If the user declares variables as integer but does no more, then CBC will treat them
as simple integer variables. In many cases the user would like to do some more fine tuning. This section shows how to create integer variables with pseudo costs. When pseudo costs are given then
it is assumed that if a variable is at 1.3 then the cost of branching that variable down will be 0.3 times the down pseudo cost and the cost of branching up would be 0.7 times the up pseudo cost. Pseudo costs can be used both for branching and for choosing a node.
The full code is in `longthin.cpp` located in the CBC Samples directory, see
Chapter 8, *
More Samples
*.

The idea is simple for set covering problems. Branching up gets us much closer to an integer solution so we will encourage that direction by branch up if variable value > 0.333333. The expected cost of going up obviously depends on the cost of the variable. The pseudo costs are choosen to reflect that fact.

The code in Example 5.1 also tries to give more importance to variables with more coefficients. Whether this sort of thing is worthwhile should be the subject of experimentation.