A metaheuristic approach to the reliable location routing problem under disruptions

• This paper studies a location–routing problem that incorporates facility disruption risks.
• Scenario-based formulations and an efficient heuristic are developed to solve the problem.
• Route reallocation phase is solved by a new Lagrangian relaxation algorithm.
• The metaheuristic is competitive when solving deterministic LRP benchmark problems.
• The model produces networks that perform well under disruption scenarios.

This paper examines a reliable capacitated location–routing problem in which depots are randomly disrupted. Customers whose depots fail must be reinserted into the routes of surviving depots. We present a scenario-based mixed-integer programming model to optimize depot location, outbound delivery routing, and backup plans. We design a metaheuristic algorithm that is based on a maximum-likelihood sampling method, route-reallocation improvement, two-stage neighborhood search and simulated annealing. Numerical tests show that the heuristic is able to generate results that would keep operating costs and failure costs well balanced. Managerial insights on scenario identification, facility deployment and model simplification are drawn.