An Exact Algorithm for the Two-Dimensional Orthogonal Packing Problem with Unloading Constraints

This paper describes a branch-and-cut algorithm for solving a two-dimensional orthogonal packing problem with unloading constraints, which often occurs as a subproblem of mixed vehicle routing and loading problems. At each node of the branching tree, cuts are generated to find a feasible integer solution to a one-dimensional contiguous bin packing problem. If an integer solution is obtained, an auxiliary problem is then solved to find a feasible two-dimensional packing of the items. Different techniques to reduce the size of the solution space and uncover infeasibility are also described. A numerical comparison with the best known exact method is reported at the end on benchmark instances.