A Base Integer Programming Model and Benchmark Suite for Liner-Shipping Network Design

Abstract

The liner-shipping network design problem is to create a set of nonsimple cyclic sailing routes for a designated fleet of container vessels that jointly transports multiple commodities. The objective is to maximize the revenue of cargo transport while minimizing the costs of operation. The potential for making cost-effective and energy-efficient liner-shipping networks using operations research (OR) is huge and neglected. The implementation of logistic planning tools based upon OR has enhanced performance of airlines, railways, and general transportation companies, but within the field of liner shipping, applications of OR are scarce. We believe that access to domain knowledge and data is a barrier for researchers to approach the important liner-shipping network design problem. The purpose of the benchmark suite and the paper at hand is to provide easy access to the domain and the data sources of liner shipping for OR researchers in general. We describe and analyze the liner-shipping domain applied to network design and present a rich integer programming model based on services that constitute the fixed schedule of a liner shipping company. We prove the liner-shipping network design problem to be strongly NP-hard. A benchmark suite of data instances to reflect the business structure of a global liner shipping network is presented. The design of the benchmark suite is discussed in relation to industry standards, business rules, and mathematical programming. The data are based on real-life data from the largest global liner-shipping company, Maersk Line, and supplemented by data from several industry and public stakeholders. Computational results yielding the first best known solutions for six of the seven benchmark instances is provided using a heuristic combining tabu search and heuristic column generation.

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

“…Several factors such as price, transit time, transshipments, port coverage, frequency, reliability, administration, equipment, environmental friendliness and schedules can be relevant and important for a shipper when considering different carriers, (Brouer et al, 2014). Hence it is important to meet these constraints when constructing and evaluating liner shipping networks.…”

“…Hence it is important to meet these constraints when constructing and evaluating liner shipping networks. The cost and transit time are often identified as the most important factors, Brouer et al, 2014;Gelareh et al, 2010;Notteboom and Vernimmen, 2009;Notteboom, 2006), however, most previous work within LSND neglects transit time and mainly considers cost. Designing networks with focus only on cost has the apparently attractive benefit that reducing cost goes hand in hand with reducing CO 2 emissions as fuel is the largest cost component.…”

“…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.…”

“…For a global network the number of ports is significantly less than the number of commodities |P | < |K|. In the WorldSmall instance provided in Brouer et al (2014) there are |P | = 47 ports and |K| = 1764 commodities and in the AsiaEurope instance there are |P | = 111 ports and |K| = 4000 commodities. The algorithm is based on a variation of the The Boost Graph Library (BGL) implementation.…”

“…The transit time is the time it takes a commodity to travel from origin to destination. Transit time is counted in days and allowed transit times may vary from one day to several months Brouer et al (2014). Liner shipping networks that are optimized only with respect to cost get an unrealistically high network utilization as containers are allowed on detours that offer unused capacity but in practice they will violate transit time restrictions.…”