Nevertheless, both the current financial crisis and the global need to cut CO₂ emissions are challenging ship owners, as they are most industries. Maritime transport optimization is one important answer to both challenges. New tools to help planners solve their task more effectively are being developed and will soon emerge on the market.

In terms of energy consumption per unit transported, shipping is by far the most efficient way of transporting goods. Wherever alternative methods of transport are available, sea transport should therefore be preferred from a global warming perspective. However, like all other carriers of goods, maritime transporters need to reduce their CO₂-emissions yet further, even though they have already made considerable cuts. Ships used only 0.025 kg of fuel to transport one container one nautical mile on the voyage from Asia to Europe in 2007, compared to 0.200 kg in 1970.

Better planning of maritime operations is one of several measures that will lower emissions per transported volume further. At the same time, this measure will reduce the cost of transport and make transport more timely and efficient — valuable contributions when it comes to keeping the wheels turning in a world economy dominated by financial problems.

Improved Fleet Utilization


Developed in Norway, TurboRouter is an O.R.-based decision support tool for ship routing and scheduling [1,2] that has already been implemented and tested by a number of shipping companies. One company compared plans obtained by using TurboRouter with solutions from manual planning. The plans generated by the tool had better fleet utilization. In the course of a three-week period, two additional spot cargoes could be transported. Since each of these cargoes comprised tens of thousands of tons and the market was good, the company's profits rose by between $1 million to $2 million during this short period of time.

This new tool enabled the planners to evaluate and compare a large number of alternative fleet schedules in a very short time, as illustrated in Figure 4. They were then able to compare the solution suggested by TurboRouter with their manual plans. Moreover, the automatically generated plan could be used in a user-friendly way as a starting point for manual changes. Conversely, a manually generated and not necessarily complete plan could be automatically filled in and optimized. This type of mixed-initiative planning is necessary to fully benefit from the complementary strengths of humans and computers for dealing with complex ship-scheduling problems. Previously, planners might spend hours building and evaluating a single fleet schedule. Sufficient time and resources to assess alternatives were seldom available.

Norwegian Pioneers of the Sea


TurboRouter was developed by MARINTEK, a subsidiary of the SINTEF Group, which is Scandinavia's largest independent research organization. Researchers and students at the Norwegian University of Science and Technology (NTNU), SINTEF's academic twin, developed the basis of the new tool — effective optimization methods for ship routing and scheduling. Of course, the successful implementation would not have been possible without the close collaboration of a number of shipping companies that provided input in the form of requirements, guidance and industrial assessment of the results.

Optimization-based decision support in maritime logistics is a strategic area of research for NTNU and SINTEF, and bulk shipping is the main focus of the research effort. The teams are highly integrated and comprise a total of 25 researchers, among them the authors of this article.

Norway boasts a long maritime tradition marked by historical achievement. Our forefathers the vikings were experts on sailing and navigation, and ruled the western oceans for centuries. In the year 1000, one of them left Iceland with his family and sailed west to Greenland. From here his son Leiv Eiriksson sailed further west and south and found Newfoundland. President Lyndon B. Johnson acknowledged in 1964 that Leiv Eiriksson "discovered" America by deciding that Oct. 9 should be "Leiv Eiriksson Day" in the United States.

Nine hundred years after Leiv Eiriksson's discovery, Norwegian Roald Amundsen was the first man to reach the South Pole. He also headed the first expedition that sailed from the Atlantic Ocean to the Pacific Ocean north of America. At that time, shipping had become one of Norway's major industries. Today, the Norwegian merchant fleet is the fifth largest in the world.

One reason that Norway has been able to maintain its position on the seas is its continuous focus on maritime research. In 1939, a large ship-model towing tank was inaugurated in Trondheim. This made it possible to perform model tests to improve vessel design, which in turn made it easier to win contracts in the global shipping market.

After petroleum production started on the Norwegian continental shelf in 1971, the need for more research into maritime constructions became apparent. A new research laboratory, the Ocean Basin, was opened in 1979 in a building adjacent to the towing tank.

Until recently, the main focus of maritime research in Norway was technical construction. However, during the last 10 years research on how to operate ships more economically and efficiently has increased in Norway, as it has in the rest of the world.

Ship Routing and Scheduling


A planner in a shipping company has to solve a complex puzzle every single day. Vessel operation costs tens of thousands dollars per day, and the income from carrying a single cargo can be in the hundreds of thousands. In spite of the complexity of the planning problem and the money at stake, most planners in shipping companies solve their puzzles manually, based on their experience.

In contrast with the situation in airlines and road-based goods transport, only a few shipping companies use O.R.-based decision support systems in building complete fleet schedules. Most companies have voyage calculation tools that consider one ship at a time, and evaluate the feasibility and economic consequences of assigning a given cargo to a specific vessel. However, considering only one ship at a time will clearly lead to suboptimal plans.

This is how complex the puzzle can be:

On any given day, the planner has a number of cargoes that must be transported within the planning horizon. Each cargo consists of a specific quantity of goods that have to be picked up in a given loading port and delivered in a given unloading port.

There is usually a time window that specifies when loading can begin, and sometimes also for discharge. The cargoes are usually known some time in advance, specifying the planning horizon.

To transport these cargoes, the planner controls a heterogeneous fleet of ships, each with a given service speed laden

and ballast, cargo-carrying capacity, fuel consumption, loading/unloading equipment and cost structure. In contrast to most land-based vehicle routing problems, the ships in the fleet will usually have different initial positions at the time of planning, and these may be any port or point at sea.

Since planning follows a rolling horizon principle where plans are updated daily, the ships may already be carrying cargoes that must be taken into account. In some modes of operation, ships always carry only one cargo at a time, while in others they carry multiple cargoes simultaneously.

The task of the planner is to find the minimum cost or maximum profit plan for assigning cargoes to the available ships in the fleet and to existing routes and schedules, while observing a large number of complex constraints. In addition to satisfying the capacity and time windows for the cargoes, several other constraints may have to be considered, such as ship-port compatibility. Whether a ship can visit a port may depend on the cargo it is carrying.

The planner must also take into account the possibility that some ships in the fleet have planned dry-docking, which means that the ship will not be available within some or all of the planning horizon. Furthermore, the cost structure of a ship is quite complex; for instance, fuel consumption depends on whether the ship is sailing, waiting, loading or unloading. The ships may even use different engines with different fuel types and costs for loading/unloading and for sailing.

An excerpt from a typical ship routing and scheduling work-sheet is shown in Figure 1, in which ship names and time windows have been modified to preserve confidentiality. The ports of loading are divided into four different regions: United Kingdom and Continental Europe (UK/CONT), Mediterranean Sea (MEDIT), Caribbean Sea (CARIB), and United States and Gulf of Mexico (US/GULF). The cargoes are shown in the top row of the table, based on the locations of their ports of loading. Each cargo is specified by its loading and discharge ports, the nature of the commodities, its weight and the time window during which loading can start. In the lower row, the available ships based in each region are specified in terms of times and ports.

Figure 1: Excerpt from a typical ship routing and scheduling work-sheet.

In O.R., the ship routing and scheduling problem is a complex member of the family of Vehicle Routing Problems (VRP). Even in its most basic form, the VRP is a very complex and computationally hard optimization problem. As described above, maritime routing problems have idiosyncrasies that typically increase their computational complexity and set them apart from VRPs that occur in other transport modes [3,4].

Things Even Get Worse!


Even though the above puzzle is complex and hard to deal with, things get even worse. In the example above, all the cargoes had to be transported by a ship in the fleet controlled by the shipping company. Planning problems with these characteristics are often classified as industrial shipping problems.

However, most bulk shipping companies operate in tramp shipping, where they usually have an amount of contract cargoes that must be transported, as in industrial shipping. In addition, however, they receive requests for optional spot cargoes. The shipping companies must evaluate these inquiries and decide which optional spot cargoes to accept and which to reject.

Sometimes, there is an opportunity to relet a cargo, which means that the shipping company can hire a vessel from another company on a voyage charter to carry the cargo for an agreed price. In such cases, the planner must consider both which spot cargoes to accept/reject and which cargoes to relet. These decisions are closely related to the routing and scheduling decisions.

Another typical feature of bulk shipping is the fact that cargo quantities are often somewhat flexible. For instance, instead of stating that the quantity of a certain cargo is 20,000 tons, it is not unusual that the quantity is given as 20,000 tons +/— 10 percent. The planner can sometimes use this flexibility to improve fleet utilization and even to make room for profitable spot cargoes. However, additional complexity is introduced, since the routing and scheduling problem now also includes the decision of optimal cargo quantities.

Figure 2: Main window of TurboRouter.

The Birth of TurboRouter


In 1996, researchers at MARINTEK and NTNU launched a project together with a couple of shipping companies. The aim was to develop an optimization-based decision support system for ship routing and scheduling, and the TurboRouter planning tool was the result.

The role of the shipping companies in this project was to provide in-depth insight into and understanding of the fleet-scheduling problems facing the shipping industry.

Some planners and shipping companies were skeptical about O.R. systems in general and about optimizing fleet scheduling in particular. They argued that it was impossible or undesirable to model all aspects needed to optimize fleet scheduling. One of their arguments was that it could be difficult to model the compatibility between ship and port. They claimed that there might be situations in which a specific ship cannot enter or leave a given port due to draft restrictions, pointing out that if the ship is not fully loaded it may still be possible at high tide. The critics pointed out that this type of constraint would be influenced by the ship's draft, which is influenced by the cargo quantity onboard and the port's draft restrictions, which are determined by tidal conditions.

Another example of aspects or constraints that are difficult to model is port opening hours. The skeptics claimed that even though it might be possible to model these aspects, it would probably require too much user input, and that planners would not have confidence in such a system. They therefore insisted on a system with a high degree of user interaction.

The research team emphasized the importance of developing the system a small step at a time and gaining the acceptance of the shipping companies involved after each step. The first step was to develop a simple general method for automatically calculating port-to-port distances, which is essential information in maritime planning. This was initially used to develop relatively simple manual planning tools that could help planners by performing all the time-consuming calculations and feasibility checks. The team subsequently developed advanced algorithms for identifying optimal or near-optimal solutions to the ship routing and scheduling problems that were being targeted. Due to the complexity of the problem and the need for quick response, a robust, heuristic approach based on local search and metaheuristics was selected.

Figure 3 shows a form in TurboRouter for mixed-initiative planning of fleet schedules.

Figure 3: User interface for planning of fleet schedules.

Combined Ship Routing and Inventory Management


In the 1990s, SINTEF and NTNU launched a research effort that targeted another challenge, in this case in collaboration with a number of maritime transport and manufacturing companies. The aim of this project was to increase the earnings of these industries and cut their emissions further through better supply chain coordination.

The new project was based on the fact that inventories often lie close to the loading and/or unloading ports of the sailing legs. Both loading operations and the transport phase itself are time-consuming and expensive. The potential for improvement is therefore great if the planning of ship schedules and inventory management at each end of the sailing leg can be coordinated.

Figure 4: Comparing alternative fleet schedules.

The integration of routing and inventory management involves a new dimension in the industrial and tramp shipping problems described above, which are complex members of the VRP family. In O.R., the extended problem is called the Inventory Routing Problem (IRP). Here again, a maritime IRP normally has characteristics that make it different from, say, a typical road-based inventory routing problem, as exemplified below. Maritime IRPs are frequently encountered in the oil and gas industry and bulk commodity industry, as well as in process industries that transport chemicals and other heavy, high-volume bulk products [5].

Each industrial maritime inventory routing problem has its own special and complicating aspects.

The first such real maritime IRP described in the O.R. literature was the transport of ammonia [6,7]. A Norwegian company operated a fleet of five ships for transporting ammonia between production and consumption harbors with limited storage, connected to 14 of its own plants. The shipper also traded ammonia with external operators, resulting in a combined tramp scheduling and maritime inventory routing problem.

Another example comes from the cement industry. The largest producer of cement in Norway is responsible for the simultaneous inventory management of 12 production silos and 49 consumption silos and the routing of a fleet of five ships (Figure 5). The fleet capacity is limited, and occasionally the demand for cement exceeds fleet capacity. The company therefore occasionally utilizes spot charters; during periods of peak demand, additional road-based transport is also needed.

Figure 5: The production and consumption ports of a cement producer in Norway.

Finally, several companies in the rapidly growing liquid natural gas (LNG) sector have recently introduced decision support systems for their complex maritime inventory routing. Traditionally, most LNG ships have been tied to specific contracts and trades, in that they were shuttled between given liquefaction plants and regasification terminals. This is about to change. The rigidity of contracts seems to be loosening up. There is a growing spot market for LNG, which creates more business opportunities serving different markets. The spot market introduces more flexibility, which in turn means a high fleet utilization factor for LNG ships.

To the best of the authors' knowledge, no generic commercial optimization-based decision support system for maritime IRPs is yet on the market. In the course of the past few years, SINTEF and NTNU have developed a tool called Invent, which is now in its test phase with several shipping companies. The tool is a generic software system that can model and solve a wide range of maritime routing problems, including traditional tramp and industrial shipping problems combined with inventory management. It handles tank allocation and the necessary cleaning operations between products. Invent is a pure solver, with no user interface. It must be integrated with an ERP system or a decision support system such as TurboRouter. An integrated system has been tested on several real IRP cases from industry, with very good results.

TurboRouter and Invent deal with large, complex problems in maritime transport. Significant research challenges remain to be solved before we can match the requirements of even more large, complex and wide-ranging applications in maritime transport. Through development and implementation of more powerful optimization methods, existing tools will grow more powerful and enable us to develop better plans in less time.

Figure 6: The LNG supply chain.




Marielle Christiansen, Bjorn Nygreen (bjorn.nygreen@iot.ntnu.no) and Kjetil Fagerholt are professors in the Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology (NTNU), Trondheim, Norway. Fagerholt is also a scientific adviser at the Norwegian Marine Technology Research Institute (MARINTEK) in Trondheim. Geir Hasle is a chief scientist in SINTEF ICT, Oslo, Norway, and adjunct professor in the University of Jyvaskyla, Finland. Atle Minsaas is a special adviser at MARINTEK.

References

1. Fagerholt, K., 2004, "A computer-based decision support system for vessel fleet scheduling — experience and future research, Decision Support Systems, Vol. 37, No. 1, pp. 35-47.
2. Fagerholt, K. and H. Lindstad, 2007, "TurboRouter: An interactive optimisation-based decision support system for ship routing and scheduling," Maritime Economics and Logistics, Vol. 9, pp. 214-233.
3. Christiansen, M., K. Fagerholt, and D. Ronen, 2004, "Ship routing and scheduling — status and perspectives," Transportation Science, Vol. 38, No. 1, pp. 1-18.
4. Christiansen, M., K. Fagerholt, B. Nygreen and D. Ronen, 2007, "Maritime Transportation," in: "Handbooks in Operations Research and Management Science: 14 Transportation," C. Barnhart and G. Laporte (eds.), pp. 189-284, North-Holland, Amsterdam.
5. Andersson, H., A. Hoff, M. Christiansen, G. Hasle and A. Lokketangen, 2008, "Industrial Aspects and Literature Survey: Combined Inventory Management and Routing," SINTEF report A7056, ISBN 978-82-14-04399-0.
6. Christiansen, M., 1999, "Decomposition of a combined inventory and time-constrained ship routing problem," Transportation Science, Vol. 33, No. 1, pp. 3-16.
7. Flatberg, T., J. Haavardtun, O. Kloster and A. Lokketangen, 2000, "Combining exact and heuristic methods for solving a vessel routing problem with inventory constraints and time windows," Ricerca Operativa, Vol. 29, No. 91, pp. 55-68.

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