Although stochastic programming is probably the most effective frameworks for handling decision problems that involve uncertain variables, it is always a costly task to formulate the stochastic model that accurately embodies our knowledge of these variables. In practice, this might require one to collect a large amount of observations, to consult with experts of the specialized field of practice, or to make simplifying assumptions about the underlying system. When none of these options seem feasible, a common heuristic has been to simply seek the solution of a version of the problem where each uncertain variable takes on its expected value (otherwise known as the deterministic counter part solution). In this paper, we show that when 1) the stochastic program takes the form of a two-stage mixed-integer stochastic linear programs, and 2) the uncertainty is limited to the objective function, the deterministic counter part solution is in fact robust with respect to the selection of a stochastic model. We also propose tractable methods that will bound the actual value of stochastic modeling: i.e., the maximum that can be achieved by investing more efforts in the resolution of the stochastic model. Our framework is applied to an airline fleet composition problem. For all three cases considered, our results indicate that resolving the stochastic model would not lead to more than a 7% improvement of expected profits.
Published February 2012 , 30 pages