Solving a real-world multi-depot multi-period petrol replenishment problem with complex loading constraints

•New complex variant of the petrol replenishment problem with multiple depots, multiple periods and time windows.•Introduction of a new primal branch-and-price diving heuristic appropriate for low to moderately dense set partitioning type problems.•Exact branch-and-price approach to assess the quality of the heuristic solutions.•Efficient generation of routes (columns) with very complex loading constraints thanks to a hashing technique and other acceleration strategies.•A case study showing the implementability of the proposed approach.