A joint optimization model for liner container cargo assignment problem using state-augmented shipping network framework

This paper proposes a state-augmented shipping (SAS) network framework to integrate various activities in liner container shipping chain, including container loading/unloading, transshipment, dwelling at visited ports, in-transit waiting and in-sea transport process. Based on the SAS network framework, we develop a chance-constrained optimization model for a joint cargo assignment problem. The model attempts to maximize the carrier’s profit by simultaneously determining optimal ship fleet capacity setting, ship route schedules and cargo allocation scheme. With a few disparities from previous studies, we take into account two differentiated container demands: deterministic contracted basis demand received from large manufacturers and uncertain spot demand collected from the spot market. The economies of scale of ship size are incorporated to examine the scaling effect of ship capacity setting in the cargo assignment problem. Meanwhile, the schedule coordination strategy is introduced to measure the in-transit waiting time and resultant storage cost. Through two numerical studies, it is demonstrated that the proposed chance-constrained joint optimization model can characterize the impact of carrier’s risk preference on decisions of the container cargo assignment. Moreover, considering the scaling effect of large ships can alleviate the concern of cargo overload rejection and consequently help carriers make more promising ship deployment schemes.     

Post-entry container port capacity expansion

Port capacity development is a critical strategy for the growth of a new port, as well as for the development of existing ones, when both new and existing ports serve the same hinterland but have different competitive conditions. To study this strategy, we develop a two-stage duopoly model that comprises the pricing and capacity decisions of two heterogeneous players serving an increasing market. We identify the necessary condition for a port to increase its profit through capacity expansion, and characterize the condition when preemptive pricing by the dominant player is neither credible nor effective in preventing the smaller player from gaining market share. We also find the pure-strategy Nash equilibrium in the capacity expansion game for two ports that have different price sensitivities, as well as different operation and capacity investment costs. We apply the model results to the container port competition between Hong Kong and Shenzhen after Shenzhen port started its container operation in 1991. Our analysis explains the transition of market power from monopoly to duopoly, the fast development of Shenzhen Port, and the possible market structure changes with the continuing increase in demand.     

Container liner fleet deployment: A systematic overview

Container liner fleet deployment (CLFD) is the assignment of containerships to port rotations (ship routes) for efficient transport of containers. As liner shipping services have fixed schedules, the ship-related operating cost is determined at the CLFD stage. This paper provides a critical review of existing mathematical models developed for the CLFD problems. It first gives a systematic overview of the fundamental assumptions used by the existing CLFD models. The operating characteristics dealt with in existing studies are then examined, including container transshipment and routing, uncertain demand, empty container repositioning, ship sailing speed optimization and ship repositioning. Finally, this paper points out four important future research opportunities: fleet deployment considering ship surveys and inspections, service dependent demand, pollutant emissions, and CLFD for shipping alliances.     

Essential elements in tactical planning models for container liner shipping

Tactical planning models for liner shipping problems such as network design and fleet deployment usually minimize the total cost or maximize the total profit subject to constraints including ship availability, service frequency, ship capacity, and transshipment. Most models in the literature do not consider slot-purchasing, multi-type containers, empty container repositioning, or ship repositioning, and they formulate the numbers of containers to transport as continuous variables. This paper develops a mixed-integer linear programming model that captures all these elements. It further examines from the theoretical point of view the additional computational burden introduced by incorporating these elements in the planning model. Extensive numerical experiments are conducted to evaluate the effects of the elements on tactical planning decisions. Results demonstrate that slot-purchasing and empty container repositioning have the largest impact on tactical planning decisions and relaxing the numbers of containers as continuous variables has little impact on the decisions.     

Shipping log data based container ship fuel efficiency modeling

Container shipping lines have been initiating various ship fuel efficiency management programs because bunker fuel costs always dominate the daily operating costs of a container ship. As the basis of these kinds of programs, we develop a viable research methodology for modeling the relationship between the fuel consumption rate of a particular container ship and its determinants, including sailing speed, displacement, sea conditions and weather conditions, by using the shipping log data available in practice. The developed methodology consists of an outlier-score-based data preprocessing procedure to tackle the fuzziness, inaccuracy and limited information of shipping logs, and two regression models for container ship fuel efficiency. Real shipping logs from four container ships (two with 13000 TEUs and two with 5000 TEUs) over a six-month sailing period are used to exhibit the applicability and effectiveness of the proposed methodology. The empirical studies demonstrate the performance of three models for fitting the fuel consumption rate of a ship and the industrial merits of ship fuel efficiency management. In addition, we highlight the potential impacts of the models developed in this study on liner shipping network analysis, as these models can serve as base models for additionally considering the influence of displacement and weather conditions on ship fuel efficiency and exhaust emissions.     

Container vessel fleet deployment for liner shipping with stochastic dependencies in shipping demand

The problem of optimal container vessels deployment is one of great significance for the liner shipping industry. Although the pioneering work on this problem dates back to the early 1990s, only until recently have researchers started to acknowledge and account for the significant amount of uncertainty present in shipping demand in real world container shipping. In this paper, new analytical results are presented to further relax the input requirements for this problem. Specifically, only the mean and variance of the maximum shipping demand are required to be known. An optional symmetry assumption is shown to further reduce the feasible region and deployment cost for typical confidence levels. Moreover, unlike previous work that tends to ignore stochastic dependencies between the shipping demands on the various routes (that are known to exist in the real world), our models account for such dependencies in the most general setting to date. A salient feature of our modeling approach is that the exact dependence structure does not need to be specified, something that is hard, if not simply impossible, to determine in practice. A numerical case study is provided to illustrate the proposed models.     

A continuum approximation approach to competitive facility location design under facility disruption risks

This paper presents game-theoretical models based on a continuous approximation (CA) scheme to optimize service facility location design under spatial competition and facility disruption risks. The share of customer demand in a market depends on the functionality of service facilities and the presence of nearby competitors, as customers normally seek the nearest functioning facility for service. Our game-theoretical models incorporate these complicating factors into an integrated framework, and use continuous and differentiable density functions to represent discrete location decisions. We first analyze the existence of Nash equilibria in a symmetric two-company competition case. Then we build a leader–follower Stackelberg competition model to derive the optimal facility location design when one of the companies has the first mover advantage over its competitor. Both models are solved effectively, and closed-form analytical solutions can be obtained for special cases. Numerical experiments (with hypothetical and empirical data) are conducted to show the impacts of competition, facility disruption risks and transportation cost metrics on the optimal design. Properties of the models are analyzed to cast interesting managerial insights.     

In Search of the Link between Ship Size and Operations

Abstract

Since 1990s the liner shipping industry has faced a period of restructuring and consolidation, and been confronted with a continuing increase in container vessel scale. The impact of these changes is noticeable in trade patterns, cargo handling methods and shipping routes, in short ‘operations’. After listing factors influencing size, growth in container ship size is explained by economies of scale in deploying larger vessels. In order to quantify economies of scale, this paper uses the liner service cash flow model. A novelty in the model is the inclusion of +6000-20-foot Equivalent Unit (TEU) vessels and the distinction in costs between single and twin propeller units on ships. The results illustrate that scale economies have been – and will continue to be – the driving force behind the deployment of larger container vessels. The paper then assesses the link between ship size and operations, given current discussions about the increase in container vessel scale. It is found that (a) ship size and operations are linked; (b) optimal ship size depends on transport segment (deep-sea vs. short-sea shipping, SSS), terminal type (transhipment terminals vs. other terminals), trade lane (East-West vs. North-South trades) and technology; and (c) a ship optimal for one trade can be suboptimal for another.     

Modeling the impacts of alternative emission trading schemes on international shipping

Various market-based measures have been proposed to reduce CO₂ emissions from international shipping. One promising mechanism under consideration is the Emission Trading Scheme (ETS). This study analyzes and benchmarks the economic implications of two alternative ETS mechanisms, namely, an open ETS compared to a Maritime only ETS (METS). The analytical solutions and model calibration results allow us to quantify the impacts of alternative ETS schemes on the container shipping sector and the dry bulk shipping sector. It is found that an ETS, whether open or maritime only, will decrease shipping speed, carrier outputs and fuel consumption for both the container and dry bulk sectors, even in the presence of a “wind-fall” profit to shipping companies. Under an open ETS, the dry bulk sector will suffer from a higher proportional reduction in output than the container sector, and will thus sell more emission permits or purchase fewer permits. Under an METS, container carriers will buy emission permits from the dry bulk side. In addition, under an METS the degree of competition within one sector will have spill-over effects on the other sector. Specifically, when the sector that sells (buys) permits is more collusive (competitive), the equilibrium permit price will rise. This study provides a framework for identifying the moderating effects of market structure and competition between firms on emission reduction schemes, and emphasizes the importance of understanding the differential impacts of ETS schemes on individual sectors within an industry when considering alternative policies.     

Benefit of speed reduction for ships in different weather conditions

Currently, the shipping industry is facing a great challenge of reducing emissions. Reducing ship speeds will reduce the emissions in the immediate future with no additional infrastructure. However, a detailed investigation is required to verify the claim that a 10% speed reduction would lead to 19% fuel savings (Faber et al., 2012).This paper investigates fuel savings due to speed reduction using detailed modeling of ship performance. Three container ships, two bulk carriers, and one tanker, representative of the shipping fleet, have been designed. Voyages have been simulated by modeling calm water resistance, wave resistance, propulsion efficiency, and engine limits. Six ships have been simulated in various weather conditions at different speeds. Potential fuel savings have been estimated for a range of speed reductions in realistic weather.It is concluded that the common assumption of cubic speed-power relation can cause a significant error in the estimation of bunker consumption. Simulations in different seasons have revealed that fuel savings due to speed reduction are highly weather dependent. Therefore, a simple way to include the effect of weather in shipping transport models has been proposed.Speed reduction can lead to an increase in the number of ships to fulfill the transport demand. Therefore, the emission reduction potential of speed reduction strategy, after accounting for the additional ships, has been studied. Surprisingly, when the speed is reduced by 30%, fuel savings vary from 2% to 45% depending on ship type, size and weather conditions. Fuel savings further reduce when the auxiliary engines are considered.     

Reversing port rotation directions in a container liner shipping network

Reversing port rotation directions of ship routes is a practical alteration of container liner shipping networks. The port rotation directions of ship routes not only affect the transit time of containers, as has been recognized by the literature, but also the shipping capacity and transshipment cost. This paper aims to obtain the optimal port rotation directions that minimize the generalized network-wide cost including transshipment cost, slot-purchasing cost and inventory cost. A mixed-integer linear programming model is proposed for the optimal port rotation direction optimization problem and it nests a minimum cost multi-commodity network flow model. The proposed model is applied to a liner shipping network operated by a global liner shipping company. Results demonstrate that real-case instances could be efficiently solved and significant cost reductions are gained by optimization of port rotation directions.     

Liner container seasonal shipping revenue management

This paper proposes a liner container seasonal shipping revenue management problem for a container shipping company. For a given weekly multi-type shipment demand pattern in a particular season, the proposed problem aims to maximize the total seasonal shipping profit by determining the number of multi-type containers to be transported and assigned on each container route, the number of containerships deployed on each ship route, and the sailing speed of containerships on each shipping leg subject to both the volume and capacity constraints of each containership. By adopting the realistic bunker consumption rate of a containership as a function of its sailing speed and payload (displacement), we develop a mixed-integer nonlinear programing with a nonconvex objective function for the proposed liner container seasonal shipping revenue management problem. A tailored branch and bound (B&B) method is designed to obtain the global ε-optimal solution of the model. Numerical experiments are finally conducted to assess the efficiency of the solution algorithm and to show the applicability of the developed model.     

Price and frequency competition in freight transportation

This paper develops a simple analytical model of price and frequency competition among freight carriers. In the model, the full price faced by a shipper (a goods producer) includes the actual shipping price plus an inventory holding cost, which is inversely proportional to the frequency of shipments offered by the freight carrier. Taking brand loyalty on the part of shippers into account, competing freight carriers maximize profit by setting prices, frequencies and vehicle carrying capacities. Assuming tractable functional forms, long- and short-run comparative-static results are derived to show how the choice variables are affected by the model’s parameters. The paper also provides an efficiency analysis, comparing the equilibrium to the social optimum, and it attempts to explain the phenomenon of excess capacity in the freight industry.     

Low cost carrier competition and route entry in an emerging but regulated aviation market – The case of China

Although China lags behind other liberalized aviation markets in low cost carrier (LCC) development, its largest LCC, Spring Airlines, has achieved rapid growth in traffic volume and revenue, as well as consistent profitability, since its inauguration in 2005. Our empirical study on the Chinese domestic market suggests that Spring adopts a “cream skimming” strategy to enter high-priced routes, allowing the carrier to achieve both a very high load factor and considerable profitability. Spring’s capacity and market share on individual routes are constrained to low levels, likely due to government regulation and/or a “puppy dog” strategy adopted by the carrier. As a result, Spring is able to achieve fast growth without triggering price wars. To incumbent full service carriers, high speed rail (HSR) services impose much more significant competitive pressure than low cost carriers. Similar to LCCs in developed markets, Spring prefers to serve markets with high traffic volumes out of its operational base in Shanghai. Overall, Spring’s entry decision is not significantly affected by competition, either from full service airlines or HSR services. Our investigation suggests that LCCs have potential to introduce more competition but are yet to be a “game changer” in China. Further deregulation of the domestic market is needed.     

A note of network equilibrium and noncooperative games

Rosenthal has shown that a user-optimized transportation network is equivalent to a pure Strategy Nash equilibrium when the network flows are discrete. Noting that most network equilibrium theorists take flows to be continuous, we extend this result to the nondiscrete case. We prove that a continuous flow, user-optimized network is a pure-strategy Nash equilibrium in a game with a continuum of pure strategies. Our “game”, however, differs from Rosenthal's in its players, strategies, and payoffs. For instance, the players in our model are not the motorists, but the origin-destination pairs. Some possible applications and extensions of our results are discussed.     

Liner ship route capacity utilization estimation with a bounded polyhedral container shipment demand pattern

This paper aims to estimate capacity utilization of a liner ship route with a bounded polyhedral container shipment demand pattern, arising in the liner container shipping industry. The proposed maximum and minimum liner ship route capacity utilization problems are formulated as a linear programming model and a min–max model, respectively. We examine two fundamental properties of the min–max model. These two nice properties enable us to develop two ε-optimal global optimization algorithms for solving the min–max model, which find a globally ε-optimal solution by iteratively cutting off the bounded polyhedral container shipment demand set with a cut. The latter algorithm overcomes non-convexity of the remaining feasible demand set generated by the former algorithm via a novel hyperplane cut. Each hyperplane cut can assure that the current vertex of the polyhedral demand set is cut off, whereas solutions that may improve the current one by more than a factor of ε are retained. Extensive numerical experiments for problems larger than those encountered in real applications demonstrate the computational efficacy of the latter algorithm.     

内河集装箱班轮优先过闸管理模式探讨

文章结合2013年最新出台的《广西壮族自治区船闸管理办法》,以及近期国家关于行政审批制度改革的相关精神和要求,对集装箱班轮优先过闸条款进行探索和研究,分析了集装箱班轮优先过闸面临的主要问题,提出了一套新的市场管理模式,即主要采取企业公开"承诺制",加上"定期、定港、定线、不定船"的管理模式,通过实施"宽进严管",以期在简政放权的同时,能够充分发挥市场作用,促进企业自律,推动内河集装箱班轮运输市场的健康发展。     

Segment-based alteration for container liner shipping network design

Container liner shipping companies only partially alter their shipping networks to cope with the changing demand, rather than entirely redesign and change the network. In view of the practice, this paper proposes an optimal container liner shipping network alteration problem based on an interesting idea of segment, which is a sequence of legs from a head port to a tail port that are visited by the same type of ship more than once in the existing shipping network. In segment-based network alteration, the segments are intact and each port is visited by the same type of ship and from the same previous ports. As a result, the designed network needs minimum modification before implementation. A mixed-integer linear programming model with a polynomial number of variables is developed for the proposed segmented-based liner shipping network alternation problem. The developed model is applied to an Asia–Europe–Oceania liner shipping network with a total of 46 ports and 11 ship routes. Results demonstrate that the problem could be solved efficiently and the optimized network reduces the total cost of the initial network considerably.     

Pricing and competition in a shipping market with waste shipments and empty container repositioning

In this paper, we study a shipping market with carriers providing services between two locations. Shipments are classified into two categories: goods and waste. Trade imbalance allows low-valued waste to be shipped at bargain rates. If imbalance persists, empty containers must be repositioned from a surplus location to a shortage location. Carriers decide prices, which will affect the demand. We build a monopoly and a duopoly model to find the optimal pricing strategy for carriers. We also analyze how the profit of a carrier is affected by price sensitivity, cost structure and competition intensity.     

A continuous network design model in stochastic user equilibrium based on sensitivity analysis

The continuous network design problem (CNDP) is known to be difficult to solve due to the intrinsic properties of non‐convexity and nonlinearity. Such kinds of CNDP can be formulated as a bi‐level programme, in which the upper level represents the designer's decisions and the lower level the travellers' responses. Formulations of this kind can be classified as either Stackelberg approaches or Nash ones according to the relationship between the upper level and the lower level parts. This paper formulates the CNDP for road expansion based on Stackelberg game where leader and follower exist, and allows for variety of travellers' behaviour in choosing their routes. In order to solve the problem by the Stackelberg approach, we need a relation between link flows and design parameters. For this purpose, we use a logit route choice model, which provides this in an explicit closed‐form function. This model is applied to two example road networks to test and briefly compare the results between the Stackelberg and Nash approaches to explore the differences between them.