Maritime Transportation

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Chapter 4

Maritime Transportation

Marielle Christiansen

Department of Industrial Economics and Technology Management, Norwegian University of Science and Technology, Trondheim, Norway

Department of Applied Economics and Operations Research, SINTEF Technology and Society, Trondheim, Norway

E-mail:[email protected]

Kjetil Fagerholt

Department of Marine Technology, Norwegian University of Science and Technology, Trondheim, Norway

Norwegian Marine Technology Research Institute (MARINTEK), Trondheim, Norway E-mail:[email protected]

Bjørn Nygreen

E-mail:[email protected]

David Ronen

College of Business Administration, University of Missouri-St. Louis, St. Louis, MO, USA E-mail:[email protected]

1 Introduction

Maritime transportation is the major conduit of international trade, but the share of its weight borne by sea is hard to come by. The authors have surveyed the academic members of the International Association of Maritime Econo- mists and their estimates of that elusive statistic range from 65% to 85%.

Population growth, increasing standard of living, rapid industrialization, ex- haustion of local resources, road congestion, and elimination of trade barriers, all of these contribute to the continuing growth in maritime transportation. In countries with long shorelines or navigable rivers, or in countries consisting of multiple islands, water transportation may play a significant role also in do- mestic trades, e.g., Greece, Indonesia, Japan, Norway, Philippines, and USA.

Table 1demonstrates the growth in international seaborne trade during the last couple of decades (compiled fromUNCTAD, 2003, 2004).

Since 1980 the total international seaborne trade has increased by 67% in terms of weight. Tanker cargo has increased modestly, but dry bulk cargo has

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Table 1.

Development of international seaborne trade (millions of tons)

Year Tanker cargo Dry cargo Total

Main bulk commodities¹

Other

1980 1871 796 1037 3704

1990 1755 968 1285 4008

2000 2163 1288 2421 5872

2001 2174 1331 2386 5891

2002 2129 1352 2467 5948

2003² 2203 1475 2490 6168

1Iron ore, grain, coal, bauxite/alumina, and phosphate.

2Estimates.

Table 2.

World fleet by vessel type (million dwt)

Year Oil

tankers

Bulk carriers

General cargo

Container ships

Other Total

1980 339 186 116 11 31 683

1990 246 234 103 26 49 658

2000 286 281 103 69 69 808

2001 286 294 100 77 69 826

2002 304 300 97 83 60 844

2003 317 307 95 91 47 857

increased by 85%. The “Other” dry cargo, which consists of general cargo (including containerized cargo) and minor dry bulk commodities, has more than doubled.

The world maritime fleet has grown in parallel with the seaborne trade.Ta- ble 2 provides data describing the growth of the world fleet during the same period (compiled fromUNCTAD, 2003, 2004).

The cargo carrying capacity of the world fleet has reached 857 million tons at the end of 2003, an increase of 25% over 1980. It is worth pointing out the fast growth in the capacity of the container ships fleet with 727% increase during the same period. These replace general cargo ships in major liner trades. To a lesser extent we see also a significant growth in the bulk carriers fleet. The gap between the increase in total trade (67%) and in the world fleet (25%) is explained by two factors. First, the boom in construction of tankers during the 1970s that resulted in excess capacity in 1980, and second, the increasing productivity of the world fleet, as demonstrated inTable 3(compiled from UNCTAD, 2003, 2004).

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Table 3.

Productivity of the world fleet

Year World fleet (million dwt)

Total cargo^∗ (million tons)

Total ton-miles

performed (thousands of millions of ton-miles)

Tons carried per dwt

Thousands of ton-miles performed per dwt

1980 6828 3704 16,777 54 255

1990 6584 4008 17,121 61 260

2000 8084 5871 23,016 73 285

2001 8257 5840 23,241 71 281

2002 8442 5888 23,251 70 275

2003 8570 6168 24,589 72 287

∗Inconsistencies between these data and the Total inTable 1are in the source. However, they do not affect the productivity statistics presented in this table.

The utilization of the world fleet has increased from 5.4 tons carried per deadweight ton in 1980 to 7.2 in 2003. At the same time the annual output per deadweight ton has increased from 25.5 thousand ton-miles to 28.7.

These statistics demonstrate the dependence of the world economy on seaborne trade. A ship involves a major capital investment (usually millions of US dollars, tens of millions for larger ships) and the daily operating cost of a ship may easily amount to thousands of dollars and tens of thousands for the larger ships. Proper planning of fleets and their operations has the potential of improving their economic performance and reducing shipping costs. This is often a key challenge faced by the industry actors in order to remain competitive.

The purpose of this chapter is to introduce the reader who is familiar with Operations Research (OR), and may be acquainted with other modes of trans- portation, to maritime transportation. The term maritime transportation refers to seaborne transportation, but we shall include in this chapter also other water-borne transportation, namely inland waterways. The chapter discusses various aspects of maritime transportation operations and presents associated decision making problems and models with an emphasis on ship routing and scheduling models. This chapter focuses on prescriptive OR models and associated methodologies, rather than on descriptive models that are usually of interest to economists and public policy makers. Therefore we do not discuss statistical analysis of trade and modal-split data, nor ship safety and casualty records and related topics. To explore these topics the interested reader may refer to journals dealing with maritime economics, such as Maritime Policy and Management and Maritime Economics and Logistics (formerly International Journal of Maritime Economics).

The ocean shipping industry has a monopoly on transportation of large volumes of cargo among continents. Pipeline is the only transportation mode that is cheaper than ships (per cargo ton-mile) for moving large volumes of cargo over long distances. However, pipelines are far from versatile because they can

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Table 4.

Comparison of operational characteristics of freight transportation modes

Operational characteristic Mode

Ship Aircraft Truck Train Pipeline

Barriers to entry small medium small large large

Industry concentration low medium low high high

Fleet variety (physical &

economic)

large small small small NA

Power unit is an integral part of the transportation unit

yes yes often no NA

Transportation unit size fixed fixed usually fixed variable NA Operating around the clock usually seldom seldom usually usually Trip (or voyage) length days–weeks hours–days hours–days hours–days days–weeks

Operational uncertainty larger larger smaller smaller smaller

Right of way shared shared shared dedicated dedicated

Pays port fees yes yes no no no

Route tolls possible none possible possible possible

Destination change while underway

possible no no no possible

Port period spans multiple operational time windows

yes no no yes NA

Vessel-port compatibility depends on load weight

yes seldom no no NA

Multiple products shipped together

yes no yes yes NA

Returns to origin no no yes no NA

NA – not applicable.

move only fluids in bulk over fixed routes, and they are feasible and econom- ical only under very specific conditions. Other modes of transportation (rail, truck, air) have their advantages, but only aircraft can traverse large bodies of water, and they have limited capacity and much higher costs than ships, thus they attract high-value low-volume cargoes. Ships are probably the least regulated mode of transportation because they usually operate in international water, and very few international treaties cover their operations.

Ship fleet planning problems are different than those of other modes of transportation because ships operate under different conditions.Table 4pro- vides a comparison of the operational characteristics of the different freight transportation modes. We wish also to point out that ships operate mostly in international trades, which means that they are crossing multiple national jurisdictions. Actually, in many aspects aircraft are similar to ships. In both modes each unit represents a large capital investment that translates into high daily cost, both pay port fees and both operate in international routes. However, most aircraft carry mainly passengers whereas most ships haul freight. Even aircraft that transport freight carry only packaged goods whereas ships carry mostly liquid and dry bulk cargo, and often nonmixable products in separate

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compartments. Since passengers do not like to fly overnight most aircraft are not operated around the clock whereas ships are operated continually. In addition, aircraft come in a small number of sizes and models whereas among ships we find a large variety of designs that result in nonhomogeneous fleets.

Both ships and aircraft have higher uncertainty in their operations due to their higher dependence on weather conditions and on technology, and because they usually straddle multiple jurisdictions. However, since ships operate around the clock their schedules usually do not have buffers of planned idleness that can absorb delays. As far as trains are concerned, they have their own dedicated right of way, they cannot pass each other except for at specific locations, and their size and composition are flexible (both number of cars and number of power units). Thus the operational environment of ships is different from other modes of freight transportation, and they have different fleet planning problems.

The maritime transportation industry is highly fragmented. The web site of Lloyd’s Register boasts of listing of “ over 140,000 ship and 170,000 ship owner and manager entries”. In order to take advantage of differences among national tax laws, financial incentives, and operating rules, the control structure of a single vessel may involve multiple companies registered in different countries.

Although ships are the least regulated mode of transportation, there are significant legal, political, regulatory, and economic aspects involved in maritime transportation. The control structure of a ship can be designed to hide the identity of the real owner in order to minimize liability and taxes. Liability for shipping accidents may be hard to pinpoint, and damages may be impos- sible to collect, because numerous legal entities from different countries are usually involved, such as: owner, operator, charterer, flag of registration, ship- yards, classification society, surveyors, and contractors. That is in addition to the crew that may have multiple nationalities and multiple native languages.

Only a small share of the world fleet competes directly with other modes of transportation. However, in certain situations such competition may be important and encouraged by government agencies. In short haul operations, relieving road congestion by shifting cargo and passengers to ships is often de- sirable and even encouraged through incentives and subsidies. A central policy objective of the European Union for the upcoming years is to improve the quality and efficiency of the European transportation system by shifting traf- fic to maritime and inland waterways, revitalizing the railways and linking up the different modes of transport. For further information regarding the Euro- pean transport policy see the European Commission’s white paper European Transport Policy for 2010: Time to Decide (European Commission, 2004). This source provides information about many of the European Union’s programs where maritime transportation plays a prominent role.

Transportation planning has been widely discussed in the literature but most of the attention has been devoted to aircraft and road transportation by trucks and buses. Other modes of transportation, i.e., pipeline, water, and rail, have

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attracted far less attention. One may wonder what the reason is for that lower attention, especially when considering the large capital investments and operating costs associated with these modes. Pipeline and rail operate over a dedicated right of way, have major barriers to entry, and relatively few operators in the market. These are some issues that may explain the lower level of attention. It is worth mentioning that research on rail planning problems has increased considerably during the last fifteen years. However, the issues mentioned for pipeline and rail do not hold for water transportation. Several explanations follow for the low attention drawn in the literature by maritime transportation planning problems:

Low visibility. In most regions people see trucks, aircraft, and trains, but not ships. Worldwide, ships are not the major transportation mode. Most cargo is moved by truck or rail. Moreover, research is often sponsored by large organizations. Numerous large organizations operate fleets of trucks, but few such organizations operate ships.

Maritime transportation planning problems are less structured. In maritime transportation planning there is a much larger variety in problem struc- tures and operating environments. That requires customization of decision support systems, and makes them more expensive. In recent years we see more attention attracted by more complex problems in transportation planning, and this is manifested also in maritime transportation.

In maritime operations there is much more uncertainty. Ships may be delayed due to weather conditions, mechanical problems and strikes (both on board and on shore), and usually, due to their high costs, very little slack is built into their schedules. This results in a frequent need for replanning.

The ocean shipping industry has a long tradition and is fragmented. Ships have been around for thousands of years and therefore the industry may be con- servative and not open to new ideas. In addition, due to the low barriers to entry there are many small, family owned, shipping companies. Most quantitative models originated in vertically integrated organizations where ocean shipping is just one component of the business.

In spite of the conditions discussed above we observe significant growth in research in maritime transportation. The first review of OR work in ship routing and scheduling appeared in 1983 (Ronen, 1983), and it traced papers back to the 1950s. A second review followed a decade later (Ronen, 1993), and recently a review of the developments over the last decade appeared (Christiansen et al., 2004). Although these reviews focused on ship routing and scheduling problems, they discussed also other related problems on all planning levels. A feature issue on OR in water transportation was published by the European Journal of Operational Research (Ronen, 1991), and a spe- cial issue on maritime transportation was published by Transportation Science (Psaraftis, 1999). A survey of decision problems that arise in container terminals is provided byVis and de Koster (2003). The increasing research interest in OR-based maritime transportation is evidenced by the growing number of

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references in the review papers. The first review paper had almost forty references covering several decades. The second one had about the same number of references most of which were from a single decade, and the most recent one has almost double that number of references for the last decade. It is worth mentioning that a large share of the research in transportation planning does not seem to be based on real cases but rather on artificially generated data. The opposite is true for maritime transportation, where the majority of problems discussed are based on real applications.

We focus our attention on planning problems in maritime transportation, and some related problems. With the fast development of commercial aircraft during the second half of the 20th century, passenger transportation by ships has diminished to ferries and cruises. Important as they are, these are small and specialized segments of maritime transportation. Therefore we shall focus here on cargo shipping. Related topics that are discussed in other chapters of this volume are excluded from this chapter, namely maritime transportation of hazardous materials (Erkut and Verter, 2007) and operations of the land- side of port terminals (Crainic and Kim, 2007). We try to confine ourselves to discussion of work that is relatively easily accessible to the reader. This chapter is intended to provide a comprehensive picture, but by no means an exhaustive one.

This chapter is organized around the traditional planning levels, strategic, tactical, and operational planning. Within these planning levels we discuss the three types of operations in maritime transportation (liner, tramp, industrial) and additional specialized topics. Although we try to differentiate among the planning levels, one should remember the interplay among them. On the one hand, the higher-level or longer-term decisions set the stage for the lower-level decisions. On the other hand, one usually needs significant amount of details regarding the shorter-term decisions in order to make good longer-term decisions. We focus here on OR problems in maritime transportation, the related models, and their solution methods. Due to the fast development of computing power and memory, information regarding the computing environment becomes obsolete very quickly, and such information will only occasionally be presented.

The rest of the chapter is organized as follows: Section2defines terms used in OR-applications in maritime transportation and describes characteristics of the industry. Sections3–5are dedicated to strategic, tactical, and operational problems in maritime transportation, respectively. In these sections we present problem descriptions, models and solution approaches for the three modes of operations in maritime transportation, namely liner, industrial, and tramp.

We also address in these sections naval operations, maritime supply chains, ship design and management, ship loading, contract evaluation, booking or- ders, speed selection, and environmental routing. The issue of robustness in maritime transportation planning is addressed in Section6. Important trends and perspectives for the use of optimization-based decision support systems in

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maritime transportation and suggestions for future research are presented in Section7, and some concluding remarks follow in Section8.

2 Characteristics and terminology of maritime transportation

Maritime transportation planning problems can be classified in the traditional manner according to the planning horizon into strategic, tactical and operational problems.

Among the strategic problems we find:

• market and trade selection,

• ship design,

• network and transportation system design (including the determination of transshipment points for intermodal services),

• fleet size and mix decisions (type, size, and number of vessels), and

• port/terminal location, size, and design.

The tactical problems include:

• adjustments to fleet size and mix,

• fleet deployment (assignment of specific vessels to trade routes),

• ship routing and scheduling,

• inventory ship routing,

• berth scheduling,

• crane scheduling,

• container yard management,

• container stowage planning,

• ship management, and

• distribution of empty containers.

The operational problems involve:

• cruising speed selection,

• ship loading, and

• environmental routing.

Handling of hazardous materials poses additional challenges. However, this chapter concentrates on the water-side of maritime transportation. Land-side operations and hazardous materials are discussed in other chapters in this volume. Before diving into discussion of OR models in maritime transportation it is worthwhile to take a closer look at the operational characteristics of maritime transportation and to clarify various terms that are used in this area. Figure 1relates the demand for maritime transportation to its supply, provides a comprehensive view of these characteristics and ties them together (adapted fromJansson and Shneerson, 1987). The following three sections describe these characteristics, starting on the supply side.

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Fig. 1. Characteristic of maritime transportation demand and supply.

2.1 Ship and port characteristics

In this chapter we use the terms ship and vessel interchangeably. Although vessel may refer to other means of transportation, we shall use it in the traditional sense, referring to a ship.

Ships come in a variety of sizes. The size of a ship is measured by its weight carrying capacity and by its volume carrying capacity. Cargo with low weight per unit of volume fills the ship’s volume before it reaches its weight capacity.

Deadweight (DWT) is the weight carrying capacity of a ship, in metric tons.

That includes the weight of the cargo, as well as the weight of fuels, lube oils, supplies, and anything else on the ship. Gross Tons (GT) is the volume of the enclosed spaces of the ship in hundreds of cubic feet.

Ships come also in a variety of types. Tankers are designed to carry liquids in bulk. The larger ones carry crude oil while the smaller ones usually carry oil products, chemicals, and other liquids. Bulk carriers carry dry bulk com- modities such as iron ore, coal, grain, bauxite, alumina, phosphate, and other minerals. Some of the bulk carriers are self-discharging. They carry their own

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unloading equipment, and are not dependent on port equipment for unloading their cargo. Liquefied Gas Carriers carry refrigerated gas under high pressure.

Container Ships carry standardized metal containers in which packaged goods are stowed. General Cargo vessels carry in their holds and above deck all types of goods, usually packaged ones. These vessels often have multiple decks or floors. Since handling general cargo is labor intensive and time consuming, general cargo has been containerized during the last four decades, thus reducing the time that ships carrying such cargo spend in ports from days to hours.

Refrigerated vessels or reefers are designed to carry cargo that requires refrig- eration or temperature control, like fish, meat, and citrus, but can also carry general cargo. Roll-on–Roll-off (Ro–Ro) vessels have ramps for trucks and cars to drive on and off the vessel. Other types of vessels are ferries, passenger ships, fishing vessels, service/supply vessels, barges (self propelled or pushed/pulled by tugs), research ships, dredgers, naval vessels, and other, special purpose vessels.

Some ships are designed as combination of the above types, e.g., ore-bulk-oil, general cargo with refrigerated compartments, passenger and Ro–Ro.

Ships operate between ports. Ports are used for loading and unloading cargo as well as for loading fuel, fresh water, and supplies, and discharging waste.

Ports impose physical limitations on the dimensions of the ships that may call in them (ship draft, length and width), and usually charge fees for their services. Sometimes ports are used for transshipment of cargo among ships, especially when the cargo is containerized. Major container lines often operate large vessels between hub ports, and use smaller vessels to feed containers to/from spoke ports.

2.2 Types of shipping services

There are three basic modes of operation of commercial ships: liner, tramp, and industrial operations (Lawrence, 1972). Liners operate according to a pub- lished itinerary and schedule similar to a bus line, and the demand for their services depends among other things on their schedules. Liner operators usu- ally control container and general cargo vessels. Tramp ships follow the avail- able cargoes, similar to a taxicab. Often tramp ships engage in contracts of affreightment. These are contracts where specified quantities of cargo have to be carried between specified ports within a specific time frame for an agreed upon payment per unit of cargo. Tramp operators usually control tankers and dry bulk carriers. Both liner and tramp operators try to maximize their profits per time unit. Industrial operators usually own the cargoes shipped and control the vessels used to ship them. These vessels may be their own or on a time charter. Industrial operators strive to minimize the cost of shipping their cargoes. Such operations abound in high volume liquid and dry bulk trades of vertically integrated companies, such as: oil, chemicals, and ores. When any type of operator faces insufficient fleet capacity the operator may be able to charter in additional vessels. Whereas liners and tramp operators may give up the excess demand and related income, industrial operators must ship all their

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cargoes. In cases of excess fleet capacity, vessels may be chartered out (to other operators), laid-up or even scrapped. However, when liners reduce their fleet size they must reshuffle their itineraries and/or schedules, which may result in reduced service frequency or withdrawal from certain markets. In both cases revenues may drop. An interesting historical account of the development of liner services in the US is provided byFleming (2002, 2003).

Industrial operators, who are usually more risk-averse and tend not to charter-out their vessels, size their fleet below their long-term needs, and comple- ment it by short-term (time or voyage/spot) charters from the tramp segment.

Seasonal variations in demand, and uncertainties regarding level of future demand, freight rates, and cost of vessels (both newbuildings and second-hand) affect the fleet size decision. However, when the trade is highly specialized (e.g., liquefied gas carriers) no tramp market exists and the industrial operator must assure sufficient shipping capacity through long-term commitments. The ease of entry into the maritime industry is manifested in the tramp market that is highly entrepreneurial. This results in long periods of oversupply of shipping capacity and the associated depressed freight rates and vessel prices. However, certain market segments, such as container lines, pose large economies of scale and are hard to enter.

Naval vessels are a different breed. Naval vessels alternate between deployment at sea and relatively lengthy port periods. The major objective in naval applications is to maximize a set of measures of effectiveness.Hughes (2002) provides an interesting personal perspective of naval OR.

2.3 Cargo characteristics

Ships carry a large variety of goods. The goods may be manufactured con- sumer goods, unprocessed fruits and vegetables, processed food, livestock, intermediate goods, industrial equipment, processed materials, and raw materials. These goods may come in a variety of packaging, such as: boxes, bags, drums, bales, and rolls, or may be unpackaged, or even in bulk. Sometimes cargoes are unitized into larger standardized units, such as: pallets, containers, or trailers. Generally, in order to facilitate more efficient cargo handling, goods that are shipped in larger quantities are shipped in larger handling units or in bulk. During the last several decades packaged goods that required multiple manual handlings, and were traditionally shipped by liners, have been containerized into standard containers. Containerization of such goods facilitates efficient mechanized handling of the cargo, and thus saves time and money, and also reduces pilferage. Shipping containers come in two lengths, 20 feet and 40 feet. A 20container carries up to approximately 28 tons of cargo with a volume of up to 1000 cubic feet. Most containers are metal boxes with an 8×8 cross-section, but other varieties exist, such as: refrigerated containers, open top, open side, and half height. In addition there are containers of nonstan- dard sizes. Large containerships can carry thousands of Twenty feet Equivalent Units (TEUs), where a 40container is counted as two TEUs.

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In addition, goods that are shipped in larger quantities are usually shipped more often and in larger shipment sizes. Cargoes may require shoring on the ship in order to prevent them from shifting during the passage, and may require refrigeration, controlled temperature, or special handling while on board the ship. Different goods may have different weight density, thus a ship may be full either by weight or by volume, or by another measure of capacity.

2.4 Geographical characteristics

Shipping routes may be classified according to their geographical character- istics (and the corresponding type and size of vessel used): deep-sea, short-sea, coastal, and inland waterways. Due to economies of scale in shipping larger size vessels are employed in deep-sea trades between continents whereas smaller size vessels usually operate in short-sea and coastal routes, where voyage legs are relatively short. As mentioned above, smaller containerships are used on short-sea routes that feed cargo to larger vessels that operate on long deep-sea routes. A similar picture can sometimes be observed with tankers where large crude carriers used for long routes are lightered at an off shore terminal to smaller vessels (often barges). Due to draft restrictions inland waterways are used mainly by barges. Barges are used to move cargoes between the hinter- land and coastal areas, often for transshipments to/from ocean-going vessels, or to move cargoes between inland ports.

2.5 Terms used in maritime transportation planning

• Shipping refers to moving cargoes by ships.

• The shipper is the owner of the transported cargo.

• A shipment is a specified amount of cargo that must be shipped to- gether from a single origin to a single destination.

• Routing is the assignment of a sequence of ports to a vessel. Environ- mental routing or weather routing is the determination of the best path in a body of water that a vessel should follow.

• Scheduling is assigning times (or time windows) to the various events on a ship’s route.

• Deployment refers to the assignment of the vessels in the fleet to trade routes. The differentiation between deployment and scheduling is not always clear cut. Deployment is usually used when vessels are desig- nated to perform multiple consecutive trips on the same route, and therefore is associated with liners and a longer planning horizon. Lin- ers follow a published sailing schedule and face more stable demand.

Scheduling does not imply allocation of vessels to specific trade routes, but rather to specific shipments, and is associated with tramp and industrial operations. Due to higher uncertainty regarding future demand in these operations, their schedules usually have a shorter planning horizon.

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• A voyage consists of a sequence of port calls, starting with the port where the ship loads its first cargo and ending where the ship unloads its last cargo and becomes empty again. A voyage may include multiple loading ports and multiple unloading ports. Liners may not become empty between consecutive voyages, and in that case a voyage starts at the port specified by the ship operator (usually a primary loading port).

Throughout this chapter we use also the following definitions:

• A cargo is a set of goods shipped together from a single origin to a single destination. In the vehicle routing literature it is often referred to as an order. The terms shipment and cargo are used interchangeably.

• A load is the set of cargoes that is on the ship at any given point in time.

• A load is considered a full shipload when it consists of a single cargo that for practical and/or contractual reasons cannot be carried with other cargoes.

• A product is a set of goods that can be stowed together in the same compartment. In the vehicle routing literature it is sometimes referred to as a commodity.

• A loading port is a pickup location (corresponds to a pickup node).

• An unloading port is a delivery location (corresponds to a delivery node).

3 Strategic planning in maritime transportation

Strategic decisions are long-term decisions that set the stage for tactical and operational ones. In maritime transportation strategic decisions cover a wide spectrum, from the design of the transportation services to accepting long-term contracts. Most of the strategic decisions are on the supply side, and these are: market selection, fleet size and mix, transportation system/service network design, maritime supply chain/maritime logistic system design, and ship design.

Due to characteristics discussed earlier maritime transportation markets are usually competitive and highly volatile over time, and that complicates strategic decisions.

In this section we address the various types of strategic decisions in maritime transportation and present models for making such decisions. Section3.1that discusses ship design is followed by Section3.2that deals with fleet size and mix decisions. Section3.3treats network design in liner shipping, and Section3.4 handles transportation system design. Finally, Section3.5addresses evaluation of long-term contracts.

In order to be able to make strategic decisions one usually needs some tactical or even operational information. Thus there is a significant overlap between strategic and tactical/operational decisions. Models used for fleet size and mix decisions and network design decisions often require evaluation of ship routing strategies. Such routing models usually fall into one of two categories, arc

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flow models or path flow models. In arc flow models a binary variable is used to represent whether a specific vessel v travels directly from port (or customer) i to port (or customer) j. The model constructs the routes that will be used by the vessels, and the model has to keep track of both travel time and load on each vessel. In path flow models the routes are predefined, one way or another, and a binary variable represents whether vessel v performs route r. A route is usually a full schedule for the vessel that specifies expected arrival times and load on the vessel along the route. Such a model can focus on the set of ports or customers to serve, and only feasible routes are considered.

3.1 Ship design

A ship is basically a floating plant with housing for the crew. Therefore, ship design covers a large variety of topics that are addressed by naval architects and marine engineers, and they include structural and stability issues, materials, on-board mechanical and electrical systems, cargo handling equipment, and many others. Some of these issues have direct impact on the ship’s commercial viability, and we shall focus here on two such issues, ship size and speed.

The issue of the optimal size of a ship arises when one tries to determine what is the best ship for a specific trade. In this section we deal with the optimal size of a single ship regardless of other ships that may be included in the same fleet. The latter issue, the optimal size and composition of a fleet, is discussed in Section3.2. The optimal ship size is the one that minimizes the ship operator’s cost per ton of cargo on a specific trade route with a specified cargo mix. However, one should realize that in certain situations factors beyond costs may dictate the ship size.

Ships are productive and generate income at sea. Port time is a “necessary evil” for loading and unloading cargo. Significant economies of scale exist at sea where the cost per cargo ton-mile decreases with increasing the ship size.

These economies stem from the capital costs of the ship (design, construction, and financing costs), from fuel consumption, and from the operating costs (crew cost, supplies, insurance, and repairs). However, at port the picture is different. Loading and unloading rates are usually determined by the land-side cargo handling equipment and available storage space. Depending on the type of cargo and whether the cargo handling is done by the land-side equipment or by the equipment on the ship (e.g., pumps, derricks), the cargo handling rate may be constant (i.e., does not depend on the size of the ship), or, for dry cargo where multiple cranes can work in parallel, the cargo handling rate may be approximately proportional to the length of the ship. Since the size of the ship is determined by its length, width, and draft, and since the proportions among these three dimensions are practically almost constant, the size of the ship is approximately proportional to the third power of its length. Therefore, in the better case, cargo-handling rates will be proportional to the 1/3 power of the ship size. However, when the cargo is liquid bulk (e.g., oil) the cargo-handling rate may not be related to the size of the ship.

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A ship represents a large capital investment that translates into a large cost per day. Port time is expensive and presents diseconomies of scale. Thus the time of port operations caps the optimal size of ship. Generally, the longer a trade route is, the larger the share of sea-days in a voyage, and the larger the optimal ship size will be. Other factors that affect the optimal ship size are the utilization of ship capacity at sea (the “trade balance”), loading and unloading rates at the ports, and the various costs associated with the ship. On certain routes there may be additional considerations that affect the size of the ship, such as required frequency of service and availability of cargo.

A ship is a long-term investment. The useful life of a ship spans 20–30 years.

Thus, the optimal ship size is a long-term decision that must be based on ex- pectations regarding future market conditions. During the life of a ship a lot of market volatility may be encountered. Freight rates may fluctuate over a wide range, and the same is true for the cost of a ship, whether it is a second hand one or a newbuilding. When freight rates are depressed they may not even cover the variable operating costs of the ship, and the owner has very few alternatives. In the short run the owner may either reduce the daily variable operating cost of the ship by slow steaming, that results in significant reduction in fuel consumption, or the owner may lay up the ship till the market improves.

Laying up a ship involves a significant set-up cost to put the ship into lay up, and, eventually, to bring it back into service. However, laying up a ship significantly reduces its daily variable operating cost. When the market is depressed, owners scrap older ships. The value of a scrapped ship is determined by the weight of its steel (the “lightweight” of the ship), but when there is high supply of ships for scrap the price paid per ton of scrap drops. Occasionally, in a very depressed market, a newly built vessel may find itself in the scrapping yard without ever carrying any cargo.

In the shorter run ship size may be limited by parameters of the specific trade, such as availability of cargoes, required frequency of service, physical limitations of port facilities such as ship draft, length, or width, and available cargo handling equipment and cargo storage capacity in the ports. In the longer run many of these limitations can be relaxed if there is an economic justifica- tion to do so. In addition there are limitations of ship design and construction technology, as well as channel restrictions in canals in the selected trade routes.

The issue of long-run optimal ship size has been discussed mainly by economists.Jansson and Shneerson (1982)presented a comprehensive model for the determination of long-run optimal ship size. They separated the ship capacity into two components:

• the hauling capacity (the ship size times its speed), and

• the handling capacity (cargo loaded or unloaded per time unit).

This separation facilitated the division of the total shipping costs into cost per ton of cargo carried in the voyage that does not depend on the length of the voyage, and cost per time unit. These two cost components are combined into a cost model that conveys the cost of shipping a ton of cargo a given distance. The

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model requires estimation of output and cost elasticities. These elasticities, combined with the route characteristics and input prices, allow estimation of the optimal size of the ship. This model requires estimation of its parameters through regression analysis. However, high shipping market volatility over time results in low reliability of such estimates. They demonstrated the use of the model by calculating the optimal size of a coal bulk carrier for a specific trade.

This work also inspects the sensitivity of the optimal ship size to four route characteristics: distance, port productivity, trade balance, and fuel costs. Most of the elasticities that are necessary for this model were estimated from several datasets in their earlier work (Jansson and Shneerson, 1978). However, that work calculated a single ship size elasticity of operating costs for each ship type. In a later study,Talley et al. (1986)analyzed short-run variable costs of tankers and concluded that the ship size elasticity of operating costs may vary according to the size of the ship of the specific type.

Modern cargo handling equipment that is customized for the specific cargo results in higher loading and unloading rates, and shorter port calls. Such equipment is justified where there is a high volume of cargo. That is usually the case in major bulk trades.Garrod and Miklius (1985)showed that under such circumstances the optimal ship size becomes very large, far beyond the capacity of existing port facilities. In addition, with such large ships the frequency of shipments drops to a point where inventory carrying costs incurred by the ship- per start playing a significant role (the shipment size is the ship capacity). When one includes the inventory costs in the determination of the optimal ship size, that size is reduced significantly. The resulting ship sizes are still much larger than existing port facilities can accommodate, and thus the main limit on ship sizes is the draft limitation of ports. However, for a higher value cargo, or for less efficient port operations, smaller vessel sizes are optimal (see, for example, Ariel, 1991). In short-sea operations competition with other modes may play a significant role. In order to compete with other modes of transportation more frequent service may be necessary. In such cases frequency and speed of service combined with cargo availability may be a determining factor in selecting the ship size.

In liner trades, where there are numerous shippers, multiple ports, and a wide variety of products shipped, the inclusion of the shippers’ inventory costs in the determination of the optimal ship size is more complex. Jansson and Shneerson (1985)presented the initial model for this case. In addition to the costs incurred by the ship owner/operator they included the costs of inventory that are incurred by the shipper (including the cost of safety stocks). The size (and cost) of the safety stocks is a function of the frequency of sailings on the route, and that frequency is affected by the ship size and the volume of trade.

Numerous assumptions regarding the trade and the costs were necessary, and the inclusion of the shippers’ costs reduced very much the optimal ship size.

One could argue with the assumptions of the model, but the conclusions make sense.

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WhereasJansson and Shneerson (1985)considered a continuous review inventory control system by the shippers,Pope and Talley (1988)looked at the case of a periodic review system that is more appropriate when using a (sched- uled) liner service. They found that “ optimal ship size is highly sensitive to the inventory management model selected, the treatment of stockouts and safety stocks, and the inventory management cost structure that prevails”, and concluded that “rather than computing optimal ship size, it may be more appropriate to compute the optimal load size”. As far as liner operations are concerned we agree with this conclusion. The optimal ship size is a long-term decision of the ship owner/operator who serves a large number of shippers.

Each shipper may face different circumstances that may change over time, and therefore should be concerned with the optimal load (shipment) size. The optimal load size is a short-term decision that may change with the changing circumstances.

A historical perspective on the development of size, speed, and other char- acteristics of large container ships is provided byGillman (1999).Cullinane and Khanna (1999)present a more recent detailed study of the economies of scale of large container ships. They take into account the considerable increase in port productivity, and take a closer look at the time in port. They find smaller diseconomies of scale (in port) than earlier studies, and show that the optimal size of a container ship continues to increase with improvements in port productivity. Taking advantage of these economies of scale to reduce shipping costs per unit while maintaining frequency of service, requires larger volumes on the trade route. This is one of the major catalysts for industry consolidation.

However,McLellan (1997)injects a dose of reality to the discussion and points out that there are practical limits to the size of large containerships imposed by port draft, container handling technology, space availability, and required investments in port and transportation infrastructure.

Whereas cargo ships come in a large variety of sizes, from under 1000 DWT up to more than 500,000 DWT, their designed speed varies in a much narrower range. When one excludes outliers the ratio between the designed speed of a fast ship and a slow ship is about 2. The designed speed of a ship is a long- term decision that affects it’s hauling capacity and is part of optimal ship size considerations. As a general rule the design speed of a ship increases by the square root of its length. This implies that the design speed is proportional to the 1/6 power of the size of the ship. This relationship was confirmed statis- tically byJansson and Shneerson (1978), and more recently byCullinane and Khanna (1999).

3.2 Fleet size and mix

One of the main strategic issues for shipping companies is the design of an optimal fleet. This deals with both the type of ships to include in the fleet, their sizes, and the number of ships of each size.

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In order to support decisions concerning the optimal fleet of ships for an operator, we have to consider the underlying structure of the operational planning problem. This means that fleet size and mix models very often include routing decisions. For the various fleet size and mix problem types discussed in this section we can develop models that are based on the tactical models described thoroughly in Section4.1. The objective of the strategic fleet size and mix problem is usually to minimize the fixed (setup) costs of the ships used and the variable operating costs of these ships. In a tactical routing and scheduling problem one usually minimizes only the operating costs of the ships. However, the routing decisions made in a strategic model can be later changed during tactical planning.

In addition, the fleet size and mix decisions have to be based on an esti- mate of demand for the transportation services. The demand forecast is highly uncertain, and stochastic techniques for considering the uncertain information are relevant for solving such strategic planning problems. Issues of robust planning are discussed in Section6. In the literature, various demand patterns are considered where either the size of the cargoes or the frequency of sailing is specified.

In tramp shipping, contract evaluation and fleet size issues are closely related. A shipping company has to find the best split between fixed long-term cargo contracts and spot cargoes. This split should be based on estimation of future prices and demand. When considering the fleet size and mix these issues should be included. This topic is further discussed in Section3.5.

In Section3.2.1we describe the fleet planning problem for a homogeneous fleet where all the vessels are of the same type, size, and cost, while the fleet size and mix for a heterogeneous fleet is the topic of Section3.2.2.

3.2.1 Homogeneous fleet size

In this section, we want to focus on a simple industrial fleet size problem for a fleet consisting of ships of the same type, size, and cost. In the end of the section some comments regarding other studies are given.

In the fleet size planning problem considered here, a homogeneous fleet of ships is engaged in transportation of full shipload cargoes from loading ports to unloading ports. This means that just one cargo is onboard a ship at a time, and each cargo is transported directly from its loading port to it’s corresponding unloading port.

All the required ship arrival times at the loading ports are fixed and known.

Further, we also assume that the loading times and sailing times are known, such that the arrival times at the unloading ports can be easily calculated. The unloading times and the sailing time from each unloading port to all loading ports are also known.

The demand is such that all cargoes, given by specified loading and unloading ports, have to be serviced. The ships should be routed from the unloading ports to the loading ports in a way that minimizes the total cost of their ballast legs. Since the fleet is homogeneous and all cargoes must be transported, the

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cost of the loaded legs is constant and we can leave it out. In addition, we want to minimize the number of necessary ships, and we assume that the number of ships needed dominates the sailing costs.

In the mathematical description of the problem, letN be the set of cargoes indexed by i and j. Cargo i is represented by a node in the network, and this node includes one loading port and one unloading port for cargo i. Since we have full information about activity times, we can determine the feasible cargo pairs (i j). If cargo i can be serviced just before cargo j by the same ship, such an (i j)-pair is feasible and represents an arc in the network. However, if the time between the loads is too long, the arc may be eliminated since using such arcs would result in unacceptable high waiting times. Similarly, if the departing time at node i plus the sailing time to j is greater than the given arrival time at j there will be no arc connecting the two cargoes. LetN_i⁻^andN_i⁺^{be the set} of all cargoes a ship can service immediately before and after servicing cargo i, respectively. Further, letV be the set of ships in the fleet indexed by v, and this set includes an assumption on the upper bound on the number of ships necessary. For each possible ship, we define an artificial origin cargo o(v) and an artificial destination cargo d(v).

The operational cost of sailing from the unloading port for cargo i to the loading port of cargo j is denoted by C_ij.

In the mathematical formulation, we use the following types of variables: the binary flow variable x_ij, i∈N^{, j} ∈N_i⁺, equals 1, if a ship services cargo i just before cargo j, and 0 otherwise. In addition, we define flow variables for the artificial origin and artificial destination cargoes: x_o(v)j, v∈V^{, j} ∈N ∪ {d(v)}, and x_id(v), v∈V^{, i}∈N∪{o(v)}. If a ship v is not operating, then xo(v)d(v)= 1.

The arc flow formulation of the industrial ship fleet size problem for one type of ships and full ship loads is as follows:

(3.1) min

i∈N

j∈N_i⁺

C_ijx_ij−

v∈V

x_o(v)d(v)

subject to

(3.2)

j∈N ∪{d(v)}

x_o(v)j = 1 ∀v ∈V

(3.3)

i∈N ∪{o(v)}

x_id(v)= 1 ∀v ∈V

(3.4)

j∈N_i⁺

x_ij+

v∈V

x_id(v)= 1 ∀i ∈N

(3.5)

i∈Nj⁻

x_ij+

v∈V

x_o(v)j = 1 ∀j ∈N

(3.6) x_ij ∈ {0 1} ∀v ∈Vⁱ∈N ∪

o(v)

j∈N_i⁺∪ d(v)

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In the first term of the objective function(3.1), we minimize the costs of the ballast legs of the ships. Since x_o(v)d(v)= 1 if ship v is not operating, the second term in the objective function minimizes the number of ships in operation. The first term is scaled in a manner that its absolute value is less than one. This means that the objective(3.1)first minimizes the number of ships in use and then as a second goal minimizes the operating costs of the ships. The second term in the objective function could easily be incorporated in the first term.

However, the present form of the objective function is chosen to highlight the twofold objective. Constraints (3.2)ensure that each ship leaves its artificial origin cargo and either services one of the real cargoes or sails directly to its artificial destination cargo. In constraints(3.3)each ship in the end of its route has to arrive at its artificial destination cargo from somewhere. Constraints (3.4)ensure that the ship that services cargo i has to either service another cargo afterward or sail to its artificial destination cargo, while constraints(3.5) say that the ship servicing cargo j has to come from somewhere. Finally, the formulation involves binary requirements(3.6)on the flow variables.

We can easily see that the formulation(3.1)–(3.6)has the same structure as an assignment problem. Therefore the integrality constraints(3.6) are not a complicating factor. The problem is easily solved by any version of the simplex method or by a special algorithm for the assignment problem.

When applying a simplex method, it would be possible to have just one common artificial origin, o, and one common artificial destination, d, cargo. Then x_o(v)j, v∈V^{, j} ∈N ∪ {d(v)}, and xid(v), v∈V^{, i}∈N ∪ {o(v)}, can be trans- formed into x_oj, j ∈ N ∪ {d}, and xid, i ∈ N ∪ {o}. While the xoj and x_id variables remain binary the variable x_odbecomes integer.

For some problems, some of the cargoes may have a common loading port and/or a common unloading port. If the given starting times are such that several cargoes are loaded or unloaded in the same port at the same time, we assume that if this has any effect on the (un)loading times it is already ac- counted for in the specified data.

In a case with the same starting times in the same ports, we might change the formulation slightly. Constraints(3.4)can be considered as the constraints for leaving the unloading port for cargo i, and(3.5)as the constraints for arriving at the loading port for cargo j. We can then aggregate constraints for cargoes with the same ports and starting times. This will give more variables at the left-hand side of the constraints and a right-hand side equal to the number of aggregated constraints. The corresponding flow variables from and to the artificial cargoes will become integers rather than binary.

If some of the cargoes have the same loading and unloading ports and the same starting times then we can switch from indexing the variables by cargo numbers to indexing them by loading port, unloading port, and both loading and unloading times. Then the variables can be integer rather than binary, and their number will be reduced. Dantzig and Fulkerson (1954)pioneered such a model using a different notation for a problem with naval fuel oil tankers.

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They solved a problem with 20 cargoes by using the transportation model. The number of ships was minimized and 6 ships were needed.

Later Bellmore (1968) modified the problem. An insufficient number of tankers and a utility associated with each cargo were assumed. The problem was to determine the schedules for the fleet that maximized the sum of the utilities of the carried cargoes, and it was shown to be equivalent to a transshipment problem.

Another homogeneous fleet size problem is considered in Jaikumar and Solomon (1987). Their objective is to minimize the number of tugs required to transport a given number of barges between different ports in a river system.

They take advantage of the fact that the service times are negligible compared with the transit times, and of the geographical structure of the port locations on the river, and develop a highly effective polynomial exact algorithm. This problem has a line (or tree) structure, and this fact is exploited in the model definition.

RecentlySambracos et al. (2004) addressed the fleet size issue for short- sea freight services. They investigate the introduction of small containers for coastal freight shipping in the Greek Aegean Sea from two different aspects.

First, a strategic planning model is developed for determining the homogeneous fleet size under known supply and demand constraints where total fuel costs and port dues are minimized. Subsequently, the operational dimension of the problem is analyzed by introducing a vehicle routing problem formulation corresponding to the periodic needs for transportation using small containers.

Many simplifying assumptions are made in this study. They conclude that a 5 % cost saving may be realized by redesigning the inter-island links.

3.2.2 Heterogeneous fleet size and mix

In this section we extend the planning problem discussed in Section3.2.1 and include decisions about the mix of different ship sizes.

We study here one particular fleet size and mix problem, where a liner shipping company wants to serve several customers that have a demand for frequent service. The problem consists of determining the best mix of ships to serve known frequencies of demand between several origin–destination port pairs. Many feasible routes are predefined, and just some of them will be used in the optimal solution. The demand is given as a minimum required number of times each port pair has to be serviced. The underlying real problem is a pickup and delivery problem. However, with predefined routes in the model, the loading and unloading aspects are not visible but hidden in the routes.

Since this is a pickup and delivery problem, the frequency demand applies to a pair of ports. The ships are heterogeneous so not all ships can sail all routes.

The capacity of a ship determines, among other factors, which routes it can sail. A ship is allowed to split its time between several routes.

The planning problem consists of deciding: (1) which ships to operate and (2) which routes each ship should sail and the number of voyages along each route. The first part is a strategic fleet mix and size problem and the second

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part is a tactical fleet deployment problem. Fleet deployment problems are discussed in Section 4.4. The second part is used here only to find the best solution to the first part. If the demand pattern changes later, the second part can be resolved for the then available fleet.

In the mathematical description of the problem, letV be the set of ships indexed by v andRvthe set of routes that can be sailed by ship v indexed by r.

The set of origin–destination port pairs is calledN indexed by i, and each such pair needs to be serviced at least D_itimes during the planning horizon.

The cost consists of two parts. We define the cost of sailing one voyage with ship v on route r as C_Vvr. The fixed cost for ship v during the planning horizon is called C_Fv. Each voyage with ship v on route r takes T_Vvrtime units, and A_ir is equal to 1 if origin–destination port pair i is serviced on route r. The length of the planning horizon is T , and we assume that the ships are available for the whole horizon. Let U_vbe an upper bound on the number of voyages ship v can sail during the planning horizon.

Here we use the following types of decision variables: u_vr, v ∈ V^{, r} ∈ Rv, represents the number of voyages along route r with ship v during the planning horizon, and s_v, v∈V, is equal to 1 if ship v is used.

The model for the strategic fleet size and mix problem with predefined routes can then be written as

(3.7) min

v∈V

r∈Rv

C_Vvru_vr+

v∈V

C_Fvs_v

subject to

(3.8)

r∈Rv

u_vr− Uvs_v 0 ∀v ∈V

(3.9)

v∈V

r∈Rv

A_iru_vr Di ∀i ∈N

(3.10)

r∈Rv

T_Vvru_vr T ∀v ∈V

(3.11) u_vr 0 and integer ∀v ∈V^r∈Rv

(3.12) s_v ∈ {0 1} ∀v ∈V

Here(3.7)is the cost of sailing the used routes together with the fixed cost of the ships in operation. Constraints(3.8)ensure that the fixed costs for the ships in operation are taken into account. Constraints(3.9)say that each port pair is serviced at least the required number of times, and constraints(3.10)ensure that each ship finishes all its routes within the planning horizon. Finally, the formulation involves integer and binary requirements on the variables.

Fagerholt and Lindstad (2000)presented this model with different notation and gave an example where the model was used to plan deliveries to Norwe- gian petroleum installations in the North Sea. Their problem had one loading port and seven unloading installations. They managed to pre-calculate all the

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feasible routes and their integer program was solved by CPLEX. The model does not ensure that services for a given port pair are properly spaced during the planning horizon. This aspect was treated manually after the model so- lutions were generated.Fagerholt and Lindstad (2000)report that the model solution implemented gave annual savings of several million US dollars.

Another study regarding fleet size and mix for liner routes was done byCho and Perakis (1996). The study was performed for a container shipping company. The type of model and solution method is similar to the one used by Fagerholt and Lindstad (2000).Xinlian et al. (2000) consider a similar problem. They present a long-term fleet planning model that aims at determining which ships should be added to the existing fleet, ship retirements, and the optimal fleet deployment plan. Another study regarding the design of an optimal fleet and the corresponding weekly routes for each ship for a liner shipping system along the Norwegian coast was presented byFagerholt (1999). The solution method is similar to the one used byFagerholt and Lindstad (2000). In Fagerholt (1999) the solution method handled only instances where the different ships that could be selected have the same speed. This is in contrast to the work inFagerholt and Lindstad (2000), where the ships can have different speeds. Yet another contribution within fleet size and mix for liner shipping is given byLane et al. (1987). They consider the problem of deciding a cost efficient fleet that meets a known demand for shipping services on a defined liner trade route. The solution method has some similarities to the approach used byFagerholt and Lindstad (2000), but the method gives no proven optimal solution since only a subset of the feasible voyage options are selected and the user determines the combination of vessel and voyage. The method has been applied on the Australia/US West coast route. Finally, resource management for a container vessel fleet is studied byPesenti (1995). This problem involves decisions on the purchase and use of ships in order to satisfy customers’ demand. A hierarchical model for the problem has been developed, and heuristic techniques, which solve problems at different decision levels, are described.

A rather special problem regarding the size of the US destroyer fleet is described inCrary et al. (2002), which illustrates the use of quantitative methods in conjunction with expert opinion. These ideas are applied to the planning scenario for the “2015 conflict on the Korean Peninsula”, one of two key sce- narios the Department of Defense uses for planning.

3.3 Liner network design

On all three planning levels the challenges in liner shipping are quite different from those of tramp or industrial. Liner ships are employed on more or less fixed routes, calling regularly at many ports. In contrast to industrial or tramp ships a liner ship serves demand of many shippers simultaneously, and its published route and frequency of service attract demand. The major challenges for liners at the strategic level are the design of liner routes and the associated frequency of service, fleet size and mix decisions and contract evaluation for