title: Forcing CPLEX to switch basis in optimal LP solution
body: <p>I am solving a classical network flow problem with CPLEX (using Java). It contains the constraint Ax=b (A being the node-arc incidence matrix, x the decision variable for link flows, and b the given right hand sides). I am interested in the shadow prizes of in-/decreasing b in one dimension. </p>
  
  <p>In a non degenerate problem the shadow prices are given by the dual variables on the constraint Ax=b. However, my problem is degenerate. Thus one optimal solution can be expressed by several combinations of basis and non-basis variables. Each of theses combinations should have different dual variables. </p>
  
  <p>At least one of theses duals should give me a the shadow price of increasing b, another dual will provide the shadow price of decreasing b. (According to W.Powell (1989): "A review of sensitivity results for linear networks and a new approximation to reduce the effects of degeneracy")</p>
  
  <p>My question is: After solving the LP with CPLEX and obtaining a first set of duals, how do I get CPLEX to perform a swap of basis and non-basis variables, so that I can obtain another set of duals?</p>