title: Linear programming - multi-objective optimization. How to build single function
body: <p>I have LP problem
  It is similar to assignment problem for workers
  I have three assignments with constraint scores(Constraint 1 is more important than constraint 2)</p>
  
  <pre><code>                     Constraint1    Constraint2   
   assign1             590            5              
  
   assign2             585            580              
  
   assign3             585            336             
  </code></pre>
  
  <p>My current greedy solver will compare assignments by the first constraint. The best one becomes a solution. Solver will compare Constraint 2  if and only if he found two assignments with the same score value for previous constraint and so on.</p>
  
  <p>For a given example in the first round assign2 and assign3 will be chosen because they have the same lowest constraint score. After second round solver choses assign3. So I need a cost function which will represent that behavior.  </p>
  
  <p>So I expect the </p>
  
  <blockquote>
    <p>assign1_cost > assign2_cost > assign3_cost.</p>
  </blockquote>
  
  <p>Is it posible to do?
  I believe that I can apply some weighted math function or something like that.  </p>