Jensen, Rune Møller

Tierney, Kevin

Liner shipping fleet repositioning consists of moving vessels between services in a liner ship- ping network in order to better orient the overall network to the world economy, and to ensure the proper maintenance of vessels. Thus, fleet repositioning involves sailing and loading activities subject to complex handling and timing restrictions. The objective of the problem is cost minimization, which translates nearly directly into the minimization of CO2 emissions and pollution. Additionally, it is important that all cost elements, including the ones that are only loosely coupled with activity choices, can be accurately modeled.Numerous liner shipping fleet repositioning problems are solved each year by the world’s shipping firms without the assistance of any decision support, even though humans can require between two to three days to find a reasonable solution. Finding optimal repositionings is important in helping shipping firms move towards their goal of greater eco-efficiency

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Liner Shipping Fleet RepositioningKevin Tierney and Rune Møller JensenIT University of Copenhagen, Rued Langgaards Vej 7, Copenhagen S, Denmark{kevt,rmj}@itu.dkLiner shipping fleet repositioning consists of moving vessels between services in a liner ship-ping network in order to better orient the overall network to the world economy, and to ensurethe proper maintenance of vessels. Thus, fleet repositioning involves sailing and loading activi-ties subject to complex handling and timing restrictions. The objective of the problem is costminimization, which translates nearly directly into the minimization of CO2 emissions and pollu-tion. Additionally, it is important that all cost elements, including the ones that are only looselycoupled with activity choices, can be accurately modeled.Numerous liner shipping fleet repositioning problems are solved each year by the world’sshipping firms without the assistance of any decision support, even though humans can requirebetween two to three days to find a reasonable solution. Finding optimal repositionings is impor-tant in helping shipping firms move towards their goal of greater eco-efficiency.Unlike the Fleet Deployment Problem (FDP) [8], in which vessels are matched to services,and the Liner Shipping Network Design Problem (LSNDP) [1], liner shipping fleet repositioningproblems have been given little attention in the literature. Indeed, the problem is not mentionedeven in Christiansen, et. al’s detailed and comprehensive reviews of liner shipping optimization [3]and maritime transportation [2]. As in fleet repositioning, airline disruption management [5, 7]has a variety of activities with objectives that are linked to action duration, such as the speedat which an airplane flies. However, airplane routes lack the cyclical structure of liner shippingservices, as well as the notion of empty equipment repositioning.Liner vessel shipping networks consist of multiple services, which are circular routes that visita sequence of ports on a weekly schedule. That is, each port on a service is visited by a vessel onthe same day each week, and a service is assigned as many vessels as are necessary to maintainweekly frequency. Liner shipping fleet repositioning problems involve a number of vessels, eachwith an initial and goal service. Each vessel must be repositioned to its goal service from itsinitial service as cheaply as possible. Given the high expense of repositioning, the goal of linershipping fleet repositioning problems is to find a scenario of activities, which involve continuoussailing time and cost configuration decisions, associated with a lowest cost optimization model.Figure 1 shows a subset of a fleet repositioning problem from our industrial partner in whicha vessel is repositioned from its service in Asia (CHX) to a new service in South America calledFig. 1: A real world repositioning from our industrial partner. A vessel is repositioned from theCHX service, through the AC3 service to Intra-WCSA.2 Kevin Tierney and Rune Møller JensenID # Ves. # SOS Port Fees # Equip. Cabo. # Act. DS DSLP DI LP1 2 0 Yes 0 Yes 182 63.99 65.24 62.91 57.762 3 0 Yes 0 Yes 252 247.9 269.45 264.1 230.73 1 1 Yes 3 Yes 255 26.70 11.63 30.66 16.004 3 2 Yes 0 Yes 471 672.9 802.6 - -5 2 2 Yes 3 Yes 491 130.2 241.1 280.5 582.36 3 3 Yes 0 Yes 501 411.9 399.2 3064 39977 3 2 No 1 Yes 617 1506 1106 4441 34108 3 2 Yes 1 No 617 2061 1712 4828 50469 3 2 Yes 1 Yes 617 2098 1785 4741 503510 3 2 Yes 3 Yes 677 4172 4139 - -Table 1: Experimental results in CPU seconds using different heuristics in LTOP with a timeoutof 2.5 hours. Each instance has several parameters including the number of vessels, sail-on-serviceopportunities, port fees and cabotage restrictions.the Intra-WCSA. Rather than na¨ively sailing across the Pacific, the repositioning was cleverlydesigned to utilize an existing service, the AC3, in order to move the vessel to South America.Sailing on existing services, like the AC3, saves money and reduces CO2 emissions.At a high level, a fleet repositioning problem consists of a set of a tuple 〈S, V, I,G,E〉, whereS is the set of services, V is the set of vessels, I : V → S assigns each vessel an initial service,G : V → S assigns each vessel a goal service, and E represents the set of equipment movementopportunities. The goal is to move all vessels in V to their goal service in G at minimal cost.We performed a computational study of a real-world liner shipping fleet repositioning scenarioconfronted by our industrial partner using Linear Temporal Optimization Planning [9], a methodthat provides linear cost optimization to automated planning [4]. Various repositioning activitiesare modeled within the LTOP framework as a combination of a linear optimization model anda planning action. We constructed a number of instances based on the scenario with varyinglevels of realism, using data on vessel fuel consumption and port costs from the ENERPLANdataset [6]. The running times of LTOP on these instances is shown in Table 11.We tested LTOP using a variety of domain independent and domain specific heuristics (DS,DSLP , DI, and LP) to guide LTOP’s branching and node selection. Instance 6 is the instancemost similar to the our case study, and is solvable in under 400 seconds with DSLP , domainspecific heuristics with some of LTOP’s domain indepedent heuristics disabled. More work isneeded examining the scaling of LTOP, as well as in adding more real world components to themodel. We also intend to model the problem as a MIP, despite the big-M constraints necessaryto model the logical aspects of the problem, and compare this with LTOP.References1. J.F. A´lvarez. Joint routing and deployment of a fleet of container vessels. Maritime Economics and Logistics,11(2):186–208, June 2009.2. M. Christiansen, K. Fagerholt, B. Nygreen, and D. Ronen. Maritime transportation. Transportation, 189–284, 2007.3. M. Christiansen, K. Fagerholt, and D. Ronen. Ship routing and scheduling: Status and perspectives. TransportationScience, 38(1):1–18, 2004.4. M. Ghallab, D. Nau, and P. Traverso. Automated Planning: Theory and Practice. Morgan Kaufmann, 2004.5. N. Kohl, A. Larsen, J. Larsen, A. Ross, and S. Tiourine. Airline disruption management–perspectives, experiencesand outlook. Journal of Air Transport Management, 13(3):149–162, 2007.6. B. Løfstedt, J.F. Alvarez, C.E.M. Plum, D. Pisinger, and M.M. Sigurd. An integer programming model and benchmarksuite for liner shipping network design. Technical Report 19, DTU Management, 2010.7. M. Løve, K.R. Sørensen, J. Larsen, and J. Clausen. Using heuristics to solve the dedicated aircraft recovery problem.Central European Journal of Operations Research, 13(2):189–207, 2005.8. B.J. Powell and A.N. Perakis. Fleet deployment optimization for liner shipping: An integer programming model.Maritime Policy and Management, 24(2):183–192, Spring 1997.9. K. Tierney and R.M. Jensen. Temporal optimization planning for fleet repositioning. In The International Schedulingand Planning Applications woRKshop (SPARK), 2011.1Our study was run on 2 GHz AMD Opteron 2425 HE processors with 4 GB of RAM and CPLEX 12.2 as an LP solver.

Liner Shipping Fleet Repositioning

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