We study a class of multi-stage stochastic programs, which incorporate modeling features from Markov decision processes (MDPs). This class includes structured MDPs with continuous state and action spaces. We extend policy graphs to include decision-dependent uncertainty for one-step transition probabilities as well as a limited form of statistical learning. We focus on the expressiveness of … Read more
We introduce two-stage stochastic min-max and min-min integer programs with bi-parameterized recourse (BTSPs), where the first-stage decisions affect both the objective function and the feasible region of the second-stage problem. To solve these programs efficiently, we introduce Lagrangian-integrated \(L\)-shaped (\(L^2\)) methods, which guarantee exact solutions when the first-stage decisions are pure binary. For mixed-binary first-stage … Read more
We consider a two-stage stochastic decision problem where the decision-maker has the opportunity to obtain information about the distribution of the random variables $\xi$ that appear in the problem through a set of discrete actions that we refer to as probing. Probing components of a random vector $\eta$ that is jointly-distributed with $\xi$ allows the … Read more
We consider a two-stage stochastic program with continuous recourse, where the distribution of the random parameters depends on the decisions. Assuming a finite sample space, we study a distributionally robust approach to this problem, where the decision-dependent distributional ambiguity is modeled with a polyhedral ambiguity set. We consider cases where the recourse function and the … Read more
In this paper, we study distributionally risk-receptive and distributionally robust (or risk-averse) multistage stochastic mixed-integer programs (denoted by DRR- and DRO-MSIPs). We present cutting plane-based and reformulation-based approaches for solving DRR- and DRO-MSIPs without and with decision-dependent uncertainty to optimality. We show that these approaches are finitely convergent with probability one. Furthermore, we introduce generalizations … Read more
We consider a robust optimization problem with continuous decision-dependent uncertainty (RO-CDDU), which has two new features: an uncertainty set linearly dependent on continuous decision variables and a convex piecewise-linear objective function. We prove that RO-CDDU is strongly NP-hard in general and reformulate it into an equivalent mixed-integer nonlinear program (MINLP) with a decomposable structure to … Read more
The type of decision dependent uncertainties (DDUs) imposes a great challenge in decision making, while existing methodologies are not sufficient to support many real practices. In this paper, we present a systematic study to handle this challenge in two-stage robust optimization~(RO). Our main contributions include three sophisticated variants of column-and-constraint generation method to exactly compute … Read more
Over the last two decades, robust optimization has emerged as a popular means to address decision-making problems affected by uncertainty. This includes single- and multi-stage problems involving real-valued and/or binary decisions, and affected by exogenous (decision-independent) and/or endogenous (decision-dependent) uncertain parameters. Robust optimization techniques rely on duality theory potentially augmented with approximations to transform a … Read more
The purpose of software partitioning is to assign code segments of a given computer program to a range of execution locations such as general purpose processors or specialist hardware components. These execution locations differ in speed, communication characteristics, and in size. In particular, hardware components offering high speed tend to accommodate only few code segments. … Read more