Reliable facility location design with round-trip transportation under imperfect information Part I: A discrete model

•Consider round-trip transportation and the optimal try-and error visiting strategy in reliable location design.•Formulate a compact model for reliable location design with round-trip transportation and under imperfect information.•Propose an efficient customized solution approach based on Lagrangian relaxation.•Compare the proposed customized algorithm and commercial solver.•Reveal the effect of influence factors on optimal location design and cost components. In this paper, we propose a discrete model to investigate reliable location design with round-trip transportation under imperfect information. The unique feature of this problem is that under each disruption scenario, a customer’s outbound and inbound trips are different when she travels to obtain a service. The discrete model is formulated as a compact non-linear integer programming problem and solved efficiently by a customized Lagrangian relaxation algorithm. Numerical experiments find that the discrete model performs well for small and medium-scale problem instances. Sensitivity analyses reveal the impacts of several parameters on both the cost components and the optimal facility layouts.