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STS425 Zaitul Marlizawati Z. et al.
First and second stage programming model can be summed up to the
large linear programming model as shown in equation (3) by taking all
possible scenarios for prices and demand uncertainty. The objective function
equation is extended to large scale linear programming model and there are
160 new constraints for demand uncertainty. R was used to generate scenarios
and construct the scenario tree. Meanwhile, the stochastic programming
model was implemented using GAMS.

Table 1. Comparison of oil refinery profit (dollar/year)
Model Profit/Expected profit
LP 117,096,783
Two stage stochastic linear 170,639,512
programming

Value of stochastic solution (VSS) is used to evaluate the uncertainty
parameters by calculating the expected profit from two-stage stochastic
model over the deterministic model.

VSS  170,639,512 117,096,783 53,542,729 
(14)
The VSS result, 53.5 million dollar which the stochastic model gain 45.73%
more than deterministic model provided a good solution by including the
uncertainty into the model. Thus we conclude that the stochastic model gives
a better prediction of oil refinery profit margin as shown in Table1.

4. Discussion and Conclusion
This paper presents a study of stochastic optimization model to find the
optimal operation mode of units and stream flows that maximize the oil
refinery profit while observing all possible constraints by including the prices
and demand uncertainty. This model is called two-stage stochastic
programming with recourse and GBM is used to describe the uncertainty by
generates the future realization of scenarios with probabilities as input to the
stochastic programming. The expected profit from the stochastic model gain
45.73% more than deterministic model provided a good solution by including
the uncertainty into the optimization model. Thus we conclude that the
stochastic model gives a better prediction of oil refinery profit margin.

Appendix
Set and Indices
I set of material or products
set of processes
set of scenarios

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