# Alternative definition for the value of stochastic solution

I have a two-stage stochastic programming problem in which the expected-value solution results in a quite different first-stage solution than the recourse problem. Although the value of VSS (defined below) is often positive, it is somewhat negligible.

The Value of Stochastic Solution (VSS) is defined as the difference between the Expectation of the Expected Value Solution (EEVS) and the optimal objective value of the Recourse Problem (RP).

This definition only considers the objective function values to determine the merits of the stochastic solution. I think this is not a good index in the sense that it does not consider the structure of the solutions. I was wondering if there are any other index for evaluating the merits of a stochastic problem in comparison to the expected value problem? I feel that this has already been studied in the literature, but I could not find a reference.

EDIT: It should mention that the stochastic program with a large number of scenarios can be solved efficiently, so I am not looking for a way to speedup solving the SP by reducing the number of first-stage variables or by reducing the number of scenarios. I just want a measure to quantify the value of stochastic solution. I thought maybe this has something to do with robustness or robust optimization, but RO is a different field.

• Formatting tip: Note that writing <sup>1</sup> yields a superscript 1 instead of resorting to MathJax. – TheSimpliFire Aug 28 '19 at 6:01