Constant Depth Decision Rules for multistage optimization under uncertainty

In this paper, we introduce a new class of decision rules, referred to as Constant Depth Decision Rules (CDDRs), for multistage optimization under linear constraints with uncertainty-affected right-hand sides. We consider two uncertainty classes: discrete uncertainties which can take at each stage most fixed number d different values, and polytopic which, stage, are elements convex hull points. Given the depth μ rule, t is expressed sum functions consecutive values underlying uncertain parameters. These arbitrary in case poly-affine uncertainties. For these classes, show that when sides problem same additive structure be reformulated system inequality where numbers variables O(1)(n+m)dμN2 n maximal dimension control variables, m N stages. As an illustration, discuss application proposed approach Multistage Stochastic Program arising hydro-thermal production planning interstage dependent inflows. problems small stages, present results numerical study optimal CDDRs similar performance, terms objective, Dual Dynamic Programming (SDDP) policies, often much smaller computational cost.