A Matheuristic for the Liner Shipping Network Design Problem with Transit Time Restrictions

Abstract

Abstract. We present a mathematical model for the liner shipping network design problem with transit time restrictions on the cargo flow. We extend an existing matheuristic for the liner shipping network design problem to consider transit time restrictions. The matheuristic is an improvement heuristic, where an integer program is solved iteratively as a move operator in a large-scale neighborhood search. To assess the effects of insertions/removals of port calls, flow and revenue changes are estimated for relevant commodities along with an estimation of the change in the vessel cost. Computational results on the benchmark suite LINER-LIB are reported, showing profitable networks for most instances. We provide insights on causes for rejecting demand and the average speed per vessel class in the solutions obtained.

Competitive Liner Shipping Network Design

“…If speed can be determined individually on each sailing leg, 3 vessels can be deployed with a speed of 14 knots between A and B and a speed of 12 knots on the remaining sailing legs maintaining the weekly frequency but resulting in a significant decrease in the bunker consumption (since the bunker consumption is a cubic function of the speed (Brouer et al, 2014a)). The computational results presented in Brouer et al (2015) support a higher average speed and low fleet deployment in networks optimized with transit time restrictions and constant speed.…”

“…Table 3 gives an overview of the instances. The transit time restrictions have been updated according to the most recent published liner shipping transit times for a small number of the origin-destination pairs as described in Brouer et al (2015). Table 3: The instances of the benchmark suite with indication of the number of ports |P |, the number of origin-destination pairs |K|, and the number of vessel classes |E|.…”

“…It extends the classical LSNDP to consider level of service as this is the main concern for the shipper. The CLSNDP we present here is based on the reference model for the LSNDP presented in Brouer et al (2014a) which has been extended in Brouer et al (2015) to consider transit time restrictions for all commodities, see A for a full description of the model. The primary change in order to accommodate transit time restrictions into the model of Brouer et al (2014a) is to decompose the multi commodity flow problem into a path flow formulation.…”

“…This is partly based on Brouer et al (2015) and extends the problem description of the LSNDP presented in Brouer et al (2014a) to handle transit times and variable speed. The model enforces a weekly frequency resulting in a weekly planning horizon.…”

“…A drawback of this formulation is that it cannot cater for transshipments of cargo which is the backbone of global liner shipping networks. Recently Brouer et al (2015) presented a capacitated multi-commodity network design formulation that imposes transit time restrictions while still allowing transshipments between services and Karsten et al (2015a) showed that time restricted multi-commodity flow problem arising as a sub-problem can be efficiently solved for a large global shipping network. The CLSNDP in this paper build upon these contributions.…”