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