Building models

This chapter shows in detail how the textual description of a real world problem is converted into a mathematical model. We introduce an example problem, optimal portfolio selection, that will be used throughout this book.

Though not requiring any prior experience of Mathematical Programming, when formulating the mathematical models we assume that the reader is comfortable with the use of symbols such as x or y to represent unknown quantities, and the use of this sort of variable in simple linear equations and inequalities, for example:

which says that `the quantity represented by x plus the quantity representetd by y must be less than or equal to six'.

You should also be familiar with the idea of summing over a set of variables. For example, if produce_i is used to represent the quantity produced of product i then the total production of all items in the set ITEMS can be written as:

This says `sum the produced quantities produce_i over all products i in the set ITEMS'.

Another common mathematical symbol that is used in the text is the all-quantifier ∀ (read `for all'): if ITEMS consists in the elements 1,4,7,9 then writing

is a shorthand for

Computer based modeling languages, and in particular the language we use, Mosel, closely mimic the mathematical notation an analyst uses to describe a problem. So provided you are happy using the above mathematical notation the step to using a modeling language will be straightforward.