JuMP reduced_cost questions

Specific Domains Optimization (Mathematical)
2

Hi @Ken_Lin, hopefully some answers:

  1. Yes
  2. The reduced cost is not the change in objective if the variable was increased by one unit, but the change in the objective with respect to an infinitesimal change in the variable that is then scaled to one unit. Think of it like df/dx instead of f(x+1) - f(x). Presumably, a small increase in toyx[3] leads to a change in the other variables that cancels out the change in objective. (If toyx[3] increases, then by the second constraint, toyx[4] must decrease, etc)
  3. toys[4] is a non-basic variable at its upper bound of 1. You can query basis information using Basis matrices · JuMP
  4. Correct. There is no way to compute a reduced cost for arbitrary x.

If you’re looking for sensitivity analysis, see

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