AC sales during an average month. Let

St = Seasonality for month t after observing month t demand

Lt = Estimate of level after observing month t demand

Tt = Estimate of trend after observing month t demand

Then the Winters’ method equations given in the text should be modified as follows:

Lt = α(I) + (1 - α)(Lt -1 + Tt - 1)

Tt = β(Lt – Lt - 1) + (1 - β)Tt - 1

St = γ(II) + (1 - γ)St -12

a. What should (I) and (II) be?

b. Suppose that month 13 is January, L12 = 30, T12 = -3, S1 = -50, and S2 = -20. Let α = γ = β = 0.5. Suppose 12 ACs are sold during month 13. At the end of month 13, what is the forecast for AC sales during month 14 using this additive model?

St = Seasonality for month t after observing month t demand

Lt = Estimate of level after observing month t demand

Tt = Estimate of trend after observing month t demand

Then the Winters’ method equations given in the text should be modified as follows:

Lt = α(I) + (1 - α)(Lt -1 + Tt - 1)

Tt = β(Lt – Lt - 1) + (1 - β)Tt - 1

St = γ(II) + (1 - γ)St -12

a. What should (I) and (II) be?

b. Suppose that month 13 is January, L12 = 30, T12 = -3, S1 = -50, and S2 = -20. Let α = γ = β = 0.5. Suppose 12 ACs are sold during month 13. At the end of month 13, what is the forecast for AC sales during month 14 using this additive model?

## Answer to relevant Questions

Winters’ method assumes a multiplicative seasonality but an additive trend. For example, a trend of 5 means that the level will increase by five units per period. Suppose that there is actually a multiplicative trend. Then ...The file S12_70.xlsx lists annual revenues (in millions of dollars) for Nike. Forecast the company’s revenue in each of the next two years with a linear or exponential trend. Are there any outliers in your predictions for ...The file S12_77.xlsx contains monthly time series data on corporate bond yields. These are averages of daily figures, and each is expressed as an annual rate.The variables are:• Yield AAA: average yield on AAA bonds• ...If all of the inputs in PC Tech’s product mix problem are nonnegative, are there any input values such that the resulting model has no feasible solutions? Model 8 has fairly high profit margins, but it isn’t included at all in the optimal mix. Use Solver Table, along with some experimentation on the correct range, to find the (approximate) selling price required for model 8 ...Post your question