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 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.     

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.     

A dynamic model and algorithm for fleet planning

By analysing the merits and demerits of the existing linear model for fleet planning, this paper presents an algorithm which combines the linear programming technique with that of dynamic programming to improve the solution to linear model for fleet planning. This new approach has not only the merits that the linear model for fleet planning has, but also the merit of saving computing time. The numbers of ships newly added into the fleet every year are always integers in the final optimal solution. The last feature of the solution directly meets the requirements of practical application. Both the mathematical model of the dynamic fleet planning and its algorithm are put forward in this paper. A calculating example is also given.     

新建船队的船队优化模型建立和比较

船队规划问题通常是通过建立连续变量线性规划模型或混合整数线性规划模型来解决,但往往会得到要求一艘船营运于多条航线的结果。而企业出于安全因素和便于管理的角度考虑,希望船队单船个体的航线能固定,这就需要采用整数规划模型来解决此类问题。针对新建船队的整体配置规划问题,在建立连续变量线性规划模型和混合整数线性规划模型的基础上,探索并建立线性整数规划模型和非线性整数规划模型并进行优化。通过对计算实例的分析比较,论述了4种优化数学模型的特点与适用范围。     

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。     

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。     

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 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.     

高速客运船队规划模型构建及应用

针对高速客运的特点,在现有船队规划线性模型基础上,构建引入船舶更新的高速客运船队规划非线性模型,对该模型求解方法进行探讨,实例验证该模型的可行性和有效性。     

Fleet deployment optimization models.Part 2

The fleet deployment problem for the one origin,one destination fixed-price contract requiring the transport of a given total amount of cargo within a given period is formulated and solved for the case that one or more cost components are given staircase functions of time. A computer program has been developed to implement the solution of this problem. The fleet deployment problem with one or more costs being random variables with known probability density functions is also formulated. Analytical expressions for hte basic probabilistic quantities, i.e the probability density function,the mean and the variance of the total operating cost, are presented. Finally, sample results are presented and discussed and some extensions for further research are suggested.     

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.     

Estimation of CO2 reduction for Japanese domestic container transportation based on mathematical models

This research discusses domestic feeder container transportation connected with international trades in Japan. Optimal round trip courses of container ship fleet from the perspective of CO₂ emission reduction are calculated and analyzed to obtain basic knowledge about CO₂ emission reduction in the container feeder transportation system. Specifically, based on the weekly origin–destination (OD) data at a hub port (Kobe) and other related transportation data, the ship routes are designed by employing a mathematical modeling approach. First, a mixed integer programming model is formulated and solved by using an optimization software that employs branch and bound algorithm. The objective function of the model is to minimize the CO₂ emission subject to necessary (and partially simplified) constraints. The model is then tested on various types of ships with different speed and capacity. Moreover, it is also tested on various waiting times at hub port to investigate the effect in CO₂ emission of the designated fleet. Both the assessment method of container feeder transportation and the transportation’s basic insights in view of CO₂ emission are shown through the analysis.     

集装箱船舶大型化对中国班轮运输的影响

通过竞争情报分析提供了各班轮公司未来船队结构和运力的变化趋势,由此观察到各班轮公司为了降低自身的营运成本,在最近几年大量订购超巴拿马型甚至更大型的集装箱船舶参与运输,但是却不能达到其预期的规模效应。原因就在于相当一部分成本随着船型的增大而线性增加,规模不经济。我们探讨了中国的班轮运输市场的几个重要特点:中外贸易的不平衡导致了货源的不平衡;未来贸易结构的调整会影响航线的布局和调派;贸易上的不稳定因素使班轮公司遇到外在的风险。这些特点会深远地影响集装箱船舶大型化的经济受益,相反的,集装箱船舶大型化的趋势也会加剧这些负面的影响,危及整个班轮运输市场。     

Methodology for ro-ro ship and fleet sizing with application to short sea shipping

A novel methodology is developed for determining the characteristics of a cargo roll-on/roll-off (ro-ro) ship and the fleet size required for a given short sea shipping route. The ship and required fleet size to satisfy the transportation demand (for each pair of speed and freight rate) are determined using a database of existing cargo ro-ro ships to obtain the main technical characteristics of the most suitable ship. The time charter, voyage costs and revenue are then calculated considering the technical characteristics of each ship. Fuel costs are corrected for the actual ship speed and loading condition. A number of restrictions in the transportation problem are considered leading to the exclusion of unfeasible solutions. The maximum profit over the period of a year is identified among the feasible pairs of speed and freight rate. This general methodology is applied in a case study that considers the route between Leixões (Portugal) and Rotterdam (Netherlands). The study allows the identification of the most suitable ship and fleet sizes for different market penetration levels and quantifies the impact on shipping company profit of changes in parameters such as fuel costs, time charter costs, emission control area, installed propulsion power and stacking factor.     

编队防空导弹攻击火力分配优化模型

海上兵力优化分配是编队防空作战中的重要问题。利用对策论和线性规划等理论和方法，研究了编队防空导弹兵力分配问题，建立了舰艇编队防空突击概率模型、编队防空导弹兵力分配优化模型及其解法。给出了一个实例，并用线性规划方法得到了最优混合策略。此方法为舰艇编队防空导弹部署优化提供了一个基本思路。     

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.     

Leadership and Commitment in the Royal Navy ☆

What is proposed here is a relatively simple procedure by which a fleet manager may select the best mix of ships to provide a given transport service. The method is confined to non-liner trades and assumes the availability of more than enough suitable ships. It further assumes that unneeded ships can be placed in idle status (or returned to owner if chartered in) without penalty.

The objective of the procedure is to select the mix of available ships and sea speeds that can perform the required service at maximum profitability to the owner.     

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.