title: Reduce size of alternate solutions in optimization
body: <p>We have a <strong>supplier/depot</strong> (index d) and several <strong>factories</strong> (index f) with demand known for different <strong>products</strong> (p) during T <strong>month</strong> (index t) ahead. There is a fleet of <strong>trucks</strong> (index v) with different <strong>truck types</strong> (index k) (e.g., some of them have fridge) which restricts carrying some products just to that truck type. We have a set of  pre-defined <strong>routes</strong> (index r) between depot and factories (there exists routes between factories themselves).</p>
  <p>A truck loads goods from the supplier and uses the pre-defined routes in which multiple factories can be visited, and finally gets back to the depot for the next load. In a month each truck may carry goods from the depot to factory j more than once. So variable <em>x_{p,k,r,f,n,t}</em> is the amount of product p that truck type v (of type k) can load from depot and through rout r take to factory f at time t. The vehicles of a type are limited by <em>V_k</em>.</p>
  <p>The counter n is the number of rounds in a month that a truck type takes the same product, route, to the same factory. The goal is to minimize the total cost.
  The simplest case is where a vehicle takes the path <strong>depot -&gt; factory 1 -&gt; depot -&gt; factory 1</strong> in a month. In this case we have two index <em>x_{p,k,r,f,1,t}</em> and <em>x_{p,k,r,f,2,t}</em> to differentiate these two rounds.
  Here is  the problem, this model generates many alternate solutions. For example if we have 4 trucks of type k, then one solution is (we call it solution 1):</p>
  <p><em>x_{p,k,r,f,1,t} = 6</em></p>
  <p><em>x_{p,k,r,f,2,t} = 4.</em></p>
  <p>Another solution (solution 2) is:</p>
  <p><em>x_{p,k,r,f,1,t} = 4</em></p>
  <p><em>x_{p,k,r,f,2,t} = 6.</em></p>
  <p>Whish is basically the same as solution 1 (just the order changes).</p>
  <p>As the problem size enlarges, many different solutions have the same total costs. We would like to think of a method to decreasing the solution space (alternate solutions), while keeping all possible objective values.</p>