The operations manager at a manufacturing facility is about to begin an energy-efficiency initiative. As this program begins, it will be helpful to have benchmark data on energy use, in order to determine whether the initiative is having an effect. The facilities department has provided data on the monthly energy use (in kilowatt hours) over the past three years, as shown in the following table:

a. Use the Holt-Winters method to estimate the monthly usage for the coming 12 months. Use smoothing parameters of α = 0.3, β = 0.4, and ( = 0.5.
b. For the forecasting problem in (a), which value of a achieves the minimum value of MSE, holding the other smoothing parameters constant?

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Year 1 Usage Year 2 Usage Year 3 Usage Jan 31,040 Jan 24,540 Jan 32,410 Feb 28,720 Feb 26,560 Feb 21,380 Mar 20,540 Mar 22,060 Mar 20,370 Apr 22,260 Apr 16,220 Apr 18,300 May 12,920 11,550 May May 10,020 9,740 Jun 13,100 Jun Jun 11,420 Jul 10,160 14,790 Jul Jul 10,020 11,800 Aug 12,360 Aug 12,740 Aug 12,890 9,240 Sep Sep Sep 13,120 10,410 Oct 9,790 Oct 11,220 Oct Nov 14,840 Nov 13,780 Nov 13,510 19,040 17,340 Dec 14,610 Dec Dec