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.     

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.     

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.     

The Impact of Container Type Diversification on Regional British Port Development Strategies

Abstract

Despite a concentration of container traffic in the southeast of the UK over the last few decades, regional ports are attempting new development strategies to capture or retain specific traffic segments. These include intra-European short-sea traffic and a potentially increasing feeder market. These trends are reflected in the movement of different container types, which result in a number of planning challenges related to changing infrastructural and operational requirements. This paper uses highly disaggregated data on container type movements to address three issues that can inform these planning challenges. First, the imbalance of trade resulting in empty container repositioning; second, the requirement for gauge-cleared rail routes to cater for the increasing proportion of high-cube containers; and third, the specialisation of European short-sea traffic at secondary UK ports. The results reveal the disproportionate repositioning of empty containers at Scottish ports and the importance of 45?ft, high-cube and pallet-wide containers at regional ports, highlighting their focus on intra-European short-sea traffic and raising difficulties relating to their lower quality of landside infrastructure (particularly rail) in comparison to the large south-eastern ports. The potential repercussions on hinterland infrastructure development raise questions about both public and private sector responses to regional port development.     

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.     

Energy-aware control for automated container terminals using integrated flow shop scheduling and optimal control

The performance of container terminals needs to be improved to handle the growth of transported containers and maintain port sustainability. This paper provides a methodology for improving the handling capacity of an automated container terminal in an energy-efficient way. The behavior of a container terminal is considered as consisting of a higher level and a lower level represented by discrete-event dynamics and continuous-time dynamics, respectively. These dynamics represent the behavior of a large number of terminal equipment. The dynamics need to be controlled. For controlling the higher level dynamics, a minimal makespan problem is solved. For this, the minimal time required by equipment for performing an operation at the lower level is needed. The minimal time for performing an operation at the lower level is obtained using Pontryagin’s Minimum Principle. The actual operation time allowed by the higher level for processing an operation at the lower level is subsequently determined by a scheduling algorithm at the higher level. Given an actual operation time, the lower level dynamics are controlled using optimal control to achieve minimal energy consumption while respecting the time constraint. Simulation studies illustrate how energy-efficient management of equipment for the minimal makespan could be obtained using the proposed methodology.     

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.     

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.     

The container retrieval problem with respect to relocation

The demand for container terminal yards is growing significantly faster than the supply of available land; therefore, containers are typically stacked high to better utilize the land space in container yards. However, in the process of container retrieval, non-productive reshuffling may be required to relocate the containers that are stacked on top of the target container. Container retrieval is directly related to the operational efficiency of terminals. Because the industry has become increasingly competitive, it has become critical to introduce a systematic approach to retrieving containers. In this study, we develop a heuristic that can generate feasible working plans for rail-mounted gantry cranes (RMGC) in container yards to minimize the number of container movements while taking the RMGC working time into consideration. The methodology takes into consideration the case that containers are grouped in terms of their retrieval order. Multi-lift RMGC models also are studied. Comprehensive numerical experiments reveal that the method runs faster than other methods published in the literature by several orders of magnitude; additionally, our method is able to solve instances larger than practical use. The number of movements approaches a theoretical lower bound, and the numerical results clearly demonstrate the tradeoff between the number of movements and the working time, and provide useful insights for yard planning.     

How do economies of density in container handling operations affect ships’ time and emissions in port? Evidence from Norwegian container terminals

Efficient port services are prerequisites for competitive and sustainable maritime transports. This paper makes advances in studying the determinants of the time that ships spend in port and the associated emissions to air. We estimate a production model for cargo handling based on a unique dataset containing each port of call at the largest container terminals in Norway in 2014. In turn, we use auxiliary engine emission factors to estimate particulate matter and nitrogen oxide emissions from ships at berth, to determine how the corresponding damage costs of air pollution vary with container throughput, location, and terminal investments. We find that Norwegian container terminals operate under increasing returns to density. Small ships that unload few containers are far from reaping economies of density, leading to high marginal time requirements for container handling and consequently high marginal external costs. From a Pigouvian taxation perspective, port charges should therefore be regressive in the number of containers handled. Moreover, we find that the external costs of maritime transports are severely understated when port operations are ignored. Our model allows determining the marginal productivities of port facilities. Thereby, it is instrumental in designing port charges that are diversified according to the quantity of containers handled and the service quality (i.e., the speed of handling operations). Regarding contextual factors, we find that establishing high-frequent liner services improves the ship working rate, while simultaneous calls at a terminal impede productivity. The type of container (loading/unloading; empty/laden) also appears to influence the duration of ship working.     

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.     

Effects of demurrage and detention regimes on dry-port-based inland container transport

Increase of congestion at container deep seaports and shortage of capacity has led inland transport systems worldwide to rely more and more on inland terminals, and on the use of high capacity modes of transport to generate economies of scale and reduce negative effects of trucking. In this setting, planning the transport of maritime containers between a deep seaport and a final inland destination must also consider due dates and soft time windows, the latter known as Demurrage and Detention (D&D). In this paper, we formalize the concept of D&D, model the multimodal planning problem, and assess the impact of different D&D regimes on the emerging inland transport systems. By means of an experimental framework, we compare different D&D policies and provide managerial insights. The experiments highlight the effects of existing D&D regimes on transport efficiency and provide guidelines for their choice in practice. D&D are shown to have a twofold effect: first to limit consolidation opportunities and force the use of trucks as buffer, and second to push containers to dwell unnecessarily at the seaports.     

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.     

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.     

Control of interacting machines in automated container terminals using a sequential planning approach for collision avoidance

The control of automated container terminals is complex since Quay Cranes (QCs), Automated Guided Vehicles (AGVs) and Automated Stacking Cranes (ASCs) interact intensively for transporting containers, while collision avoidance of equipment must be ensured. This paper proposes a methodology to generate collision-free trajectories of free-ranging AGVs in automated container terminals, while minimizing the makespan of the whole container handling system. A hierarchical control architecture is proposed to integrate the scheduling of interacting machines and trajectory planning of AGVs. Following a so-called overall graph sequence by a scheduler, the collision-free trajectories of AGVs are determined by solving a collection of mixed integer linear programming problems sequentially. Simulation results illustrate the potential of the proposed methodology.     

Nonlinear pricing for stochastic container leasing system

With the substantial upsurge of container traffic, the container leasing company thrives on the financial benefits and operational flexibility of leasing containers requested by shippers. In practice, container lease pricing problem is different from the consumer product pricing in consideration of the fair value of container, limited customer types and monopolistic supply market. In view of the durability of container and the diversified lease time and quantity, the pricing is a challenging task for the leasing company. This paper examines the monopolist’s nonlinear pricing problems in static and dynamic environments. In particular, the leasing company designs and commits a menu of price and hire quantity/time pairs to maximize the expected profit and in turn customers choose hire quantities/time to maximize their surpluses according to their hire preferences. In a static environment, closed-form solutions are obtained for different groups of customers with multiple types subject to capacity constraint. In a dynamic environment, we address two customer types and derive closed-form solutions for the problem of customers with hire time preference. Further, we show that the effect of the capacity constraint increases with time of the planning horizon when customers have the same hire time preference; while in the case with different hire time preferences, the capacity constraint has opposite effects on the low and high type customers. Last, the case of customers with hire quantity preference is discussed. We focus on the lease with alternative given sets of hire time and use dynamic programming to derive the numerical optimal hire time sequence.     

Optimal pricing for priority service and space allocation in container ports

This paper focuses on the determination of optimal space allocation and optimal pricing for priority systems in container ports. The problem is formulated taking into account the intrinsic and logistic cargo value, and a capacity constraint that considers the various physical requirements of the containers. Prices and space allocations are found for various cases, showing explicitly the role of each element. The resulting models extend classical price differentiation theory, i.e. the inverse elasticity rule, in various directions. Finally, the implications of these results and the corresponding information requirements are clearly established.     

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.     

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.     

Sequencing twin automated stacking cranes in a block at automated container terminal

In the considered automated container terminal (ACT) that is designed for Shanghai Yangsha Terminal, two automated stacking cranes (ASCs) are configured for each block and they interact with automated lifting vehicles (ALVs) at the two ends of a block individually. To increase the capacity, container yards with multiple rows of blocks perpendicular to the terminal’s shoreline are considered. To utilize the yard spaces, the twin ASCs are devised to share the same tracks installed at the two sides of a block, while interferences between the ASCs challenge the routing and sequencing operations. To isolate the control and simplify the coordination of the two ASCs, the interference between ASCs is formulated by analyzing the minimal temporal intervals between any two tasks. Three models are then established to sequence the container handling tasks under the minimization of the makespan. An exact algorithm and a genetic algorithm are designed to solve the problem. Numerical experiments show that the algorithms are competitive comparing to on-the-shelf solvers. Practical implications are investigated based on the formulations and experimental results. The managerial implications and technological aspects of applying the formulations and algorithms to practical situations to real-world ACTs are discussed.