In this work, we address a production and inventory routing problem for a liquid oxygen supply chain comprising production facilities, distribution network, and distribution resources. The key decisions of the problem involve production levels of production plants, delivery schedule and routing through heterogeneous vehicles, and inventory strategies for national stock-out prevention. Due to the problem complexity, we propose a two-level hybrid solution approach that solves the problem using both exact and metaheuristic methods. At the upper level, we develop a mixed-integer linear programming (MILP) model that determines production and inventory decisions and customer allocation. In the lower level, the original problem is reduced to several multi-trip heterogeneous vehicle routing problems by fixing the optimal production, inventory, and allocation decisions and clustering customers. A well-recognised metaheuristic, guided local search method, is adapted to solve the low-level routing problems. A real-world case study in the UK illustrates the applicability and effectiveness of the proposed optimisation framework
