Desaulniers, Guy

Koza, David Franz

Røpke, Stefan

Global container liner shipping networks are composed of services and each service represents a roundtrip that connects a set of ports following a published schedule. The majority of services is operated at a weekly frequency, and each port on a service is visited at the same time each week. Commonly, all vessels deployed on a service are of the same capacity. Liner services are connected through common port calls that allow liner network operators to move cargo from one service to another. The movement of containers between services is called transshipment and enables large liner shipping companies to transport containers between almost any possible pair of ports around the globe. Current state-of-the-art models and methods (e.g. Karsten et al., 2017) for liner shipping network design problems only determine the routes and sailing speeds for individual services, but approximate transshipment times by a constant. In practice, the transshipment time between two services depends on how well the schedules of the individual services are synchronized. In the network of the world’s largest overseas cargo carrier, around half of all transported containers are transshipped, and the transshipment times may significantly affect the total transit time of containers between their origin and destination port

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Downloaded from orbit.dtu.dk on: Mar 30, 2019Integrated Liner Shipping Network Design and Scheduling, or: Solving a large servicenetwork design problemKoza, David Franz; Desaulniers, Guy; Røpke, StefanPublication date:2018Document VersionPeer reviewed versionLink back to DTU OrbitCitation (APA):Koza, D. F., Desaulniers, G., & Røpke, S. (2018). Integrated Liner Shipping Network Design and Scheduling, or:Solving a large service network design problem. Paper presented at ROUTE 2018, Snekkersten, Denmark.Integrated Liner Shipping Network Design and Scheduling, or:Solving a large service network design problemD.F. Kozaa, G. Desaulniersb, S. Ropkeaa Department of Management Engineering, Technical University of Denmark,dakoz@dtu.dk, ropke@dtu.dkb GERAD & Department of Mathematics and Industrial Engineering, Polytechnique Montre´al, Canada,guy.desaulniers@gerad.caGlobal container liner shipping networks are composed of services and each service represents aroundtrip that connects a set of ports following a published schedule. The majority of servicesis operated at a weekly frequency, and each port on a service is visited at the same time eachweek. Commonly, all vessels deployed on a service are of the same capacity. Liner services areconnected through common port calls that allow liner network operators to move cargo fromone service to another. The movement of containers between services is called transshipmentand enables large liner shipping companies to transport containers between almost any possiblepair of ports around the globe.Current state-of-the-art models and methods (e.g. Karsten et al., 2017) for liner shipping net-work design problems only determine the routes and sailing speeds for individual services, butapproximate transshipment times by a constant. In practice, the transshipment time betweentwo services depends on how well the schedules of the individual services are synchronized. Inthe network of the world’s largest overseas cargo carrier, around half of all transported contain-ers are transshipped, and the transshipment times may significantly affect the total transit timeof containers between their origin and destination port.The Integrated Liner Shipping Network Design and Scheduling Problem (LSNDSP) extends theclassic liner shipping network design problem by defining schedules for all services, and by con-sidering the interdependency between these. The goal is to construct a network of scheduledservices and to determine feasible container routes through the network such that the revenuefrom transporting cargo minus the cost of operating the services and handling cargo is maxi-mized. A service is defined by the deployed vessel class and its capacity, a cyclic route and aschedule. The schedule implicitly defines the sailing speed on each sailing leg. The length of aservice is required to be a multiple of a week and the number of vessels operating the serviceis equal to its duration to ensure a weekly frequency. A demand represents a weekly quantityof containers for a particular origin-destination pair of ports. Each demand is associated witha unit revenue. Additionally, transit time limits apply, reflecting a demand’s time-sensitivity.Cargo can be transshipped between services, but every transshipment implies additional costs1ABCD0 24 48 72 96 120 144TimePortFigure 1: Illustration of a time-space graph G. Solid arcs represent sailings between ports and dashedarcs represent transshipments. The colored arcs denote examples of cargo paths; the bluepath from port D to port C is direct, whereas the red path from port A to port D requires atransshipment at port C. Backward arcs represent sailings or transshipments that end in thefollowing week.for cargo handling at the transshipment port. The transshipment time depends on the schedulesof the unloading and the loading service. If a minimum transshipment time is not met, cargomay have to wait one week for the next vessel to arrive. A limit on the number of transshipmentsmay be defined for a demand, reflecting the shippers preference towards direct shipping routes.A demand can, but does not have to be served by the cargo carrier, and it can be fulfilledpartially.We model the problem over a directed time-space graph G(V,A), with vertices V representinga port at a particular time within a week (168h), and arcs A representing sailings (AS) ortransshipments (AT ). Figure 1 illustrates a solution over a small time-space graph of four portsand a time discretization of 24 hours. The problem formulation over graph G is a variation ofservice network design problems, which are generalizations of (capacitated) fixed-charge networkdesign problems (Crainic, 2000). The LSNDSP is NP-hard in the strong sense.To solve the problem we propose a column-and-row generation (CRG) matheuristic that com-bines linear programming techniques with heuristics. The method can be used to construct newliner networks or to extend or improve existing liner networks. In our talk we will discuss someInstance Graph G(V,A) Model|V | |A| |AS | |AT | constraints binary varsBaltic 168 7,812 5,460 2,352 5,988 8,652WAF 280 42,168 38,248 3,920 39,127 51,016Mediterranean 546 108,206 101,108 7,644 103,660 165,816Pacific 630 542,262 534,072 8,820 537,948 1,044,708Table 1: Graph and model properties for each data instance under a time discretization of 12 hours.2Instance CRG matheuristic Karsten et al. (2017)exact transship. time 48h transship. time 48h transship. timeBaltic Best -2.84·105 -2.84·105 -0.05·105Average -2.24·105 -2.08·105 1.74·105WAF Best -5.92·106 -5.90·106 -5.48·106Average -5.76·106 -5.77·106 -4.89·106Mediterranean Best 2.54·106 2.11·106 2.19·106Average 2.73·106 2.33·106 2.65·106Pacific Best 2.69·106 -0.33·106 1.13·106Average 3.71·106 1.06·106 3.44·106Table 2: Best and average objective function values (cost in USD) per instance, comparing results obtainedby the CRG matheuristic under exact and approximated (48h) transshipment times with results fromKarsten et al. (2017)of the applied linear and integer programming techniques in detail.We tested the method on data instances from the publicly available LINER-LIB benchmarksuite, which was developed in collaboration with a large liner shipping company (Brouer et al.,2014). Table 1 shows the resulting graph and model size for the four considered instances.Table 2 displays the objective function values obtained by the CRG matheuristic for the LSNDSPas well as for the LSNDSP under the simplifying assumption of constant transshipment times.The displayed values represent cost minus revenues, thus lower values reflect better solutions. Inthe third column, the objective function values found by the solution method for the liner ship-ping network design problem by Karsten et al. (2017) are reported. Under equal assumptions,the proposed CRG matheuristic consistently finds better solutions for all addressed instances.We further observe that a 48-hours approximation of transshipment times may result in anoverestimation of profits.ReferencesBrouer, B. D., Alvarez, J. F., Plum, C. E. M., Pisinger, D., and Sigurd, M. M. (2014). A baseinteger programming model and benchmark suite for liner-shipping network design. Trans-portation Science, 48(2):281–312.Crainic, T. G. (2000). Service network design in freight transportation. European Journal ofOperational Research, 122(2):272 – 288.Karsten, C. V., Brouer, B. D., and Pisinger, D. (2017). Competitive liner shipping networkdesign. Computers & Operations Research, 87:125 – 136.3

Integrated Liner Shipping Network Design and Scheduling, or: Solving a large service network design problem

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Integrated Liner Shipping Network Design and Scheduling, or: Solving a large service network design problem

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