OVERVIEW

The basic problem of linear programming (LP) is to maximize or minimize a function of several variables subject to a number of constraints. The functions being optimized and the constraints are linear. General linear programming deals with allocation of resources, seeking their optimization. In the context of an oil refinery, an LP model is a mathematical model of the refinery, simulating all refinery unit yields, unit capacities, utility consumption, and the like as well as product blending operations of the refinery by means of linear equations, each equation subject to a number of constraints. These equations are compiled in a matrix of rows and columns, the columns representing the unknowns or variables and the rows or equations representing the relations between variables. The values in the matrix are simply the coefficients that apply to unknowns in each equation. As the number of unknowns are more than the number of constraints relating them, a large number of solutions might satisfy all the problem parameters.

The optimal solution must be chosen from the set of only those solutions that satisfy all the problem parameters and, at the same time, maximize refinery profit or minimize operating cost. To aid the search for an optimum solution, LP is driven by a row in the matrix containing cost and revenue (the objective function row).

DEVELOPMENT OF THE REFINERY LP MODEL

In the oil industry, prior to the advent of LP techniques, all optimization studies were done by calculating several hand balances, moving toward ...