Partial Benders Decomposition: General Methodology and Application to Stochastic Network Design

Author:

Crainic Teodor Gabriel1ORCID,Hewitt Mike2ORCID,Maggioni Francesca3,Rei Walter4ORCID

Affiliation:

1. Département d'analytique, opérations et technologies de l'information, École des Sciences de la Gestion, Université du Québec à Montréal, Montréal, Québec H2X 3X2, Canada;

2. Department of Information Systems and Supply Chain Management, Quinlan School of Business, Loyola University Chicago, Chicago, Illinois 60611;

3. Department of Economics, Università degli studi di Bergamo, 24127 Bergamo, Italy

4. Centre Interuniversitaire de Recherche sur les Réseaux d'Entreprise, la Logistique et le Transport (CIRRELT), Montréal, Québec H3T 1J4, Canada;

Abstract

Benders decomposition is a broadly used exact solution method for stochastic programs, which has been increasingly applied to solve transportation and logistics planning problems under uncertainty. However, this strategy comes with important drawbacks, such as a weak master problem following the relaxation step that confines the dual cuts to the scenario subproblems. In this paper, we propose a partial Benders decomposition methodology, based on the idea of including explicit information from the scenario subproblems in the master. To investigate the benefits of this methodology, we apply it to solve a general class of two-stage stochastic multicommodity network design models. Specifically, we solve the challenging variant of the model where both the demands and the arc capacities are stochastic. Through an extensive experimental campaign, we clearly show that the proposed methodology yields significant benefits in computational efficiency, solution quality, and stability of the solution process.

Publisher

Institute for Operations Research and the Management Sciences (INFORMS)

Subject

Transportation,Civil and Structural Engineering

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