An exact algorithm for the single liner service design problem with speed optimisation: .

This paper models a single liner service design and operations problem. The model selects the portsto be included, their sequence, the sailing speed of vessels, the number of vessels and the amountsof cargo to transport by the service. The objective is to maximise profit. First, a relaxation with amixed-integer nonlinear programming (MINLP) formulation is proposed. We show how to obtainthe optimal speed value. Once this value is obtained, the mathematical programming formulation becomes a mixed-integer linear program (MILP). Then, a two-step exact algorithm is presented to solve the problem. Using real data, the optimal solution was found in less than 1 min for small-size problems and in few hours for relatively large-size problems. More tests were carried out on randomly generated data sets with up to 25 ports. The results of these tests are rather promising, and they enabled us to identify the performance limits of the algorithm.