Lab session 4 – ISE 216 Q1. Below are the numbers of motorcycles, which are still under warranty, that show up for repairs with engine problems at authorized repair shops for Şimşek company. The Şimşek company executives are worried about what is going to happen with the number of motorcycles with engine problems, not only it is possibly going to ruin their brand’s reputation but also they have to pay the repair cost since the motorcycles are under manufacturer’s warranty. They provided us the real data for the months 1 through 7 also the forecasts they made using exponential smoothing with α = 0.2. Month (t) Actual # of cars Exponential with Engine Smoothing problems (α = 0.2) (Dt) (Ft) 120 120,00 1 120 120,00 2 163 120,00 3 170 128,60 4 181 136,88 5 195 145,70 6 212 155,56 7 220 166,85 a. How good is this forecast? Why do you think so? b. The management seems to think that a double exponential smoothing method will give much better results. Do you agree, why? c. Use S0 = 120 and G0 = 60 to apply double exponential smoothing to find one-step-ahead forecasts of the periods 1-3 using α =0.4 and β =0.5. d. Apply regression analysis to find S5 and G5 and then forecast the periods 6 and 7 at period 5 using double exponential smoothing. Q2. Consider the following demand data for 5 years for each month. 2009 2010 2011 2012 2013 January 120 120 120 110 90 Feb. 163 163 163 145 130 March 170 170 170 160 170 April 180 180 180 170 167 May 195 195 195 160 180 June 120 125 125 100 110 July 163 160 160 195 170 August 120 110 110 125 100 September 163 145 145 160 195 October 140 137 137 156 125 November 181 170 170 180 190 December 195 200 190 200 220 ct a. What is N? b. Find the seasonal factors using the simple method. c. Forecast the demand for May of 2014 using MA(4) d. Forecast the demand for March of 2014 using exponentail smoothing (α = β= γ= 0.2) using the data starting from september 2013. e. Apply Winter’s method and update St, Gt, and ct (for three months in 2014) by starting S0=110, G0=0, and seasonality factors are taken as found in part b. t Dt December 2014 January 2014 120 Feb. 2014 163 March 2014 170 St Gt 110 0 ct Q3. Consider the below data given for two seasons (a season is composed of four periods). Estimate S0, G0 and seasonal factors using Winter’s initialization and 2-season data given below. 2012 2013 Quarter 1 Quarter 2 120 163 128 171 Quarter 3 170 178 Quarter 4 180 188