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. (2015a)), proving corresponding performance bounds. Our approach is straightforward to implement using of-the-shelf software as illustrated in our numerical experiments.
Citation
CentER Discussion Paper No. 2016-039