QUESTION 15 Data for the annual (total) and quarterly power demand (in MW) for a

Question

QUESTION 15 Data for the annual (total) and quarterly power demand (in MW) for a county is provided below for the last 4 years. You would like to forecast next years total (annual) demand as well as quarterly demand. Forecasting quarterly demand is important as power demand often has seasonality. You want to ensure that the infrastructure can support the quarter with the highest (peak) demand Quarter ear 1 105 130 151 98 ear 2 96 116 162 101 ear 3 ear 4 110 129 168 108 15 109 134 173 109 25 nnual Demand (Total) 84 75 (a) Use exponential smoothing with apha = 0.4 to forecast annual (total) demand for year 5, Record your answer to 2 decimal places. Show your working (b) Estimate the seasonal indices. Then use your answer in part (a) to provide a quarterly forecast for the next year.

Explanation / Answer

A)Using exponential smoothing with alpha =0.4

Formula : Forecast for T = Forecast of T -1 + Alpha (Actual for T-1 - Forecast for T -1)

Where T is the time period and T -1 is the previous time period.

So the forecast for the year 5 would be :

Forecast for year 4 + 0.4 *(Actual for year 4 - forecast for year 4)

= 494.24 + 0.4*(525 -494.24)

=506.54

B) Seasonal indices calculation:

Average method is used here.

Annual demand forecast for year 5 is computed in part A as 506.54.

So quarterly demand = 506.54/4 = 126.635 units.

Notes :

A)For year 1 forecast is assumed to be same as actual value. From year 2 onwards forecast is computed by taking forecast of previous year .

Example : Forecast for year 2 = Forecast for year 1 + Alpha *(Actual - forecast of year 1)

Forecast of year 1 =484

Actual of year 1 =484

Alpha = 0.4

Forecast for year 2 = 484 + 0.4*(484 -484)

=484 and so on.

B)For table 2 : Average demand column is computed by : Sum of all for years of that quarter/4

Total of the average demand column is computed and divided by 4 to get equal quarterly demand value.

Seasonal index = Average demand / Quarterly demand.

Forecast for quarter = Quarterly demand * Seasonal index.

Example: For quarter 1 : Average demand = (105 +96 +110 +109 )/4 = 105.

Similarly average demand for all quarters is computed and their sum is 499.75.

Quarterly demand = 499.75/4 =124.9375

Seasonal index = Average demand / Quarterly demand = 105/124.9375 =0.8404.

And so on.

Year Actual demand for T Actual - Forecast for T-1 Alpha *(Actual -Forecast for t-1) Forecast for T 1 484 484 2 475 0 0 484 3 515 -9 -3.6 480.4 4 525 34.6 13.84 494.24

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