Fleet deployment optimization models. Part 1

The problem of minimum-cost operation of a fleet of ships that has to carry a specific amount of cargo between two ports in a given time period for a specific, fixed contract price is studied. Detailed and realistic operating cost functions are developed. Sensitivity analyses are performed to study the effects of small or large changes in one or more cost components on the total costs. A realistic model for the annual transport capacity as a function of speed is also used, in contrast with the linear relation most often used in the literature. The full load and ballast speeds for those ships of the fleet that we operate are selected to minimize the total fleet operating costs including lay-up costs for unused vessels, using nonlinear optimization algorithms.     

Fleet deployment optimization for liner shipping Part 2. Implementation and results

We use linear programming (LP) for solving the problem of the optimal deployment of an existing fleet of multipurpose or fully containerized ships, among a given set of routes, including information for lay-up time, if any, and type and number of extra ships to charter, based on a detailed and realistic model for the calculation of the operating costs of all the ship types in every route and on a suitable LP formulation developed in earlier work of the authors. The optimization model is also applicable to the problem of finding the best fleet compostion and deployment, in a given set of trade routes, which may be the case when a shipping company is considering new or modified services, or a renewal of the existing fleet. In addition, two promising mixed linear-integer programming formulations are suggested.     

Designing optimal routes in a liner shipping problem

A real liner shipping problem of deciding optimal weekly routes for a given fleet of ships is considered and a solution method for solving the problem is proposed. First, all feasible routes for each ship are generated together with the cost and the duration for each route. The routes are given as input to an integer programming (IP) problem. By solving the IP problem, routes for each ship are selected such that total transportation costs are minimized and the demand at each port is satisfied. The total duration for the routes that are selected for a given ship must not exceed one week.

The real liner shipping problem is solved together with four randomly generated test problems. The computational results show that proposed solution method is suitable for designing optimal routes in several liner shipping problems.     

Designing optimal routes in a liner shipping problem

A real liner shipping problem of deciding optimal weekly routes for a given fleet of ships is considered and a solution method for solving the problem is proposed. First, all feasible routes for each ship are generated together with the cost and the duration for each route. The routes are given as input to an integer programming (IP) problem. By solving the IP problem, routes for each ship are selected such that total transportation costs are minimized and the demand at each port is satisfied. The total duration for the routes that are selected for a given ship must not exceed one week.

The real liner shipping problem is solved together with four randomly generated test problems. The computational results show that proposed solution method is suitable for designing optimal routes in several liner shipping problems.     

Fleet deployment optimization for liner shipping Part 1. Background, problem formulation and solution approaches

The background and the literature in liner fleet scheduling is reviewed and the objectives and assumptions of our approach are explained. We develop a detailed and realistic model for the estimation of the operating costs of liner ships on various routes, and present a linear programming formulation for the liner fleet deployment problem. Independent approaches for fixing both the service frequencies in the different routes and the speeds of the ships, are presented.     

Fleet deployment in liner shipping: a case study

The fleet deployment problem is an important planning problem in liner shipping. It deals with optimally assigning voyages to available vessels in the fleet and determining vessel routes and schedules in a way that minimizes costs or maximizes profit. This paper presents a new model for a fleet deployment problem in liner shipping, and we also propose a multi-start local search heuristic to solve the problem. The heuristic has been embedded in a prototype decision support system (DSS) that has been implemented and tested at Höegh Autoliners, a major global provider of ro-ro (roll-on roll-off) vehicle transportation services. The heuristic was able to produce high-quality solutions within a few minutes to a real planning problem with more than 55 vessels and 150 voyages over a planning horizon of 4–6 months. Tests indicated that the solutions suggested by the DSS gave between 2 and 10% improvements compared with solutions from manual planning. What is almost equally important is that using the DSS can ease the planning process.     

Fleet deployment optimization for liner shipping: an integer programming model

Extending and improving an earlier work of the second author, an Integer Programming (IP) model is developed to minimize the operating and lay-up costs for a fleet of liner ships operating on various routes. The IP model determines the optimal deployment of an existing fleet, given route, service, charter, and compatibility constraints. Two examples are worked with extensive actual data provided by Flota Mercante Grancolombiana (FMG). The optimal deployment is solved for their existing ship and service requirements and results and conclusions are given.     

A combined tramp ship routing,fleet deployment,and network design problem

In this paper, a tramp ship routing model of fleet deployment in a hub-and-spoke network is presented. This model simultaneously determines the selection of hubs, the assignment of spokes to hubs, the deployment of feeder-containerships as well as containership routing between spokes and spokes, hubs and spokes, and hubs and hubs. Even though some parts have been studied, this complex combination of shipping problems has never been addressed. Because the problem is NP-hard, a genetic algorithm (GA) with local search is proposed. In the algorithm, a cut-off procedure is applied to fleet deployment in a sub-route strategy. A number of randomly generated problem instances are solved by both a mathematical program and the GA with local search. A simple but realistic heuristic algorithm is also developed. Both the GA with local search and the heuristic algorithm are used to solve a number of real case instances. A comparison of the results shows the efficiency of the GA with local search. The developed model can be used as a route-decision support tool for shipping companies that provide long-haul shipping services in a hub-and-spoke network.     

编队作战需求下舰船修理周期结构的优化

舰船全寿命期内的部署和修理活动需要在其修理周期结构的指导下进行,而编队的使用则需要编队内各舰艇的修理周期结构的相互配合,从而使编队拥有更高的部署能力。文章建立了编队修理周期结构的优化模型,考虑了同一舰级下舰艇相互代替使用的情况,更能真实反映编队的部署和修理情况,采用遗传算法对编队的部署能力进行优化分析,实例证明优化后可以显著提高编队的部署能力,为进一步研究编队的部署维修奠定了基础,同时在单舰的修理周期结构上加上了编队使用需求这一约束条件,拓展了研究舰船修理周期结构的思路。     

Strategic fleet size planning for maritime refrigerated containers

In the present economic climate, it is often the case that profits can only be improved, or for that matter maintained, by improving efficiency and cutting costs. This is particularly notorious in the shipping business, where it has been seen that the competition is getting tougher among carriers, thus alliances and partnerships are resulting for cost effective services in recent years. In this scenario, effective planning methods are important not only for strategic but also operating tasks, covering their entire transportation systems. Container fleet size planning is an important part of the strategy of any shipping line. This paper addresses the problem of fleet size planning for refrigerated containers, to achieve cost-effective services in a competitive maritime shipping market. An analytical model is first discussed to determine the optimal size of an own dry container fleet. Then, this is extended for an own refrigerated container fleet, which is the case when an extremely unbalanced trade represents one of the major investment decisions to be taken by liner operators. Next, a simulation model is developed for fleet sizing in a more practical situation and, by using this, various scenarios are analysed to determine the most convenient composition of refrigerated fleet between own and leased containers for the transpacific cargo trade.     

Future cost scenarios for reduction of ship CO2 emissions

International shipping is a significant contributor to Global Greenhouse Gas (GHG) emissions, responsible for approximately 3% of global CO₂ emissions. The International Maritime Organization is currently working to establish GHG regulations for international shipping and a cost effectiveness approach has been suggested to determine the required emission reductions from shipping. To achieve emission reductions in a cost effective manner, this study has assessed the cost and reduction potential for present and future abatement measures based on new and unpublished data. The model used captures the world fleet up to 2030, and the analysis includes 25 separate measures. A new integrated modelling approach has been used combining fleet projections with activity-based CO₂ emission modelling and projected development of measures for CO₂ emission reduction. The world fleet projections up to 2030 are constructed using a fleet growth model that takes into account assumed ship type specific scrapping and new building rates. A baseline trajectory for CO₂ emission is then established. The reduction potential from the baseline trajectory and the associated marginal cost levels are calculated for 25 different emission reduction measures. The results are given as marginal abatement cost curves, and as future cost scenarios for reduction of world fleet CO₂ emissions. The results show that a scenario in which CO₂ emissions are reduced by 33% from baseline in 2030 is achievable at a marginal cost of USD 0 per tonne reduced. At this cost level, emission in 2010 can be reduced by 19% and by 24% in 2020. A scenario with 49% reduction from baseline in 2030 can be achieved at a marginal cost of USD 100 per tonne (27% in 2010 and 35% in 2020). Furthermore, it is evident that further increasing the cost level beyond USD 100 per tonne yield very little in terms of further emission reduction. The results also indicate that stabilising fleet emissions at current levels is obtainable at moderate costs, compensating for fleet growth up to 2030. However, significant reductions beyond current levels seem difficult to achieve. Marginal abatement costs for the major ship types are also calculated, and the results are shown to be relatively homogenous for all major ship types. The presented data and methodology could be very useful for assisting the industry and policymakers in selecting cost effective solutions for reducing GHG emissions from the world fleet.     

Optimal reefer slot conversion for container freight transportation

Given a fleet of container ships of varying capacity, a cost-efficient approach for improving fleet utilization and reducing the number of delayed containers is to optimize the sequence of container ships in a given string, a problem which belongs to the large ship-deployment class. A string sequence with ‘uniformly’ distributed ship capacity is more likely to accommodate a random container shipment demand. The number of one’s total ship slots acts as a gauge of the capacity of the container ships. Meanwhile, there are two types of ship slots: dry slots and reefer slots. A dry slot only accommodates a dry container, while a reefer slot can accommodate either a dry or a reefer container. The numbers of dry and reefer slots for ships in a string are different. Therefore, in this study, we propose a model that considers both dry and reefer slots and use it to elucidate the optimal ship-deployment sequence. The objective is to minimize the delay of dry and reefer containers when the demand is uncertain. Furthermore, based on the optimal sequence deduced, the study also investigates the need to convert some dry slots to reefer slots for the container ships.     

Multi-period liner ship fleet planning with dependent uncertain container shipment demand

This paper deals with a realistic multi-period liner ship fleet planning problem by incorporating stochastic dependency of the random and period-dependent container shipment demand. This problem is formulated as a multi-period stochastic programming model with a sequence of interrelated two-stage stochastic programming (2SSP) problems characterized ship fleet planning in each single period. A solution method integrating dual decomposition and Lagrangian relaxation method is designed for solving the developed model. Numerical experiments are carried out to assess applicability and performance of the proposed model and solution algorithm. The results further demonstrate importance of stochastic dependence of the uncertain container shipment demand.     

基于遗传算法的编队条件下舰船修理周期结构优化

舰船的部署和修理活动在全寿命期内是按其修理周期结构进行,而编队的使用则需要编队内各舰艇的修理周期结构的相互配合,通过组合优化各舰艇的修理周期结构,可以使编队拥有更多的部署时间。在舰船修理周期结构的定量描述模型基础上,构建了编队的修理调度模型,并采用遗传算法对编队的部署能力进行了优化分析。实例分析结果表明:优化后编队的部署时间可达到近110个月,相对于未优化前提高了50个月。     

船舶动态信息采集与传输关键技术研究

现代化智能型的船舶运输控制系统包括船舶信息管理与控制、船舶动态信息采集与传输、船队运行综合调度等三大模块。船舶动态信息采集与传输是该系统的关键部分。首先介绍船舶动态管理系统选用的软件,系统的特点和功能,并解析系统的结构。着重详尽描述船舶动态信息传输的工作原理和过程。最后介绍船舶管理信息系统及其船舶动态调度的情况。本研究成果为实施船舶的有效调度管理,为实现船岸一体化控制管理奠定基础。     

An analysis of decision-making processes in multicultural maritime scenarios

This paper presents a simple formulation in the form of a pipe network for modelling the global container-shipping network. The cost-efficiency and movement-patterns of the current container-shipping network have been investigated using heuristic methods. The model is able to reproduce the overall incomes, costs, and container movement patterns for the industry as well as for the individual shipping lines and ports. It was found that the cost of repositioning empties is 27% of the total world fleet running cost and that overcapacity continues to be a problem. The model is computationally efficient. Implemented in the Java language, it takes one minute to run a full-scale network on a Pentium IV computer.     

On cost-efficiency of the global container shipping network

This paper presents a simple formulation in the form of a pipe network for modelling the global container-shipping network. The cost-efficiency and movement-patterns of the current container-shipping network have been investigated using heuristic methods. The model is able to reproduce the overall incomes, costs, and container movement patterns for the industry as well as for the individual shipping lines and ports. It was found that the cost of repositioning empties is 27% of the total world fleet running cost and that overcapacity continues to be a problem. The model is computationally efficient. Implemented in the Java language, it takes one minute to run a full-scale network on a Pentium IV computer.     

The argument for twin screw tankers

According to the CTX tanker casualty database, machinery failures are an important cause of tanker oil spillage. This paper argues that the current large (over 10,000 deadweight) tanker fleet is experiencing at least two full losses of power or steering per day, and probably more than ten. If this fleet were twin screw, properly implemented, this number would be cut by a factor of one thousand. At the same time, tanker low speed maneuverability would be improved dramatically. All this could be done for a net cost of less than that of the double hull.     

基于信息熵的编队反潜作战信息质量评估方法研究

由于传统方法难以分析比较舰艇编队反潜信息质量,文章采用信息熵的计算方法,依据编队反潜作战实际,建立了编队反潜作战信息质量评估模型,并以此为基础,提出建立编队反潜作战信息质量评估数据库,通过检索快速获取当前态势和时间下编队反潜作战信息质量,为舰艇编队反潜作战信息质量和效能研究提供了有益思路,并为作战指挥快速决策提供了有利依据。     

Marginal and total exceedance probabilities of environmental contours

Various methods have been proposed for defining an environmental contour, based on different concepts of exceedance probability. In the inverse first-order reliability method (IFORM) and the direct sampling (DS) method, contours are defined in terms of exceedances within a region bounded by a hyperplane in either standard normal space or the original parameter space, corresponding to marginal exceedance probabilities under rotations of the coordinate system. In contrast, the more recent inverse second-order reliability method (ISORM) and highest density (HD) contours are defined in terms of an isodensity contour of the joint density function in either standard normal space or the original parameter space, where an exceedance is defined to be anywhere outside the contour. Contours defined in terms of the total probability outside the contour are significantly more conservative than contours defined in terms of marginal exceedance probabilities. In this work we study the relationship between the marginal exceedance probability of the maximum value of each variable along an environmental contour and the total probability outside the contour. The marginal exceedance probability of the contour maximum can be orders of magnitude lower than the total exceedance probability of the contour, with the differences increasing with the number of variables. For example, a 50-year ISORM contour for two variables at 3-h time steps, passes through points with marginal return periods of 635 years, and the marginal return periods increase to 10,950 years for contours of four variables. It is shown that the ratios of marginal to total exceedance probabilities for DS contours are similar to those for IFORM contours. However, the marginal exceedance probabilities of the maximum values of each variable along an HD contour are not in fixed relation to the contour exceedance probability, but depend on the shape of the joint density function. Examples are presented to illustrate the impact of the choice of contour on simple structural reliability problems for cases where the use of contours defined in terms of either marginal or total exceedance probabilities may be appropriate. The examples highlight that to choose an appropriate contour method, some understanding about the shape of a structure's failure surface is required.