Page 222 - Special Topic Session (STS) - Volume 1

STS425 Zaitul Marlizawati Z. et al.
realization of scenario and the recourse costs are imposed based on


corrective action. These corrective actions are associated with z and z ,
, i s
, i s
amount of unsatisfied demand and excess finished products i per realization
of scenario s . The recourse costs are denoted as penalty cost incurred due to
shortfall and surpluses in oil refinery production planning due to the
uncertainty of finished products demand. In oil refinery field, stochastic
programming seeks to maximize profit of the first stage decision plus
expected profit of the second stage recourse decision.
A new reformulated objective function is the form of

  E
Max Z  Z  E Z , s demand (5)
1
consists of summation of maximization of the expected profit (considered as
revenue from products sales minus raw material cost and operating cost) and
minimization of summation of expected recourse penalty due to shortfall and
surpluses in production.

i i 
J
Z     P  c x j , i I , j  (6)
j
i I j J

denotes the raw material and operating costs, while the expectation objective
function with random price coefficient is given by

  
E Z  s , i s , i s ,i I random  , I s S
p c y
p ir c
e
i I s S  (7)
where p is the probability of scenario for prices uncertainty, c is the
s
, i s
coefficient for prices uncertainty that obtained from scenario tree and y is
, i s
a production flow rate of products type i corresponding to scenario s . The
expected recourse penalty due to uncertainties in demand for the second
stage cost is given by

E , s demand  p c z  , i s  c z  , i s  ,i  I deman d  , I s S (8)


random

i
 i
s
i I s  S
where p is the probability of scenario s for demand uncertainty, z and

s
, i s

z are an amount of underproduction and overproduction of product type i
, i s


per realization of scenario s and c and c are penalty costs for shortfall and
i
i
surplus in production of product type i .The objective function (5) is subject
to constraints
x  x j  J
, j t j , 1t (9)
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