In this paper we propose and analyze inexact and stochastic versions of the CGALP algorithm developed in the authors’ previous paper, which we denote ICGALP, that allows for errors in the computation of several important quantities. In particular this allows one to compute some gradients, proximal terms, and/or linear minimization oracles in an inexact fashion … Read more
Hurricanes can cause severe property damage and casualties in coastal regions. Diesel fuel plays a crucial role in hurricane disaster relief. It is important to optimize fuel supply chain operations so that emergency demand for diesel can be mitigated in a timely manner. However, it can be challenging to estimate demand for fuel and make … Read more
We consider a certain class of hierarchical decision problems that can be viewed as single-leader multi-follower games, and be represented by a virtual market coordinator trying to set a price system for traded goods, according to some criterion that balances supply and demand. The objective function of the market coordinator involves the decisions of many … Read more
In this paper, we study the decision process of assigning elective surgery patients to available surgical blocks in multiple operating rooms (OR) under random surgery durations, random postoperative length-of-stay in the intensive care unit (ICU), and limited capacity of ICU. The probability distributions of random parameters are assumed to be ambiguous, and only the mean … Read more
We consider stochastic problems in which both the objective function and the feasible set are affected by uncertainty. We address these problems using a K-adaptability approach, in which K solutions for the underlying problem are computed before the uncertainty dissolves and afterwards the best of them can be chosen for the realised scenario. This paradigm … Read more
The purpose of this article is to establish epigraphical convergence of the sample averages of a random lower semi-continuous functional associated with a Harris recurrent Markov chain with stationary distribution $\pi$. Sample averages associated with an ergodic Markov chain with stationary probability distribution will epigraphically converge from $\pi$-almost all starting points. The property of Harris … Read more
We introduce a unified framework for the study of multilevel mixed integer linear optimization problems and multistage stochastic mixed integer linear optimization problems with recourse. The framework highlights the common mathematical structure of the two problems and allows for the development of a common algorithmic framework. Focusing on the two-stage case, we investigate, in particular, … Read more
We describe an algorithmic framework generalizing the well-known framework originally introduced by Benders. We apply this framework to several classes of optimization problems that fall under the broad umbrella of multilevel/multistage mixed integer linear optimization problems. The development of the abstract framework and its application to this broad class of problems provides new insights and … Read more
Wasserstein balls, which contain all probability measures within a pre-specified Wasserstein distance to a reference measure, have recently enjoyed wide popularity in the distributionally robust optimization and machine learning communities to formulate and solve data-driven optimization problems with rigorous statistical guarantees. In this technical note we prove that the Wasserstein ball is weakly compact under … Read more
Mine planning optimization aims at maximizing the profit obtained from extracting valuable ore. Beyond its theoretical complexity (the open-pit mining problem with capacity constraints reduces to a knapsack problem with precedence constraints, which is NP-hard), practical instances of the problem usually involve a large to very large number of decision variables, typically of the order … Read more