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.     

An epsilon-optimal algorithm considering greenhouse gas emissions for the management of a ship’s bunker fuel

This paper provides an algorithm to minimize the fixed ordering, purchase, and inventory-carrying costs associated with bunker fuel together with ship time costs; and environmental costs associated with greenhouse gas emissions. It determines the optimum ship speed, bunkering ports, and amounts of bunker fuel for a given ship’s route. To solve the problem, we use an epsilon-optimal algorithm by deriving a property. The algorithm is illustrated by applying it to typical sample data obtained and the effects of bunker prices, carbon taxes, and ship time costs on the ship speed are analyzed. The results indicate that the ship speed and CO₂ emissions are highly sensitive to the factors considered.     

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.     

Forecasting bunker prices; A nonstationary,multivariate methodology

This paper suggests a methodological approach for the forecasting of marine fuel prices. The prediction of the bunker prices is of outmost importance for operators, as bunker prices affect heavily the economic planning and financial viability of ventures and determine decisions related to compliance with regulations. A multivariate nonstationary stochastic model available in the literature is being retrieved, after appropriate adjustment and testing. The model belongs to the class of periodically correlated stochastic processes with annual periodic components. The time series are appropriately transformed to become Gaussian, and then are decomposed to deterministic seasonal characteristics (mean value and standard deviation) and a residual time series. The residual part is proved to be stationary and then is modeled as a Vector AutoRegressive Mooving Average (VARMA) process. Finally, using the methodology presented, forecasts of a tetra-variate and an octa-variate time series of bunker prices are produced and are in good agreement with actual values. The obtained results encourages further research and deeper investigation of the driving characters of the multivariate time series of bunker prices.     

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.     

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.     

A tailored branch-and-price approach for a joint tramp ship routing and bunkering problem

This paper deals with a practical tramp ship routing problem while taking into account different bunker prices at different ports, which is called the joint tramp ship routing and bunkering (JSRB) problem. Given a set of cargoes to be transported and a set of ports with different bunker prices, the proposed problem determines how to route ships to carry the cargoes and the amount of bunker to purchase at each port, in order to maximize the total profit. After building an integer linear programming model for the JSRB problem, we propose a tailored branch-and-price (B&P) solution approach. The B&P approach incorporates an efficient method for obtaining the optimal bunkering policy and a novel dominance rule for detecting inefficient routing options. The B&P approach is tested with randomly generated large-scale instances derived from real-world planning problems. All of the instances can be solved efficiently. Moreover, the proposed approach for the JSRB problem outperforms the conventional sequential planning approach and can incorporate the prediction of future cargo demand to avoid making myopic 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.     

Determinants of vessel-accident bunker spills

The study investigates determinants of vessel-accident bunker fuel spillage. A vessel-accident bunker spillage equation is estimated using Tobit regression and data of individual non-oil-cargo vessel accidents that were investigated by the US Coast Guard during 2001–2008. The results indicate that the bunker spillage of a freight ship and an offshore supply vessel accident will be greater than that of a passenger ship accident. Also, the bunker spillage of a non-oil-cargo vessel accident will be greater if the vessel accident is an abandonment and occurs at night, but less if the accident involves a vessel that has diesel propulsion and even less if the vessel has both diesel propulsion and a steel hull.     

Liner ship route schedule design with port time windows

This paper examines a practical tactical liner ship route schedule design problem, which is the determination of the arrival and departure time at each port of call on the ship route. When designing the schedule, the availability of each port in a week, i.e., port time window, is incorporated. As a result, the designed schedule can be applied in practice without or with only minimum revisions. This problem is formulated as a mixed-integer nonlinear nonconvex optimization model. In view of the problem structure, an efficient holistic solution approach is proposed to obtain global optimal solution. The proposed solution method is applied to a trans-Atlantic ship route. The results demonstrate that the port time windows, port handling efficiency, bunker price and unit inventory cost all affect the total cost of a ship route, the optimal number of ships to deploy, and the optimal schedule.     

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.     

Bunker levy schemes for greenhouse gas (GHG) emission reduction in international shipping

A fuel levy is one of the market-based measures (MBMs) currently under consideration at the International Maritime Organization. MBMs have been proposed to improve the energy efficiency of the shipping sector and reduce its emissions. This paper analyses the economic and environmental implications of two types of levy on shipping bunker fuels by means of an analytical model built on the cobweb theorem. A unit-tax per ton of fuel and an ad-valorem tax, enforced as a percentage of fuel prices, are examined. In both cases, a speed and fuel-consumption reduction equivalent to an improvement in the energy efficiency of the sector would be expected as a result of the regulation enforcement. The speed reduction in the unit-tax case depends on fuel prices and the tax amount, whereas in the ad-valorem case it relies upon the enforced tax percentage.Both schemes lead to industry profit decline, the extent of which depend on the structure of the levy and market conditions. Since there is concern that the costs resulting from the policy will be passed from shipping companies to their customers along the supply chain, the paper dwells on how the costs arising from the enforcement of the levy will be actually allocated between ship-owners and operators, and cargo-owners. In a market characterised by high freight rates and with no or limited excess capacity, a higher percentage of the total tax amount is transferred from ship-owners to shippers. In case of a recession the opposite happens.     

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.     

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.     

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.     

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.     

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.     

Estimation of the perceived value of transit time for containerized cargoes

This paper proposes a novel method for estimating the perceived value of transit time of containers by shipping lines. The key idea is that a shipping line’s published schedule is the optimal decision that minimizes the sum of fuel cost and time-associated costs of the containers adopted by the shipping line. Using the proposed method, we find that the adopted values of transit time for nine trans-Pacific services operated by Orient Overseas Container Line and five trans-Pacific services operated by Maersk Line are between US$5/TEU/day and US$30/TEU/day. We further demonstrate how the adopted value can be used for designing the optimal transit times between ports, analyzing the viability of slow-steaming, checking whether ships should speed up to catch up to connecting ships on other services, and helping to predict the market share of less polluting fuels in view of rules on air emission.     

Real option analysis for environmental compliance: LNG and emission control areas

A wide array of technical and operational solutions is available to shipowners in order to comply with existing and upcoming environmental regulation within Emission Control Areas (ECAs). Liquefied Natural Gas (LNG) is a promising alternative since it offers potential cost savings in addition to ensuring compliance with ECA regulation. But investment to retrofit existing vessels to be able to use LNG carries significant upfront costs, and a high degree of uncertainty remains on the differential between the prices of LNG and conventional maritime fuels, as well as on the availability of LNG and the reliability of its supply chain. New technologies such as LNG inherently carry substantial risk and an ill-chosen investment strategy may have irreversible consequences that could jeopardise the future of the shipping company. One important question is whether interested owners should invest in LNG now to comply with ECA rules in 2015 and reap the benefits of lower LNG prices, or whether it would be advisable to wait until some of the uncertainty is resolved.While traditional discounted cash flow techniques are unable to account for the value of managerial flexibility linked, for example, to the possibility of deferring an investment, real option analysis can be used to analyse such cases. The paper discusses the optimal time for investment in LNG retrofit and takes specific account of the value of an investment deferral strategy versus the advantages obtainable from the immediate exploitation of fuel price differentials. Through the use of a real option model the paper shows that there is a trade-off between low fuel prices and capital expenses for investment in LNG retrofit. The development in LNG is critically dependent on its future price as well as the reduction in capital costs and ship retrofitting costs. In this respect, policy makers can play a critical role in providing support to advance technical knowledge, maintain LNG prices at favourable levels and in avoiding ambiguity on regulation.     

Liner shipping network design with emission control areas: A genetic algorithm-based approach

To curb emissions, containerized shipping lines face the traditional trade-off between cost and emissions (CO₂ and SO_x) reduction. This paper considers this element in the context of liner service design and proposes a mixed integer linear programming (MILP) model based on a multi-commodity pickup and delivery arc-flow formulation. The objective is to maximize the profit by selecting the ports to be visited, the sequence of port visit, the cargo flows between ports, as well as the number/operating speeds of vessels on each arc of the selected route. The problem also considers that Emission Control Areas (ECAs) exist in the liner network and accounts for the vessel carrying capacity. In addition to using the MILP solver of CPLEX, we develop in the paper a specific genetic algorithm (GA) based heuristic and show that it gives the possibility to reach an optimal solution when solving large size instances.