The Two‐Echelon Multicommodity Location‐Routing Problem With Stochastic and Correlated Demands

This study introduces the two‐echelon multicommodity location routing problem with stochastic and correlated demands. We propose a two‐stage stochastic programming formulation, with second‐echelon facilities location and commodity allocation decisions defining the first stage, while recourse decisions, which are made in the second stage, establish how the observed demands are distributed. The overall objective is to minimize the cost of the first‐stage design decisions plus the total expected routing cost incurred in the second stage. We propose a Progressive Hedging matheuristic that heuristically solves the formulation, incorporating a series of algorithmic enhancements to accelerate the exploration of the solution space. These enhancements include: (1) population structures to obtain alternative and diverse solutions for the scenario subproblems that need to be solved throughout the search process; (2) alternative strategies to define the reference solutions that are used to guide and accelerate the overall search; and (3) a reset procedure that reduces the risk of the method becoming trapped in local optima. We assess the efficiency and effectiveness of all proposed strategies through extensive computational experiments, evaluating their capability to generate high‐quality solutions across various problem characteristics and demand correlations.