A Path Based Model for a Green Liner Shipping Network Design Problem

Abstract—Liner shipping networks are the backbone ofinternational trade providing low transportation cost, whichis a major driver of globalization. These networks are underconstant pressure to deliver capacity, cost effectiveness and envi-ronmentally conscious transport solutions. This article proposesa new path based MIP model for the Liner shipping NetworkDesign Problem minimizing the cost of vessels and their fuelconsumption facilitating a green network. The proposed modelreduces problem size using a novel aggregation of demands.A decomposition method enabling delayed column generationis presented. The subproblems have similar structure to Ve-hicle Routing Problems, which can be solved using dynamicprogramming.Index Terms—liner shipping, network design, mathematicalprogramming, column generation, green logistics I. I NTRODUCTION G LOBAL liner shipping companies provide port to porttransport of containers, on a network which representsa billion dollar investment in assets and operational costs.The liner shipping network can be viewed as a transporta-tion system for general cargo not unlike an urban mass transitsystem for commuters, where each route (service) providestransportation links between ports and the ports allow fortranshipment in between routes (services). The liner shippingindustry is distinct from other maritime transportation modesprimarily due to a fixed public schedule with weekly fre-quency of port calls as an industry standard (Stopford 1997).The network consists of a set of services. A service connectsa sequence of ports in a cycle at a given frequency, usuallyweekly. In Figure 1 a service connecting Montreal-Halifaxand Europe is illustrated. The weekly frequency means thatseveral vessels are committed to the service as illustrated byFigure 1, where four vessels cover a round trip of 28 daysplaced with one week in between vessels. This roundtrip forthe vessel is referred to as a rotation. Note that the Montrealservice carries cargo to the Mediterranean and Asia. Thisillustrates that transhipments to other connecting servicesis at the core of liner shipping. Therefore, the design of aservice is complex, as the set of rotations and their interactionthrough transhipment is a transportation system extending thesupply chains of a multiplum of businesses. Figure 2 illus-trates two services interacting in transporting goods betweenMontreal-Halifax and the Mediterranean, while individually