5. Introducing the integer linear program

The model presented in this section is a Linear Integer Program (LIP), which combines integer variables with binary variables. The objective function and all constraints are linear.

We begin by presenting the model parameters.

• Dimensions :

  I _s

   : 

  total length of short billets
  

  I _l

   : 

  total length of long billets
  

  L

   : 

  overall billet lengths
  

  J

   : 

  all the billets that can be produced for a...