A discussion of some types of non-linearities that are difficult to incorporate into a linear programming model. One of these occurs in the scheduling of refinery operations where linear programming methods are widely used. The specific problem is one of determining simultaneously the quantities of various components of gasoline and tetraethyl lead to blend to form regular or premium type gasolines. It is believed that the general approach can be used for other non-linear situations. Linearization is accomplished by viewing the lead requirements of a blend first as a known general function of two variables, each of which is a linear function of the quantities in the blend. The general function is approximated by a convex linear combination of a mesh of representative points.
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