Data-driven Multistage Distributionally Robust Optimization with Nested Distance: Time Consistency and Tractable Dynamic Reformulations

We study multistage distributionally robust optimization in which the uncertainty set consists of stochastic processes that are close to a scenario tree in the nested distance (Pflug and Pichler (2012)). Compared to other choices such as Wasserstein distance between stochastic processes, the nested distance accounts for information evolution, making it hedge against a plausible family … Read more

A Fast Combinatorial Algorithm for the Bilevel Knapsack Problem with Interdiction Constraints

\(\) We consider the bilevel knapsack problem with interdiction constraints, a fundamental bilevel integer programming problem which generalizes the 0-1 knapsack problem. In this problem, there are two knapsacks and \(n\) items. The objective is to select some items to pack into the first knapsack such that the maximum profit attainable from packing some of … Read more

Compromise Policy for Multi-stage Stochastic Linear Programming: Variance and Bias Reduction

This paper focuses on algorithms for multi-stage stochastic linear programming (MSLP). We propose an ensemble method named the “compromise policy”, which not only reduces the variance of the function approximation but also reduces the bias of the estimated optimal value. It provides a tight lower bound estimate with a confidence interval. By exploiting parallel computing, … Read more

Optimizing Vaccine Distribution in Developing Countries under Natural Disaster Risk

For many developing countries, COVID-19 vaccination roll-out programs are not only slow but vaccination centers are also exposed to the risk of natural disaster, like flooding, which may slow down vaccination progress even further. Policy-makers in developing countries therefore seek to implement strategies that hedge against distribution risk in order for vaccination campaigns to run … Read more

Multi-Echelon Inventory Management for a Non-Stationary Capacitated Distribution Network

We present an inventory management solution for a non-stationary capacitated multi-echelon distribution network involving thousands of products. Assuming backlogged sales, we revisit and leverage the seminal multi-echelon inventory management results in the literature to establish the structural properties of the problem, and derive an efficient and practical solution method. In particular, we describe how the … Read more

Convergence of Trajectory Following Dynamic Programming algorithms for multistage stochastic problems without finite support assumptions

We introduce a class of algorithms, called Trajectory Following Dynamic Programming (TFDP) algorithms, that iteratively refines approximation of cost-to-go functions of multistage stochastic problems with independent random variables. This framework encompasses most variants of the Stochastic Dual Dynamic Programming algorithm. Leveraging a Lipschitz assumption on the expected cost-to-go functions, we provide a new convergence and … Read more

Solving large-scale unit-commitment problems using dual dynamic programming and open-source solvers

The astonishing dimensions and complexity of power systems render them impossible to be managed without the help of cutting-edge software. Due to a lack of scalable, reliable and well documented free and open-source solutions, system operators, regulators, and government agencies often rely on proprietary software to provide them information that ultimately will be used to … Read more

Robust Phi-Divergence MDPs

In recent years, robust Markov decision processes (MDPs) have emerged as a prominent modeling framework for dynamic decision problems affected by uncertainty. In contrast to classical MDPs, which only account for stochasticity by modeling the dynamics through a stochastic process with a known transition kernel, robust MDPs additionally account for ambiguity by optimizing in view … Read more

Randomized Policy Optimization for Optimal Stopping

Optimal stopping is the problem of determining when to stop a stochastic system in order to maximize reward, which is of practical importance in domains such as finance, operations management and healthcare. Existing methods for high-dimensional optimal stopping that are popular in practice produce deterministic linear policies — policies that deterministically stop based on the … Read more

Parallel Dual Dynamic Integer Programming for Large-Scale Hydrothermal Unit-Commitment

Unit commitment has been at the center of power system operation for well over 50 years. Yet, this problem cannot be considered solved due to its size and complexity. Today, operators rely on off-the-shelf optimization solvers to tackle this challenging problem, and often resort to simplifications to make the problem more tractable and solvable in … Read more