Multistage stochastic decision problems: Approximation by recursive structures and ambiguity modeling

Keywords Stochastic programming; Scenario tree generation; Recursive algorithms; Model error; Distributionally robust solutions HIGHLIGHTS * This is an elaboration of the semiplenary talk I held in Athens at EURO 2021. * The paper summarizes some earlier work, a new aspect is however included by emphasizing the recursive structure of data structures and algorithms. * The role of the ambiguity radius as a tradeoff between model information and efficiency of the optimal decisions is elaborated for several informative examples. Abstract Stochastic multistage decision problems appear in many - if not all - application areas of Operations Research. While to define such problems is easy, to solve them is quite difficult, since they are of infinite dimension. Numerical solution can only be found by solving an approximate, easier problem. In this paper, we show good approximations can be found, where we emphasize the recursive structure of the involved algorithms and data structures. In a second part, the problem of coping with the model error of approximations is discussed. We present algorithms for finding distributionally robust solutions for the model error problem. We also review some application cases of such situations from the literature. Author Affiliation: Faculty of Economics and Statistics, University of Vienna, Wien Oskar-Morgenstern Platz, Vienna A-1090, Austria Article History: Received 6 December 2021; Revised 20 March 2022; Accepted 2 April 2022 (footnote)[white star] This paper is an elaboration of a semiplenary talk held at the EURO21 conference in Athens Byline: Georg Ch. Pflug [georg.pflug@univie.ac.at]