Sample: Stating a MIP Problem

A mixed integer programming (MIP) problem may consist of both integer and continuous variables. The integer variables may be restricted to the values 0 (zero) and 1 (one), in which case they are referred to as binary variables. Or they may take on any integer values, in which case they are referred to as general integer variables. A variable that may take either the value 0 or a value between a lower and an upper bound is referred to as semi-continuous. A semi-continuous variable that is restricted to integer values is referred to as semi-integer. (Continuous variables in a mixed integer programming problem are not restricted to integer values.) The following illustrates a mixed integer programming problem, which is solved in the example program ilomipex1.cpp / mipex1.c, discussed later in this chapter:

Maximize 

 
x1 
+ 
2x2 
+ 
3x3 
+ 
x4 

 

 
subject to 
- 
x1 
+ 
x2 
+ 
x3 
+ 
10x4 
 
20 

 

 
x1 
- 
3x2 
+ 
x3 

 

 
 
30 

 

 

 

 
x2 

 

 
- 
3.5x4 
= 
0 
with these bounds 

 
0 
 
x1 
 
40 

 

 

 

 

 

 
0 
 
x2 
 
+ 

 

 

 

 

 

 
0 
 
x3 
 
+ 

 

 

 

 

 

 
2 
 
x4 
 
3 

 

 

 

 

 

 

 

 
x4 
integer 

 

 

 

 

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