two-stage stochastic programming – Optimization Online

Route `Em and Count `Em: A Two-Stage Stochastic Programming Model for Anti-Submarine Operations

Published: 2026/07/11

Tracking targets in undersea warfare requires successful detection by an active search asset. Maximizing detection likelihood requires strategic placement and routing of the search assets in the search region over the planning horizon. We develop a two-stage stochastic integer programming model that maximizes the expected total reward for target detections under uncertainty in target motion … Read more

Skip or Insert? A Priori Optimization for the Vehicle Routing Problem with Time Windows and Stochastic Customers

Published: 2026/06/21

Combinatorial Optimization, Production and Logistics, Stochastic Programming benders decomposition, cut-and-branch, integer l-shaped method, stochastic customers, time windows, two-stage stochastic programming, valid inequalities, vehicle routing

We study an extension of the vehicle routing problem with time windows by incorporating stochastic customers, i.e., ad-hoc service requests. The uncertainty in stochastic customers is captured through scenarios. Two a priori optimization approaches, a classical and a new one lead to two different problems, both of which are modeled as scenario-based two-stage stochastic programs. … Read more

Heuristics for two-stage stochastic K-adaptability

Published: 2026/02/06

Stochastic Programming heuristics, k-adaptability, two-stage stochastic programming

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K-adaptability for two-stage stochastic optimization

Published: 2025/11/21

Global Optimization, Stochastic Programming Branch-and-Bound, k-adaptability, two-stage stochastic programming

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MUSE-BB: A Decomposition Algorithm for Nonconvex Two-Stage Problems using Strong Multisection Branching

Published: 2024/06/28

Global Optimization, Parallel Algorithms, Stochastic Programming clustering, convergence analysis, decomposition, multisection, two-stage stochastic programming

We present MUSE-BB, a branch-and-bound (B&B) based decomposition algorithm for the deterministic global solution of nonconvex two-stage stochastic programming problems. In contrast to three recent decomposition algorithms, which solve this type of problem in a projected form by nesting an inner B&B in an outer B&B on the first-stage variables, we branch on all variables … Read more

A two-stage stochastic programming approach incorporating spatially-explicit fire scenarios for optimal firebreak placement

Published: 2023/11/24, Updated: 2023/12/11

(Mixed) Integer Linear Programming, Stochastic Programming Firebreak placement, Spatially-explicit fire scenarios, two-stage stochastic programming, Widlfire management, Wildfire simulation

Ensuring the effective placement of firebreaks across the landscape is a critical issue in wildfire prevention, as their success relies on their ability to block the spread of future fires. To address this challenge, it is essential to recognize the stochastic nature of fires, which are highly unpredictable from start to finish. The issue is … Read more

Leveraging Decision Diagrams to Solve Two-stage Stochastic Programs with Binary Recourse and Logical Linking Constraints

Published: 2022/11/03

Stochastic Programming benders decomposition, binary decision diagrams, conditional-value-at-risk, two-stage stochastic programming

Two-stage stochastic programs with binary recourse are challenging to solve and efficient solution methods for such problems have been limited. In this work, we generalize an existing binary decision diagram-based (BDD-based) approach of Lozano and Smith (Math. Program., 2018) to solve a special class of two-stage stochastic programs with binary recourse. In this setting, the … Read more

A Machine Learning Approach to Solving Large Bilevel and Stochastic Programs: Application to Cycling Network Design

Published: 2022/09/23

Bo Lin

Integer Programming, Stochastic Programming, Transportation bilevel optimization, cycling network design, machine learning, model reduction, two-stage stochastic programming

We present a novel machine learning-based approach to solving bilevel programs that involve a large number of independent followers, which as a special case include two-stage stochastic programming. We propose an optimization model that explicitly considers a sampled subset of followers and exploits a machine learning model to estimate the objective values of unsampled followers. … Read more

Planning of Container Crossdocking for an Express Shipment Service Network

Published: 2022/06/15

Applications - OR and Management Sciences, Stochastic Programming, Transportation benders decomposition, container crossdocking planning, express shipment service, level bundle method, two-stage stochastic programming

In air transportation, container crossdocking refers to a loaded container that is transferred at an airport from an incoming flight to an outgoing flight without handling the freight on the container. It reduces handling time and handling cost relative to unloading the container and sorting the freight, and is an economical alternative if a sufficient … Read more

Neur2SP: Neural Two-stage Stochastic Programming

Published: 2022/05/25

Stochastic Programming deep learning, supervised learning, two-stage stochastic programming

Stochastic programming is a powerful modeling framework for decision-making under uncertainty. In this work, we tackle two-stage stochastic programs (2SPs), the most widely applied and studied class of stochastic programming models. Solving 2SPs exactly requires evaluation of an expected value function that is computationally intractable. Additionally, having a mixed-integer linear program (MIP) or a nonlinear … Read more