A matheuristic for the liner shipping network design problem

Abstract

We present a matheuristic, an integer programming based heuristic, for the Liner Shipping Network Design Problem. The heuristic applies a greedy construction heuristic based on an interpretation of the liner shipping network design problem as a multiple quadratic knapsack problem. The construction heuristic is combined with an improvement heuristic with a neighborhood defined by the solution space of a mixed integer program. The mixed integer program optimizes the removal and insertion of several port calls on a liner shipping service. The objective function is based on evaluation functions for revenue and transshipment of cargo along with in/decrease of vessel-and operational cost for the current solution. The evaluation functions may be used by heuristics in general to evaluate changes to a network design without solving a large scale multicommodity flow problem.

The time constrained multi-commodity network flow problem and its application to liner shipping network design

“…Neither exact nor heuristic solution methods are yet able to solve LSND instances with the size of a global carrier to (near) optimality, but a promising approach is to rely on a two-tier structure as in Álvarez (2011);Brouer and Desaulniers (2012);Brouer et al (2014), where route planing, fleet deployment and sailing speed is determined in the upper tier corresponding to determining the cost of the network, while the lower tier determines the revenue of the network by flowing the available cargo. In the following, we consider the cargo flow subproblem, which is one of the main challenges in LSND.…”

“…Also a load edge, L, is included to account for loading cost and time as well as an unload edge, U . Hence in contrast to Brouer and Desaulniers (2012) the graph only includes relevant load/unload edges. Figure 5 shows the pseudo code for the contraction algorithm.…”

“…visited by more than one rotation). We use the network structure presented in Brouer and Desaulniers (2012) as a reference, denoted the Full Graph. Additionally to reduce the size of the reduced graph used during the SPP calculations we only consider the load and unload edges which are relevant to the considered set of commodities as well as the relevant forfeited edges in contrast to Brouer and Desaulniers (2012).…”

“…Brouer and Desaulniers (2012), and may be the most intuitive representation of a transship-ment as all rotations visiting a port are directly connected to all other rotations visiting the same port. This allows different costs and transit times between different rotations, which can be calculated directly according to some given schedule including buffer time.…”

“…We use networks constructed based on six of these instances, see Table 1. The networks have been constructed using the mat-heuristic that does not consider transit time described in Brouer and Desaulniers (2012). We report results for networks from each instance.…”