Analysis and algorithms for the transtainer routing problem in container port operations

The problem of minimizing the time taken to load the containers from the container stack yard onto the ship is called the transtainer routing problem. We first do a theoretical investigation of the problem to understand the structural properties of the problem. We then use these results to prove that the problem is NP-Complete. The problem is then formulated as an integer program. A branch-and-bound based enumerative method is developed to obtain an exact solution to the problem. An algorithm to solve the matching problem on a line at the root node of the branch-and-bound tree is developed. Several lower bounds to prune the size of the tree are also developed. A result which states that there cannot exist a polynomial time heuristic with a bounded worst case unless P = NP is proved. Based on this result, an enumerative heuristic with a worst-case performance ratio of 1.5 is designed. Computational tests on randomly generated problems are conducted to evaluate the exact and heuristic algorithms.