# Mathematical Programming and Blending Problem

There is a considerable amount of work in the area of planning for refinery operations including the linear programming based commercial software, such as GRTMPS (Haverly Systems), PIMS (Aspen Technology), and RPMS (Honeywell Hi-Spec Solutions).

Gasoline blending is a crucial step in refinery operation because gasoline can yield 60-70% of a refinery’s profit. The process involves the mixing of various stocks, which are the intermediate products from the refinery, along with some additives, such as antioxidants and corrosion inhibitors, to produce blends with certain qualities. A variety of support systems have been developed to address the planning and scheduling of blending operations.

In our example, we suppose that two products, and are to be made, subject to the following limits:

1. Blendstock availability x+y<=50;

In the objective function the anticipated revenues for the two products are:

x= \$ 4.50/BBL and y= \$ 6.50 /BBL

Therefore the best deterministic answer is where x =20 and y=30

Once a blending problem has been modeled, analysts can then conduct various simulations and analyses on the model. The Visual Basic Application provides a powerful, yet easy to use set of analysis tools. To perform this simulation program, we need to determine the lower and the upper boundaries of additive coefficients ( ) for the products, and the anticipated revenue of each product with confidence interval; we can then generate random variables for experience. The execution of the simulation is based on random sampling based on the Monte Carlo simulation.

We conclude that the Monte Carlo simulation approach shown in this publication is a very promising technique to optimize oil and gas portfolios based on typical LP applications:

Distribution studies

o Delivery planning;

o Plant location studies.

Production problems

o Plant/Refinery scheduling.

Utility problems

o Usage of steam/Heat/electricity/Other fuels.

Investment problems

o How many plants to build and what type.

Trimming problems

o Optimizing cutting patterns, minimizing wastage.

Financial problems

o Investment portfolios;

o Maximizing return/Minimizing risk.

Obviously, there is a real need for a planning model under uncertainty to answer the following questions:

What are the decisions ultimately to be made in the scope of regulations and mechanisms which bring timely, adequate, diversified and resilient supplies of energy into the market?

What data is available?

Who will use the model?

How long can we spend to design it?

Who requires the model?