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.     

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.     

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.     

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.     

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.     

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.     

A cost-based maritime container assignment model

A recently proposed frequency-based maritime container assignment model (Bell et al., 2011) seeks an assignment of full and empty containers to paths that minimises expected container travel time, whereas containers are in practice more likely to be assigned to minimise expected cost. A cost-based container assignment model is proposed here. It is assumed that routes and service frequencies are given so ship operating costs are also fixed. The objective is to assign containers to routes to minimise container handling costs, container rental and inventory costs. The constraints in the model are extended to include route as well as port capacities. It is shown that the problem remains a linear program. A numerical example is presented to illustrate the properties of the model. The paper concludes by considering the many applications of the proposed maritime container assignment model.     

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.     

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.     

A frequency-based maritime container assignment model

This paper transfers the classic frequency-based transit assignment method of Spiess and Florian to containers demonstrating its promise as the basis for a global maritime container assignment model. In this model, containers are carried by shipping lines operating strings (or port rotations) with given service frequencies. An origin–destination matrix of full containers is assigned to these strings to minimize sailing time plus container dwell time at the origin port and any intermediate transhipment ports. This necessitated two significant model extensions. The first involves the repositioning of empty containers so that a net outflow of full containers from any port is balanced by a net inflow of empty containers, and vice versa. As with full containers, empty containers are repositioned to minimize the sum of sailing and dwell time, with a facility to discount the dwell time of empty containers in recognition of the absence of inventory. The second involves the inclusion of an upper limit to the maximum number of container moves per unit time at any port. The dual variable for this constraint provides a shadow price, or surcharge, for loading or unloading a container at a congested port. Insight into the interpretation of the dual variables is given by proposition and proof. Model behaviour is illustrated by a simple numerical example. The paper concludes by considering the next steps toward realising a container assignment model that can, amongst other things, support the assessment of supply chain vulnerability to maritime disruptions.     

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.     

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.     

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.     

Bi-objective optimization for the container terminal integrated planning

In this paper, we study the joint optimization of the tactical berth allocation and the tactical yard allocation in container terminals, which typically consist of berth side and yard side operations. The studied two objectives are: (i) the minimization of the violation of the vessels’ expected turnaround time windows with the purpose of meeting the timetables published by shipping liners, and (ii) the minimization of the total yard transportation distance with the aim to lower terminal operational cost. We propose a bi-objective integer program which can comprehensively address the import, export and transshipment tasks in port daily practice. Traditionally, a container transshipment task is performed as a couple of import and export tasks, called indirect-transshipment mode, in which the transit container are needed to be temporally stored in the yard. As the way of transferring containers directly from the incoming vessel to the outgoing vessel, called direct-transshipment mode, has potential to save yard storage resources, the proposed model also incorporates both indirect- and direct-transshipment modes. To produce Pareto solutions efficiently, we devise heuristic approaches. Numerical experiments have been conducted to demonstrate the efficiency of the approaches.     

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.     

Traffic consolidation in East Asian container ports: A network flow analysis

The proliferation of hub-and-spoke operations in maritime container transportation has resulted in the widespread consolidation of traffic flows. Utilising liner shipping network configurations, this paper assesses the impact of freight traffic consolidation in the container port industry by exploring the spatial pattern of traffic flow movements and identifying the variety of roles that container ports play within this context. On the basis of the network concept, the spatial inequality of freight traffic consolidation is determined by the density and direction of all meaningful connections (i.e. significant flows) identified by applying Multiple Linkage Analysis (MLA) to an initial traffic flow matrix.The effectiveness of the chosen methodology is tested empirically using a sample comprising the 18 major container ports in East Asia, together with another 21 important container ports located on the East–West trading route. Based on this sample network, the spatial structure of traffic flow consolidation reveals the nature and structure of hub-and-spoke operations within a port system, the relative hub-dependence of ports, the variety of roles which individual ports play within the overall structure of inter-port interactions and the hierarchical configuration of the port industry structure. The paper concludes that MLA offers new insights into the distributional inequality of traffic flows, the spatial and economic interactions between ports and the extent to which hinterlands overlap. Furthermore, the analysis clearly shows that inter-port relationships can no longer be evaluated as isolated phenomena; any change in a specific port’s competitiveness will directly impact upon the structure of the whole maritime transportation system. Port authorities and terminal operators will need, therefore, to carefully analyse and disentangle specific inter-port relationships in order to provide the most appropriate basis for their decision making.     

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 impact of job assignment rules for straddle carriers on the throughput of container terminals

Straddle carriers represent a critical resource in the handling of containers within a container terminal. It is essential that they are deployed in an as efficient manner as possible. The research presented in this paper is motivated by the need to critically evaluate job assignment rules for straddle carriers that operate in a multiple straddle environment. This is achieved by developing a discrete event simulation model using industrial simulation software to model a container terminal located in Melbourne, Australia. The model accounts for variables such as the number of straddle carriers needed, the speed of straddle carriers, the arrival rate of trucks, and the job assignment rule. A principal finding of the study is that increasing the number of straddles in the present set‐up from 6 to 7 has a negligible effect on daily throughput. However, an increase in the number of straddles to 7 is expected to have a profound effect on reducing the average waiting time of trucks within the terminal from over 16 minutes to under 9 minutes, a decrease of 46.5%. However, a further increase in the number of straddles results in no further increase in daily throughput. It was observed that the throughput of the terminal is very sensitive to the speeds at which straddles travel. The management of the terminal has proposed a new heuristic job assignment rule for straddles, because the present rule does not assign the jobs to straddles closest to the truck requesting to load or unload a container. As a result a new heuristic job assignment rule was tested. The simulation results revealed that both the old and new rules performed equally well using performance indicators such as average container flow time, daily throughput, average waiting time of jobs, number of jobs in the queue, and straddle utilisation. Therefore, the new rule will not improve these performance measures if implemented