Methods for strategic liner shipping network design

In this paper the combined fleet-design, ship-scheduling and cargo-routing problem with limited availability of ships in liner shipping is considered. A composite solution approach is proposed in which the ports are first aggregated into port clusters to reduce the problem size. When the cargo flows are disaggregated, a feeder service network is introduced to ship the cargo within a port cluster. The solution method is tested on a problem instance containing 58 ports on the Asia–Europe trade lane of Maersk. The best obtained profit gives an improvement of more than 10% compared to the reference network based on the Maersk network.     

Hub-and-spoke network design and fleet deployment for string planning of liner shipping

All shipping liner companies divide their service regions into several rotations (strings) in order to operate their container vessels. A string is the ordered set of ports at which a container vessel will call. Each port is usually called at no more than twice along one string, although a single port may be called at several times on different strings. The size of string dictates the number of vessels required to offer a given frequency of service. In order to better use their shipping capacity, groups of Liner Service Providers sometimes make a short term agreement to merge some of their service routes (in a certain region) into one main ocean going rotation and p feeder rotations. In order to minimize the weighted sum of transit time, and fixed deployment costs, this paper proposes a mixed integer linear programming model of the network design, and an allocation of proper capacity size and frequency setting for every rotation. Given that none of the existing general-purpose MIP solvers is able to solve even very small problem instances in a reasonable time, we propose a Lagrangian decomposition approach which uses a heuristic procedure and is capable of obtaining practical and high quality solutions in reasonable times. The model will be applied on a real example, and we shall present some of the results obtained by our model which show how it facilitates a better use of assets and a significant reduction in the use of fuel, therefore allowing a more environmentally friendly service.     

A service flow model for the liner shipping network design problem

Global liner shipping is a competitive industry, requiring liner carriers to carefully deploy their vessels efficiently to construct a cost competitive network. This paper presents a novel compact formulation of the liner shipping network design problem (LSNDP) based on service flows. The formulation alleviates issues faced by arc flow formulations with regards to handling multiple calls to the same port. A problem which has not been fully dealt with earlier by LSNDP formulations. Multiple calls are handled by introducing service nodes, together with port nodes in a graph representation of the problem, and by introducing numbered arcs between a port and a novel service node. An arc from a port node to a service node indicate whether a service is calling the port or not. This representation allows recurrent calls of a service to a port, which previously could not be handled by LSNDP models. The model ensures strictly weekly frequencies of services, ensures that port-vessel draft capabilities are not violated, respects vessel capacities and the number of vessels available. The profit of the generated network is maximized, i.e. the revenue of flowed cargo subtracted operational costs of the network and a penalty for not flowed cargo. The model can be used to design liner shipping networks to utilize a container carrier’s assets efficiently and to investigate possible scenarios of changed market conditions. The model is solved as a Mixed Integer Program. Results are presented for the two smallest instances of the benchmark suite LINER-LIB-2012 presented in Brouer, Alvarez, Plum, Pisinger, and Sigurd (2013).     

Impact analysis of maritime cabotage legislations on liner hub-and-spoke shipping network design

Maritime cabotage is a legislation published by a particular coastal country, which is used to conduct the cargo transportation between its two domestic ports. This paper proposes a two-phase mathematical programming model to formulate the liner hub-and-spoke shipping network design problem subject to the maritime cabotage legislations, i.e., the hub location and feeder allocation problem for phase I and the ship route design with ship fleet deployment problem for phase II. The problem in phase I is formulated as a mixed-integer linear programming model. By developing a hub port expanding technique, the problem in phase II is formulated as a vehicle routing problem with pickup and delivery. A Lagrangian relaxation based solution method is proposed to solve it. Numerical implementations based on the Asia–Europe–Oceania shipping services are carried out to account for the impact analysis of the maritime cabotage legislations on liner hub-and-spoke shipping network design problem.     

Ship routing and scheduling in the new millennium

We review research on ship routing and scheduling and related problems during the new millennium and provide four basic models in this domain. The volume of research in this area about doubles every decade as does the number of research outlets. We have found over a hundred new refereed papers on this topic during the last decade. Problems of wider scope have been addressed as well as more specialized ones. However, complex critical problems remain wide open and provide challenging opportunities for future research.     

Application of structural equation modeling to evaluate the intention of shippers to use Internet services in liner shipping

Operations research (OR) is the application of modeling techniques to formulate and analyze systems and problems for management decision-making. Structural equation modeling (SEM) is a modeling technique applied to social or behavioral systems to understand and explain relationships that may exist among elements of systems. Recently, the measurement of unobservable variables has gained increasing attention in operations management (OM) research, and the OR discipline has begun to recognize the value of applying SEM to analyze behavioral-related OR problems. To provide OR researchers with a better understanding of the application of this useful statistical modeling technique, this paper presents a tutorial on the application of SEM. Specifically, we investigate the key factors that affect the adoption of Internet services in the context of liner shipping services. Although [Fishbein, M.A., Ajzen, I., 1975. Belief, Attitude, Intention and Behavior: An Introduction to Theory and Research, Addison-Wesley, Reading, MA; Davis, F.D., 1989. Perceived usefulness, perceived ease of use, and user acceptance of information technology. MIS Quarterly 13 (3), 319–339; Ajzen, I., 1985. From intention to actions: A theory of planned behavior. In: Kuhl, J., Bechmann, J. (Eds.), Action Control: From Cognition to Behavior. Springer Verlag, New York, pp. 11–39; Ajzen, I., 1991. The theory of planned behavior. Organizational Behavior and Human Decision Processes 50, 179–211] have made important contributions to understanding users’ behavior of technology acceptance, shippers’ resistance to end-user systems is still a common problem in the liner shipping industry. To better predict, explain, and increase shippers’ acceptance of technology, we need to understand why shippers accept or reject Internet services provided by their liner shipping carriers. Another objective of this paper is to propose and empirically test a theoretical framework that relates the intention of shippers to use Internet services in liner shipping with its antecedents such as perceived usefulness, perceived ease of use, and the perceptions of security protection. Tests of the structural model confirm Davis’s (1989) notion that perceived ease of use explains the intention of shippers to use Internet services, and that perceived ease of use has a strong positive effect on perceived usefulness. The results also indicate that security protection influences perceived ease of use. The SEM analyses in this study offer OR researchers a methodological guide on how to assess the efficacy of both a measurement model that relates observed indicators to latent factors and a structural model that poses relationships between constructs.     

Optimal operating strategy for a long-haul liner service route

This paper proposes an optimal operating strategy problem arising in liner shipping industry that aims to determine service frequency, containership fleet deployment plan, and sailing speed for a long-haul liner service route. The problem is formulated as a mixed-integer nonlinear programming model that cannot be solved efficiently by the existing solution algorithms. In view of some unique characteristics of the liner shipping operations, this paper proposes an efficient and exact branch-and-bound based ε-optimal algorithm. In particular, a mixed-integer nonlinear model is first developed for a given service frequency and ship type; two linearization techniques are subsequently presented to approximate this model with a mixed-integer linear program; and the branch-and-bound approach controls the approximation error below a specified tolerance. This paper further demonstrates that the branch-and-bound based ε-optimal algorithm obtains a globally optimal solution with the predetermined relative optimality tolerance ε in a finite number of iterations. The case study based on an existing long-haul liner service route shows the effectiveness and efficiency of the proposed solution method.     

Designing robust liner shipping schedules: Optimizing recovery actions and buffer times

It is important for liner shipping companies to maintain cost efficient and robust liner shipping networks. Regularly, they set up pro-forma schedules, yet it is difficult to stay on time. We consider the problem of managing the delays. Therefore, we need to determine an optimal recovery policy and buffer time allocation to the ship route in order to minimize the total costs associated with delays and recovery actions, such as increasing sailing speed. We introduce a general framework consisting of a mixed integer programming formulation to solve discrete stochastic decision problems with short and long term decisions and apply this framework to the above described problem. Furthermore, we propose and test four heuristics for this problem. We compared the results of our method with an existing liner shipping route schedule and found a cost decrease of 28.9% after optimizing the buffer time distribution compared to the cost of sailing the current route schedule at constant speed.     

Liner ship fleet deployment with week-dependent container shipment demand

This paper addresses a practical liner ship fleet deployment problem with week-dependent container shipment demand and transit time constraint, namely, maximum allowable transit time in container routing between a pair of ports. It first uses the space–time network approach to generate practical container routes subject to the transit time constraints. This paper proceeds to formulate the fleet deployment problem based on the practical container routes generated. In view of the intractability of the formulation, two relaxation models providing lower bounds are built: one requires known container shipment demand at the fleet deployment stage, and the other assumes constant container shipment demand over the planning horizon. An efficient global optimization algorithm is subsequently proposed. Extensive numerical experiments on the shipping data of a global liner shipping company demonstrate the applicability of the proposed model and algorithm.     

Short-term liner ship fleet planning with container transshipment and uncertain container shipment demand

This paper proposes a short-term liner ship fleet planning problem by taking into account container transshipment and uncertain container shipment demand. Given a liner shipping service network comprising a number of ship routes, the problem is to determine the numbers and types of ships required in the fleet and assign each of these ships to a particular ship route to maximize the expected value of the total profit over a short-term planning horizon. These decisions have to be made prior to knowing the exact container shipment demand, which is affected by some unpredictable and uncontrollable factors. This paper thus formulates this realistic short-term planning problem as a two-stage stochastic integer programming model. A solution algorithm, integrating the sample average approximation with a dual decomposition and Lagrangian relaxation approach, is then proposed. Finally, a numerical example is used to evaluate the performance of the proposed model and solution algorithm.     

A mathematical model of inter-terminal transportation

We present a novel integer programming model for analyzing inter-terminal transportation (ITT) in new and expanding sea ports. ITT is the movement of containers between terminals (sea, rail or otherwise) within a port. ITT represents a significant source of delay for containers being transshipped, which costs ports money and affects a port’s reputation. Our model assists ports in analyzing the impact of new infrastructure, the placement of terminals, and ITT vehicle investments. We provide analysis of ITT at two ports, the port of Hamburg, Germany and the Maasvlakte 1 & 2 area of the port of Rotterdam, The Netherlands, in which we solve a vehicle flow combined with a multi-commodity container flow on a congestion based time–space graph to optimality. We introduce a two-step solution procedure that computes a relaxation of the overall ITT problem in order to find solutions faster. Our graph contains special structures to model the long term loading and unloading of vehicles, and our model is general enough to model a number of important real-world aspects of ITT, such as traffic congestion, penalized late container delivery, multiple ITT transportation modes, and port infrastructure modifications. We show that our model can scale to real-world sizes and provide ports with important information for their long term decision making.     

A minimax distribution-free procedure for a newsvendor problem with free shipping

In this paper, we study the optimal policies of retailers who operate their inventory with a single period model (i.e., newsvendor model) under a free shipping offer where a fixed shipping fee is exempted if an order quantity is greater than or equal to a given minimum quantity. Zhou et al. (2009) have explored this model, and we further investigate their analysis for the optimal ordering policies which they did not sufficiently develop. Based on the investigation, we extend the base model in order to deal with the practically important aspect of inventory management when the exact distribution function of demand is not available. We incorporate the aspect into the base model and present the optimal policies for the extended model with a numerical example. Finally, we conduct extensive numerical experiments to evaluate the performance of the extended model and analyze the impacts of minimum free shipping quantity and the fixed shipping fee on the performance.     

Berth allocation at indented berths for mega-containerships

This paper addresses the berth allocation problem at a multi-user container terminal with indented berths for fast handling of mega-containerships. In a previous research conducted by the authors, the berth allocation problem at a conventional form of the multi-user terminal was formulated as a nonlinear mathematical programming, where more than one ship are allowed to be moored at a specific berth if the berth and ship lengths restriction is satisfied. In this paper, we first construct a new integer linear programming formulation for easier calculation and then the formulation is extended to model the berth allocation problem at a terminal with indented berths, where both mega-containerships and feeder ships are to be served for higher berth productivity. The berth allocation problem at the indented berths is solved by genetic algorithms. A wide variety of numerical experiments were conducted and interesting findings were explored.     

A tree search procedure for the container pre-marshalling problem

In the container pre-marshalling problem (CPMP) n items are given that belong to G different item groups (g = 1, … , G) and that are piled up in up to S stacks with a maximum stack height H. A move can shift one item from one stack to another one. A sequence of moves of minimum length has to be determined that transforms the initial item distribution so that in each of the stacks the items are sorted by their group index g in descending order. The CPMP occurs frequently in container terminals of seaports. It has to be solved when export containers, piled up in stacks, are sorted in a pre-marshalling process so that they can be loaded afterwards onto a ship faster and more efficiently. This article presents a heuristic tree search procedure for the CPMP. The procedure is compared to solution approaches for the CPMP that were published so far and turns out to be very competitive. Moreover, computational results for new and difficult CPMP instances are presented.     

A heuristic for the routing and carrier selection problem

We consider the problem of simultaneously selecting customers to be served by external carriers and routing a heterogeneous internal fleet. Very little attention was devoted to this problem. A recent paper proposed a heuristic solution procedure. Our paper shows that better results can be obtained by a simple method and corrects some erroneous results presented in the previous paper.     

A targeting strategy for the deployment of a tethered satellite system

^** Email: hans.troger{at}tuwien.ac.at One of the most important operations during a tethered satellitesystem mission is the deployment of a subsatellite from a spaceship.We restrict to the simple, but practically important case thatthe system is moving on a circular Keplerian orbit around theEarth. The main problem during deployment due to the local gravitygradient vector is that due to the Coriolis acceleration thetwo satellites do not move along the straight radial relativeequilibrium position in the orbital frame. Instead, a strongdeviation from the local vertical direction occurs, which afterthe deployment process is finished results in weakly dampedlarge-amplitude oscillations, which in some cases are even transientchaotic. This chaotic dynamics will be used to steer the satellitewith small control actions into the final radial relative equilibriumposition far away from the spaceship. Both deployment time andenergy input are computed and compared to other deployment strategies.     

A Constraint Programming model for fast optimal stowage of container vessel bays

Container vessel stowage planning is a hard combinatorial optimization problem with both high economic and environmental impact. We have developed an approach that often is able to generate near-optimal plans for large container vessels within a few minutes. It decomposes the problem into a master planning phase that distributes the containers to bay sections and a slot planning phase that assigns containers of each bay section to slots. In this paper, we focus on the slot planning phase of this approach and present a Constraint Programming and Integer Programming model for stowing a set of containers in a single bay section. This so-called slot planning problem is NP-hard and often involves stowing several hundred containers. Using state-of-the-art constraint solvers and modeling techniques, however, we were able to solve 90% of 236 real instances from our industrial collaborator to optimality within 1 second. Thus, somewhat to our surprise, it is possible to solve most of these problems optimally within the time required for practical application.     

An optimization based approach for deployment of roadway incident response vehicles with reliability constraints

In recent years transportation agencies have introduced patrol based response programs to remove roadway incidents rapidly. With the evolution of technology incident detection and notification from remote traffic operation centers is possible and patrols to detect incidents are not necessary. Instead, the response units can be placed at various depots in urban areas and dispatched to incident sites upon notification. In this paper, we propose a reliability based mixed integer programming model to find best locations of incidence response depots and assign response vehicles to these depots so that incidents can be cleared efficiently at a minimum cost. The approach is unique as it considers fixed and variable costs of vehicles and depots, occurrences of major and minor incidents, and reliability of response service in the same model. Numerical results are generated for an example problem and sensitivity analysis is conducted to explore the relationships between parameters of the problem.     

Hybrid heuristics for a short sea inventory routing problem

We consider a short sea fuel oil distribution problem where an oil company is responsible for the routing and scheduling of ships between ports such that the demand for various fuel oil products is satisfied during the planning horizon. The inventory management has to be considered at the demand side only, and the consumption rates are given and assumed to be constant within the planning horizon. The objective is to determine distribution policies that minimize the routing and operating costs, while the inventory levels are maintained within their limits. We propose an arc-load flow formulation for the problem which is tightened with valid inequalities. In order to obtain good feasible solutions for planning horizons of several months, we compare different hybridization strategies. Computational results are reported for real small-size instances.