Question

The first quart forecast is _____

The second quarter forecast is _____

The third quarter forecast is _____

The fourth quarter forecast is _____

The manager of a utility company in the Texas panhandle wants to develop quarterly forecasts of power loads for the next year. The power loads are seasonal, and the data on the quarterly loads in megawatts (MW) for the last four years are as follows: Year 1 Year 4 Year 2 98.1 Quarter Year 3 127.6 118.6 140.4 139.6 149.2 136.2 160.6 148.7 41628 156.7 179.5 169.0 The manager estimates the total demand for the next year at 685 MW. Use the multiplicative seasonal method to develop the forecast for each quarter. (Round all intermediate calculations to three decimal places.) The first quarter forecast is MW. (Enter your response rounded to one decimal place.)

Answer 1

Forecast for quarter 1 = 131.7 MW
Forecast for quarter 2 = 162.7 MW
Forecast for quarter 3 = 183.9 MW
Forecast for quarter 4 = 206.7 MW

Explanation Below

The given data along with the total loads for each year are as shown in the below image. The total load for a year is the sum of loads for all the quarters for the particular year.

Quarter Year 1 Year 2 Year 3 Year 4 1 103.7 98.1 121.6 102.8 127.6| 118.6| 140.4| 139.6 2 149.2 136.2 160.6 148.7 4 162.8 156.7 179.5 169 Tota543.3509.6602.1560.1

First we need to find the normal quarterly load for every quarter of all year. Normal average load is the total load for a year divided by number of quarters which is 4. Thus we have the below

Normal quarterly load for year 1 = 543.4/4 = 135.825

Normal quarterly load for year 2 = 509.6/4 = 127.4

Normal quarterly load for year 3 = 602.1/4 = 150.525

Normal quarterly load for year 4 = 560.1/4 = 140.025

Next step is to calculate the seasonal index for all the quarters for all the years. Seasonal index for a quarter for a particular year is calculated by dividing the actual load for the quarter by the normal quarterly load for that year calculated in step 1.

For example the seasonal index for quarter 1, year 1 = 103.7/135.825 = 0.763

Similarly the seasonal index for quarter 1, year 2 = 98.1/127.4 = 0.77

The below tables summarizes the seasonal index calculated for all the quarters

Quarter Year1 Year 2 Year 3 Year 4 ,734 0.939 0.931 0.9330.997 1.098 1.0697 1.062 763 6 1.19 1231.192 1.207 2 2

The next step is to calculate the average seasonal index for each quarter. Average seasonal index for a quarter is the average of all the seasonal index for that quarter for all the years.

Average Seasonal Index for quarter 1 = (0.763+0.77+0.808+0.734)/4 = 0.769
Average Seasonal Index for quarter 2 = (0.939+0.931+0.933+0.997)/4 = 0.95
Average Seasonal Index for quarter 3 = (1.098+1.069+1.067+1.062)/4 = 1.074
Average Seasonal Index for quarter 4 = (1.199+1.23+1.192+1.207)/4 = 1.207

The last step is to calculate the forecast for next year for each quarter. The forecast is calculated by multiplying the seasonal index calculated in the above step by the normal quarterly load for next year. Normal quarterly load for next year is the total load divided by 4. Hence normal quarterly load for next year = 685/4 = 171.25.

Forecast for next years quarter is thus (seasonal index)*(171.25)

Forecast for quarter 1 = 0.769*171.25 = 131.691 $\approx$ 131.7 MW
Forecast for quarter 2 = 0.950*171.25 = 162.688 $\approx$ 162.7 MW
Forecast for quarter 3 = 1.074*171.25 = 183.923 $\approx$ 183.9 MW
Forecast for quarter 4 = 1.207*171.25 = 206.699 $\approx$ 206.7 MW