Orientational variable-length strip covering problem: A branch-and-price-based algorithm

•Proposed the orientational variable-length strip covering problem.•Provided a set-cover-problem-like formulation based on grid discretization.•Developed a branch-and-price-based algorithm framwork for the problem.•Proved a dominance rule to reduce the solution space of the subproblems.•Proposed an efficient approximate pricing strategy using nested fatherchild grids.