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 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.     

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.     

A tabu search algorithm to solve the integrated planning of container on an inter-terminal network connected with a hinterland rail network

Transport demand for containers has been increasing for decades, which places pressure on road transport. As a result, rail transport is stimulated to provide better intermodal freight transport services. This paper investigates mathematical models for the planning of container movements in a port area, integrating the inter-terminal transport of containers (ITT, within the port area) with the rail freight formation and transport process (towards the hinterland). An integer linear programming model is used to formulate the container transport across operations at container terminals, the network interconnecting them, railway yards and the railway networks towards the hinterland. A tabu search algorithm is proposed to solve the problem. The practical applicability of the algorithm is tested in a realistic infrastructure case and different demand scenarios. Our results show the degree by which internal (ITT) and external (hinterland) transport processes interact, and the potential for improvement of overall operations when the integrated optimization proposed is used. Instead, if the planning of containers in the ITT system is optimized as a stand-alone problem, the railway terminals may suffer from longer delay times or additional train cancellations. When planning the transport of 4060 TEU containers within one day, the benefits of the ITT planning without considering railway operations account for 17% ITT cost reduction but 93% railway operational cost growth, while the benefits of integrating ITT and railway account for a reduction of 20% in ITT cost and 44% in railway operational costs.     

Shipping Lines and Logistics

Abstract

It has been acknowledged that logistics is a driving force that shapes the integration of the transport chain. This paper argues that while the liner shipping industry exhibits increased horizontal integration, its vertical integration remains limited. A clear distinction is drawn between freight logistics, container logistics and vessel logistics. Freight logistics is defined as part of the supply chain process, the focus of which is the goods being transported. The purpose of container logistics is to optimize the movements of the containers themselves, an operation that is directly related to vessel logistics which is concerned with maximizing vessel utilization. The paper demonstrates that shipping lines have to find the correct balance between these three types of logistics. Their interest in vertical integration is primarily because the management of container logistics provides direct support to vessel logistics. Their involvement in freight logistics remains unclear and uncertain.     

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.     

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.     

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.     

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.     

Intermodal freight transport planning – A receding horizon control approach

This paper investigates intermodal freight transport planning problems among deep-sea terminals and inland terminals in hinterland haulage for a horizontally fully integrated intermodal freight transport operator at the tactical container flow level. An intermodal freight transport network (IFTN) model is first developed to capture the key characteristics of intermodal freight transport such as the modality change phenomena at intermodal terminals, physical capacity constraints of the network, time-dependent transport times on freeways, and time schedules for trains and barges. After that, the intermodal freight transport planning problem is formulated as an optimal intermodal container flow control problem from a system and control perspective with the use of the proposed IFTN model. To deal with the dynamic transport demands and dynamic traffic conditions in the IFTN, a receding horizon intermodal container flow control (RIFC) approach is proposed to control and to reassign intermodal container flows in a receding horizon way. This container flow control approach involves solving linear programming problems and is suited for transport planning on large-sized networks. Both an all-or-nothing approach and the proposed RIFC approach are evaluated through simulation studies. Simulation results show the potential of the proposed RIFC approach.     

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.     

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.     

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.     

Storage space allocation in container terminals

Container terminals are essential intermodal interfaces in the global transportation network. Efficient container handling at terminals is important in reducing transportation costs and keeping shipping schedules. In this paper, we study the storage space allocation problem in the storage yards of terminals. This problem is related to all the resources in terminal operations, including quay cranes, yard cranes, storage space, and internal trucks. We solve the problem using a rolling-horizon approach. For each planning horizon, the problem is decomposed into two levels and each level is formulated as a mathematical programming model. At the first level, the total number of containers to be placed in each storage block in each time period of the planning horizon is set to balance two types of workloads among blocks. The second level determines the number of containers associated with each vessel that constitutes the total number of containers in each block in each period, in order to minimize the total distance to transport the containers between their storage blocks and the vessel berthing locations. Numerical runs show that with short computation time the method significantly reduces the workload imbalance in the yard, avoiding possible bottlenecks in terminal operations.     

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.     

The impact of terminal handling charges on overall shipping charges: an empirical study

Before the introduction of terminal handling charges (THCs), traditional freight rates included both ocean freight charges and terminal charges at ports. Since the introduction of THCs in 1991, the freight rate has become a “port-to-port” charge that covers only the sea leg, while the on-shore costs of using the container terminals are charged separately as THCs. Although both THCs and freight rates are collectively set by conferences, in this study we argue that the former are easier to enforce because they are invariant to other attributes such as haulage distance, inland transport services and types of commodity being shipped. This argument is consistent with the empirical findings from this study that suggest the separation of ocean freight rates from terminal charges has increased the overall shipping charges. In addition, we find that THCs affect the Hong Kong container handling industry by lowering its throughput.     

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.     

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.