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.     

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.     

Game-theoretical models for competition analysis in a new emerging liner container shipping market

This paper develops three game-theoretical models to analyze shipping competition between two carriers in a new emerging liner container shipping market. The behavior of each carrier is characterized by an optimization model with the objective to maximize his payoff by setting optimal freight rate and shipping deployment (a combination of service frequency and ship capacity setting). The market share for each carrier is determined by the Logit-based discrete choice model. Three competitive game strategic interactions are further investigated, namely, Nash game, Stackelberg game and deterrence by taking account of the economies of scale of the ship capacity settings. Three corresponding competition models with discrete pure strategy are formulated as the variables in shipment deployment are indivisible and the pricing adjustment is step-wise in practice. A ɛ -approximate equilibrium and related numerical solution algorithm are proposed to analyze the effect of Nash equilibrium. Finally, the developed models are numerically evaluated by a case study. The case study shows that, with increasing container demand in the market, expanding ship capacity setting is preferable due to its low marginal cost. Furthermore, Stackelberg equilibrium is a prevailing strategy in most market situations since it makes players attain more benefits from the accommodating market. Moreover, the deterrence effects largely depend on the deterrence objective. An aggressive deterrence strategy may make potential monopolist suffer large benefit loss and an easing strategy has little deterrence effect.     

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.     

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.     

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.     

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.     

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.     

Liner container assignment model with transit-time-sensitive container shipment demand and its applications

This paper proposes a practical tactical-level liner container assignment model for liner shipping companies, in which the container shipment demand is a non-increasing function of the transit time. Given the transit-time-sensitive demand, the model aims to determine which proportion of the demand to fulfill and how to transport these containers in a liner shipping network to maximize the total profit. Although the proposed model is similar to multi-commodity network-flow (MCNF) with side constraints, unlike the MCNF with time delay constraints or reliability constraints that is NP-hard, we show that the liner container assignment model is polynomially solvable due to its weekly schedule characteristics by developing two link-based linear programing formulations. A number of practical extensions and applications are analyzed and managerial insights are discussed. The polynomially solvable liner container assignment model is then applied to address several important decision problems proposed by a global liner shipping company.     

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.     

Service type assignment and container routing with transit time constraints and empty container repositioning for liner shipping service networks

A decision tool is developed for a liner shipping company to deploy its fleet considering vessel speeds and to find routes for cargos with repositioning of empty containers and transit time constraints. This problem is referred as the simultaneous Service type Assignment and container Routing Problem (SARP) in the sequel. A path-flow based mixed-integer linear programming formulation is suggested for the SARP. A Branch and Bound (BB) algorithm is used to solve the SARP exactly. A Column Generation (CG) procedure, embedded within the BB framework, is devised to solve the linear programming relaxation of the SARP. The CG subproblems arises as Shortest Path Problems (SPP). Yet incorporating transit time requirements yields constrained SPP which is NP-hard and solved by a label correcting algorithm. Computational experiments are performed on randomly generated test instances mimicking real life. The BB algorithm yields promising solutions for the SARP. The SARP with and without transit time constraints is compared with each other. Our results suggest a potential to increase profit margins of liner shipping companies by considering transit time requirements of cargos.     

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.     

Profit-based maritime container assignment models for liner shipping networks

We propose the problem of profit-based container assignment (P-CA), in which the container shipment demand is dependent on the freight rate, similar to the “elastic demand” in the literature on urban transportation networks. The problem involves determining the optimal freight rates, the number of containers to transport and how to transport the containers in a liner shipping network to maximize the total profit. We first consider a tactical-level P-CA with known demand functions that are estimated based on historical data and formulate it as a nonlinear optimization model. The tactical-level P-CA can be used for evaluating and improving the container liner shipping network. We then address the operational-level P-CA with unknown demand functions, which aims to design a mechanism that adjusts the freight rates to maximize the profit. A theoretically convergent trial-and-error approach, and a practical trial-and-error approach, are developed. A numerical example is reported to illustrate the application of the models and approaches.     

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.     

Routing and fleet deployment in liner shipping with spot voyages

The routing, scheduling and fleet deployment is an important integrated planning problem faced by liner shipping companies which also lift load from the spot market. This paper is concerned with coordinating the decisions of the assignment of ships to contractual and spot voyages, and the determination of ship routes and schedules in order to maximize profit. We propose a new model for representing voyages as nodes of a directed graph which is used to build a mixed integer programming formulation. Besides contractual and spot nodes, another type of node is put forward to represent a combination of a contractual voyage with one or more spot voyages. In addition, the concept of dominated nodes is introduced in order to discard them and reduce the effort of the search for an optimal solution. A set of test problems has been generated taking into account real world assumptions. The test problems are solved by an optimization software and computational results are reported. The results show the potential of the approach to solve test problems of moderate size.     

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。     

The fleet renewal problem with regional emission limitations: Case study from Roll-on/Roll-off shipping

In this paper, the maritime fleet renewal problem (MFRP) is extended to include regional limitations in the form of emission control areas. The motivation for including this aspect is that strengthening of emission regulations in such areas is expected to be challenging for deep sea shipping in the years to come. In the proposed model, various means to cope with these stricter emission regulations are evaluated for new vessels, and the possibility of upgrading existing vessels with new emission reduction technology is introduced. We consider future fuel prices to be important for the problem, and have chosen to treat them as uncertain, and thus, a stochastic programming model is chosen. A fleet renewal problem faced by the liner shipping operator Wallenius Wilhelmsen Logistics, concerning whether to use low sulphur fuel or have an exhaust gas scrubber system installed to comply with sulphur regulation in emission control areas from 2015, is used as a case study. Furthermore, tests show that the savings from including the aspect of emission control areas in the MFRP are substantial.     

Strategic maritime container service design in oligopolistic markets

This paper considers the maritime container assignment problem in a market setting with two competing firms. Given a series of known, exogenous demands for service between pairs of ports, each company is free to design liner services connecting a subset of the ports and demand, subject to the size of their fleets and the potential for profit. The model is designed as a three-stage complete information game: in the first stage, the firms simultaneously invest in their fleet; in the second stage, they individually design their services and solve the route assignment problem with respect to the transport demand they expect to serve, given the fleet determined in the first stage; in the final stage, the firms compete in terms of freight rates on each origin–destination movement. The game is solved by backward induction. Numerical solutions are provided to characterize the equilibria of the game.     

Lightweighting shipping containers: Life cycle impacts on multimodal freight transportation

Freight transportation by truck, train, and ship accounts for 5% of the United States’ annual energy consumption (U.S. Energy Information Administration, 2017a). Much of this freight is transported in shipping containers. Lightweighting containers is an unexplored strategy to decrease energy and GHG emissions. We evaluate life cycle fuel savings and environmental performance of lightweighting scenarios applied to a forty-foot (12.2 meters) container transported by ship, train, and truck. Use phase burdens for both conventional and lightweighted containers (steel reduction, substitution with aluminum, or substitution with high tensile steel) were compared to life cycle burdens. The study scope ranged from the transportation of one container 100 km to the lifetime movement of the global container fleet on ships. Case studies demonstrated the impact of lightweighting on typical multimodal freight deliveries to the United States. GREET 1 and 2 (Argonne National Laboratory, 2016a,b) were used to estimate the total fuel cycle burdens associated with use phase fuel consumption. Fuel consumption was determined using modal Fuel Reduction Values (FRV), which relate mass reduction to fuel reduction. A lifetime reduction of 21% in the fuel required to transport a container, and 1.4% in the total fuel required to move the vehicles, cargo, and containers can be achieved. It was determined that a 10% reduction in mass of the system will result in a fuel reduction ranging from 2% to 8.4%, depending on the mode. Globally, container lightweighting can reduce energy demand by 3.6 EJ and GHG emissions by 300 million tonnes CO₂e over a 15-year lifetime.