Driven by ambitious renewable portfolio standards, variable energy resources (such as wind and solar) are expected to impose unprecedented levels of uncertainty to power system operations. The current practice of planning operations with deterministic optimization tools may be ill-suited for a future where uncertainty is abundant. To overcome the reliability challenges associated with the large-scale … Read more
We introduce the Stochastic Maintenance Fleet Transportation Problem for Offshore wind farms (SMFTPO), in which a maintenance provider determines an optimal, medium-term planning for maintaining multiple wind farms while controlling for uncertainty in the maintenance tasks and weather conditions. Since the maintenance provider is typically not the owner of a wind farm, it needs to … Read more
Multi-stage stochastic programming is a well-established framework for sequential decision making under uncertainty by seeking policies that are fully adapted to the uncertainty. Often, e.g. due to contractual constraints, such flexible and adaptive policies are not desirable, and the decision maker may need to commit to a set of actions for a certain number of … Read more
We propose a new algorithm for solving multistage stochastic mixed integer linear programming (MILP) problems with complete continuous recourse. In a similar way to cutting plane methods, we construct nonlinear Lipschitz cuts to build lower approximations for the non-convex cost to go functions. An example of such a class of cuts are those derived using … Read more
We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix, and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions ensuring convexity. … Read more
This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear … Read more
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more
We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We consider an approach in which the decision-maker (DM) considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the … Read more
Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems. Multi-component maintenance optimization, which joins the stochastic failure processes with the combinatorial maintenance grouping problems, remains as an open issue. To address this challenge, we study this problem in a finite planning horizon by … Read more