Page 224 - Special Topic Session (STS) - Volume 1

STS425 Zaitul Marlizawati Z. et al.
 2 t 
e 2  e   t 
with the probability p  . If we calculate the limit we obtain
e  t   e   t 
 2 t 
e 2  e   t  1
lim p  lim  . Thus the probability for next prices and
t   0 t   0 e  t   e   t  2
demands upward and downward value is 0.5. Insert p  0.5 to equation (13)
   2    2
t 
t 
       t         t 
and we get u e  2  d  e  2  represent as high ( )H and
low ( )L value in the scenario tree. Uncertainties are discretely represented by
scenario realization modeled as a scenario tree.

3. Results
In this study, we consider ten uncertain parameters for prices and finished
products demand uncertainty. Each parameter takes on two values, high value
which is denoted as H and low value which is denoted as L. The probability of
each occurring high and low value is 0.5. We obtain 32 scenarios (2 ) with the
5
probability of occurrence of each scenario is 0.03125 by multiplying the
probabilities of uncertain parameter in each scenario as presented in the
scenario tree in Figure 1. For example, in scenario 1, {, , , , } is a set of
event sequences denotes as high prices for Gasoline, Naphta, Kerosene, Diesel,
Fuel oil as well as demand uncertainty scenario tree shown in Figure 2.

Figure 1. Scenario tree for prices of finish products uncertainty

Figure 2. Scenario tree for demand of finish products uncertainty

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