HW#2 FORECASTING (Omar Nadeem)

EMP504 Quantitative Methods in Management HW#2 FORECASTING Omar Nadeem PROBLEM 1) 5-15   Develop a 4-month moving average forecast for Wallace Garden Supply, and compute the MAD.   Answer  4 month moving average, 1st 4 month moving avg can be calculated for may, May: (10+12+13+16)/4 = 12.75 June: (12+13+16+19)/4 = 15 July: (13+16+19+23)/4 = 17.75 August: (16+19+23+26)/4 = 21 September: (19+23+26+30)/4 = 24.5 October: (23+26+30+28)/4 = 26.75 November: (26+30+28+18)/4 = 25.5

December: (30+28+18+16)/4 = 23 January: (28+18+16+14)/4 = 19 The MAD = 7.78 The mean absolute deviation is the average distance between each data point and the mean Mean of the 4 month average = (12.75+15+17.75+21+24.5+26.75+25.5+23+19)/9 = 20.58 Distance of each point from the mean, May = |20.58-12.75| = 7.83 June = |20.58-15| = 5.58 July = |20.58-17.75| = 2.83 August = |20.58-21| = 0.42 Sep = |20.58-24.5| = 3.92 Oct = |20.58-26.75| = 6,17 Nov = |20.58-25.5| = 4.92 Dec = |20.58-23| = 2.42 Jan= |20.58-19| = 1.58 Average of the Distance is the MAD which is 3.96 PROBLEM 2)

The forecast for quarter 10 (Fall quarter of Senior Year) is just the moving average for the quarter before that, i.e. the moving average for quarter 9 (Spring quarter of Junior Year) = q9 = 3.2 . (b) Applying exponential smoothing with a smoothing constant of 0.2 we get: Q1 = Y1 = 2.4 Q2 = 0.2Y2 + 0.8Q1 = 0.2(2.9) + 0.8(2.4) = 2.5 Q3 = 0.2Y3 + 0.8Q2 = 0.2(3.1) + 0.8(2.5) = 2.62 Q4 = 0.2Y4 + 0.8Q3 = 0.2(3.2) + 0.8(2.62) = 2.736 Q5 = 0.2Y5 + 0.8Q4 = 0.2(3) + 0.8(2.736) = 2.7888 Q6 = 0.2Y6 + 0.8Q5 = 0.2(2.9) + 0.8(2.7888) = 2.81104 Q7 = 0.2Y7 + 0.8Q6 = 0.2(2.8) + 0.8(2.81104) = 2.808832 Q8 = 0.2Y8 + 0.8Q7 = 0.2(3.6) + 0.8(2.808832) = 2.967066 Q9 = 0.2Y9 + 0.8Q8 = 0.2(3.2) + 0.8(2.967066) = 3.013653 As before, the forecast for quarter 10 (Fall quarter of Senior Year) is just the value for quarter 9 (Spring quarter of Junior Year) = Q9 = 3.013653 = 3.0 (since GPA is restricted to 1 place of decimal). PROBLEM 3) Given this information what are the Sales and Profits, Forcasts for Jan 05; Last Value Method, Moving average Method using quarterly information, and Exponential Smoothing for the last month. Actual Forecasts Month Sales Profit Sales Profit Jan $25 $2.1 $25 $2.1 Feb $27 $2.5 $26 $2.4 Mar $23 $1.9 $26.5 $2.5 Apr $22 $2.1 $26 $2.4 May $26 $2.4 $26.5 $2.5 Jun $28 $2.6 $27 $2.6 Jul $31 $3.0 $28 $2.7 Aug $25 $2.2 $29 $2.8 Sep $28 $2.4 $27 $2.6 Oct $29 $2.7 $28 $2.7 Nov $32 $2.9 $29 $2.9 Dec $37 $3.1 $31 $3.1 Alpha factor = 0.6 Answer 1. Last Value method ignores all other data points except last one.

      so sales forecast is = SALE of dec = $ 37            profit  forecast is = profit of last dec = $ 3.1. 2. Moving Average method with quarterly information         sale of (OCT +NOV+DEC)/3 = (29+32+37)/3 =  $ 32.66          Similarly profit = $ 2.9. 3. Exponential smoothing             Formula is  Ft = Ft-1 + a (At-1 – Ft-1)  Where:  Ft – 1 = forecast for the previous period,  At – 1 = Actual demand for the period,  a = weight (between 0 and 1). Our case it is 0.6.  so for sales Ft = 31 + 0.6( 37-31) = $ 34.6             Profit Ft = 3.1 + 0.6( 31.-3.1)= $ 3.1 

3 518 443.9 74.1 4 563 466.13 96.87 5 584 495.19 88.81 6   521.83     MAD 74.56 alpha 0.3 PROBLEM 5) Answer Month Income Smoothing constant α = 0.3 Error Feb 70 65 Mar 68.5 0.3*70+0.7*65 = 66.5 2 Apr 64.8 67.1 2.3 May 71.7 66.41 5.29 June 71.3 67.9 3.30 July 72.8 68.98 3.81 Total 16.705 MAD = Error/n = 16.705/5 = 3.341 Month Income Smoothing constant α = 0.3 Error Feb 70 65

Mar 68.5 0.1*70+0.9*65 = 65.5 3 Apr 64.8 65.8 1 May 71.7 65.7 6 June 71.3 66.3 5 July 72.8 66.8 6 Total 21 MAD = Error/n = 21/5 = 4.2 The forecast which is having a low MAD value gives a better forecast. Smoothing constants with alpha = 0.03 is better forecast.