The model is capable of solving instances up to (5 × 3).
We propose an efficient heuristic approach for solving instances of the Single String Planning Problem (SSPP) arising in the liner shipping industry.
So, heuristic methods are necessary to be used for solving instances with large size in a reasonable amount of time.
We propose designs for solving instances of Hamiltonian path, Traveling Salesman, Clique, Independent Set, Vertex Cover, Partition, 3-SAT, 3D-matching, and the Permanent.
The GPU implementation of SGS also shows an excellent scalability behavior when solving instances with a large number of test cases.
Our numerical experiments show that the method is very efficient in solving instances of this problem with respect to both the problem size and the computational time.
In a computational study we compare these alternatives with respect to the lower bounds obtained from the corresponding linear programming relaxations and their capability of solving instances to proven optimality.
However, the computing time of this latter approach may vary in a substantial way when solving instances of different type – although of the same size – which is not the case for algorithm DP, whose computing time is more stable.
In the previous section (Table 6), we solved instance 5 by considering from the outset the difference among surgeons in terms of skill: the resulting cost was €3,650, which is significantly lower than €6,048.
The proposed exact methods are able to optimally solve instances with up to 60 nodes.
We then propose a primal decomposition method to solve instances of the problem to optimality.
