Efficient Methods for Several Classes of Ambiguous Stochastic Programming Problems Under Mean-MAD Information
CentER Discussion Paper Series No. 2016-039
48 Pages Posted: 29 Sep 2016
Date Written: September 22, 2016
Abstract
We consider decision making problems under uncertainty, assuming that only partial distributional information is available - as is often the case in practice. In such problems, the goal is to determine here-and-now decisions, which optimally balance deterministic immediate costs and worst-case expected future costs. These problems are challenging, since the worst-case distribution needs to be determined while the underlying problem is already a difficult multistage recourse problem. Moreover, as found in many applications, the model may contain integer variables in some or all stages. Applying a well-known result by Ben-Tal and Hochman (1972), we are able to efficiently solve such problems without integer variables, assuming only readily available distributional information on means and mean-absolute deviations. Moreover, we extend the result to the non-convex integer setting by means of convex approximations (see Romeijnders et al. (2016a)), proving corresponding performance bounds. Our approach is straightforward to implement using of-the-shelf software as illustrated in our numerical experiments.
Keywords: robust, ambiguous, integer, recourse, stochastic, multi-stage
JEL Classification: C61
Suggested Citation: Suggested Citation