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.     

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.     

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.     

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.     

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.     

An analysis of institutional pressures,green supply chain management,and green performance in the container shipping context

This paper presents a study which utilized a conceptual framework with institutional theory as its base to empirically evaluate the impact of institutional pressures, internal green practices, and external green collaborations on green performance. Factor analysis was employed to identify the key institutional pressures (i.e. coercive, normative and mimetic pressures), internal green practices (i.e. green shipping practices and green operations), external green collaborations (i.e. green collaboration with supplier, green collaboration with partner, and green collaboration with customer), and green performance (i.e. reduction of pollutants, and perceived green brand) dimensions. We collected data from surveyees employed by 129 container shipping companies and agencies in Taiwan, and applied a structural equation model (SEM) to test the research hypotheses. The findings revealed that institutional pressures have positive effects on internal green practices; internal green practices positively influence external green collaborations; internal green practices and external green collaborations positively influence green performance but institutional pressure is not positively associated with external green collaborations. Theoretical contributions and managerial implications are presented to help container shipping operators improve green performance.     

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.     

An operational activity-based method to estimate CO2 emissions from container shipping considering empty container repositioning

This paper develops an operational activity-based method to estimate CO₂ emissions from container shipping in contrasts to the traditional aggregated activity-based method. Two case studies investigate the impacts of empty container repositioning policies and port handling capacity on CO₂ emission index. The results show that the aggregated method could well overestimate CO₂ emissions and the operational activity-based method is more appropriate. The paper also demonstrates that high port-handling capacity and efficient empty container repositioning could reduce CO₂ emissions in seaborne container transportation.     

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.     

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.     

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 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.     

Case studies of shipping along Arctic routes. Analysis and profitability perspectives for the container sector

Arctic sea routes have for long attracted interest from observers and shipping companies because of their shorter distances between the Atlantic and the Pacific. The prevalence of sea ice prevented the real development of a significant traffic, but did not prevent research from trying to assess the economic viability of these routes. With the actual present melting of sea ice in the Arctic, this effort at modeling the profitability of Arctic shipping routes received a new impetus. However, the conclusions of these studies vary widely, depending on the chosen parameters and their value. What can be said of these models, from 1991 until 2013, and to what extent can a model be drawn, capitalizing on twenty years of simulations?     

Integrated operations planning and revenue management for rail freight transportation

In the rail industry, profit maximization relies heavily on the integration of logistics activities with an improved management of revenues. The operational policies chosen by the carrier have an important impact on the network yield and thus on global profitability. This paper bridges the gap between railroad operations planning and revenue management. We propose a new bilevel mathematical formulation which encompasses pricing decisions and network planning policies such as car blocking and routing as well as train make-up and scheduling. An exact solution approach based on a mixed integer formulation adapted to the problem structure is presented, and computational results are reported on randomly generated instances.     

Comparing the unit emissions of daily frequency and slow steaming strategies on trunk route deployment in international container shipping

This study examines NO_x, SO₂, CO₂, HC, and PM reductions for international container shipping carriers from slow steaming and from making use of daily frequency strategies. The options are examined using activity-based methods for surveys on Far East-Europe routes. It is found that both strategies examined are effective in reducing emissions, with daily frequency more effective in reducing emission levels when slow steaming is not employed.     

A linear programming-based method for the network revenue management problem of air cargo

One critical operational issue of air cargo operation faced by airlines is the control over the sales of their limited cargo space. Since American Airlines’ successful implementation in the post-deregulation era, revenue management (RM) has become a common practice for the airline industry. However, unlike the air passenger operation supported by well-developed RM systems with advanced decision models, the decision process in selling air cargo space to freight forwarders is usually based on experience, without much support from optimization techniques. This study first formulates a multi-dimensional dynamic programming (DP) model to present a network RM problem for air cargo. In order to overcome the computational challenge, this study develops two linear programming (LP) based models to provide the decision support operationally suitable for airlines. In addition, this study further introduces a dynamic adjustment factor to alleviate the inaccuracy problem of the static LP models in estimating resource opportunity cost. Finally, a numerical experiment is performed to validate the applicability of the developed model and solution algorithm to the real-world problems.     

The effectiveness of a European speed limit versus an international bunker-levy to reduce CO2 emissions from container shipping

In the fight to reduce CO₂ emissions from international shipping, a bunker-levy is currently under consideration at the International Maritime Organization (IMO). Faced with the inability of the IMO to reach an agreement in the short term, the European Commission is now contemplating a unilateral measure of a speed limit for all ships entering European Union (EU) ports. This paper argues that this measure is counterproductive for two reasons. Firstly, because it may ultimately generate more emissions and incur a cost per ton of CO₂ which is more than society is willing to pay. Secondly, because it is sub-optimal compared to results obtained if an international bunker-levy was to be implemented. These elements are illustrated using two direct transatlantic services operated in 2010.     

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.     

Sulphur abatement globally in maritime shipping

In 2016, the International Maritime Organization (IMO) decided on global regulations to reduce sulphur emissions to air from maritime shipping starting 2020. The regulation implies that ships can continue to use residual fuels with a high sulphur content, such as heavy fuel oil (HFO), if they employ scrubbers to desulphurise the exhaust gases. Alternatively, they can use fuels with less than 0.5% sulphur, such as desulphurised HFO, distillates (diesel) or liquefied natural gas (LNG). The options of lighter fuels and desulphurisation entail costs, including higher energy consumption at refineries, and the present study identifies and compares compliance options as a function of ship type and operational patterns.The results indicate distillates as an attractive option for smaller vessels, while scrubbers will be an attractive option for larger vessels. For all vessels, apart from the largest fuel consumers, residual fuels desulphurised to less than 0.5% sulphur are also a competing abatement option. Moreover, we analyse the interaction between global SO_X reductions and CO₂ (and fuel consumption), and the results indicate that the higher fuel cost for distillates will motivate shippers to lower speeds, which will offset the increased CO₂ emissions at the refineries. Scrubbers, in contrast, will raise speeds and CO₂ emissions.