Page 221 - Special Topic Session (STS) - Volume 1

STS425 Zaitul Marlizawati Z. et al.
maximize midterm production planning of oil refinery considered as revenue
from products sales minus the raw material cost and operating cost. In this
study, the simplified oil refinery operation based on Khor et al. [2] study is
used to describe a formulation of the deterministic linear program which the
production flowrate variables are in barrel/year.

2.2 Stochastic Model
Two-stage stochastic models are the common model in oil refinery
stochastic optimization problem and general formulation for this stochastic
approach was defined by Dantzig [8]

maxC x E Q  T   ,x    . s t Ax b , x  (1)
0


Q   ,x   
Where is the optimal value for the second stage problem,

t
. s
max q y t Tx Wy h  , y  0 (2)

The decision variables are divided to the two stages in the two-stage
stochastic model. The first stage variables are decided before the realization
x
b
of uncertain parameter denoted by . Matrix A , vector and vector C are
known with certainty. Meanwhile the second stage variables are decided after
the realization of uncertain parameter denoted by y and also interpreted as
corrective measures against any infeasibility arising due to realization of
uncertainty. In the second stage problem, elements , , ℎ are viewed
as random.
In this study, the framework of two-stage stochastic programming with

recourse for discretely distributed random vector is considered, equation
(1) and (2) takes on the form
T
max C x  T  p q y sc subject to Ax b
sc sc
sc SC (3)
Wy  h  Tx , x  0, y  0, sc SC (4)
sc
sc
sc
The probability of scenario will occur, ( ≥ 0, ∑ = 1 , ∈ ).

=1

2.2.1 Mathematical programming model
Let us define the variables of the two-stage stochastic model in this study.
The amount of crude oil type i , P and production capacity of process j , x
i
j
are the first stage decision variables. After the prices and demand for finished
s
products uncertainty are revealed, y production flowrate of product i per
i
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