船队规划数学建模与算法研究
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摘要
船队规划是航运企业发展战略中的一项重要决策,是决定企业能否长期生存发展的关键问题。随着世界航运规模的不断扩大,这项研究工作的重要性显得格外突出。针对船队规划问题,本文系统地归纳和评述了大量的相关文献,发现目前对于复杂情况下多航线、多型船、大规模的船队规划研究仍不是很理想；对于班轮运输的船队规划研究较为缺乏；对于不确定条件下的船队规划研究刚刚起步。因此,船队规划的研究工作需要进一步改进和完善。围绕上述问题,本文主要进行了以下几方面的研究工作：
(1)建立了复杂市场环境下多种类型投资的船队规划数学模型,将船舶投资、更新、配线和运用规模等决策同时进行优化。在此基础上,考虑了船舶航速变化对规划决策产生的非线性影响,建立了船队规划的非线性模型,并设计了求解此类问题的混合粒子群优化算法。
(2)研究了多港口挂靠直达航线和干、支线结合分程运输航线的班轮船队规划问题,建立了同一航线上配置相同船型和同一航线上配置多种船型两种情况下的船队规划数学模型。考虑到模型的求解复杂性,提出了原模型的改进模型,同时设计了拉格朗日松弛启发式混合求解算法。
(3)针对变动的实际营运环境,研究了不确定条件下的船队规划决策问题。通过引入基于情景分析的鲁棒优化方法,采用具有已知概率的情景集合描述市场需求的不确定性,建立了需求不确定条件下船队规划的鲁棒优化模型。通过算例分析,证明了鲁棒优化模型的有效性。
(4)以某大型航运企业船队为例进行分析,利用Benders分解算法对在多航线复杂情况下,由多种类型船舶构成的大规模船队规划问题进行求解,验证所提出的模型及算法对于大规模实际问题的应用效果。
The fleet planning, as an important decision in the development strategies, determines the survival and the long-term development of the shipping companies. With the constant expansion of the world's shipping scale, importance of the research on the fleet planning is becoming more and more obvious. Through reviewing and summarying lots of literature on fleet planning, we found that the solutions to the large-scale, multi-route, multi-ship fleet planning problems in complex situation is still not very satisfying, relatively little work has been done in the liner fleet planning, and the research on fleet planning under uncertainty has taken the initial step at present. So the research on fleet planning needs to be further improved. Based on the above problems, the main studies in this paper are as follows:
(1) A mathematical model of fleet planning with multimode investment in complex market environments is established, which can optimize the decisions on ship investment, updating, routing and fleet size simultaneously. In consideration of the nonlinear influence to the decision-making caused by the ship speed changing on this basis, a nonlinear model for fleet planning is established, and a hybrid particle swarm optimization algorithm is developed to solve the nonlinear model.
(2) Two type of fleet planning problems of multi-call liners and trunk line and feeder system are researched. Mathematical models are presented respectively to optimize liner fleet planning problems in the two cases that the same type or variety types of ships are deployed on the same route. Taking the complexity of solving these models into account, the original model is further improved and a Lagrangian relaxation heuristic algorithm is designed.
(3) In view of the varying actual operating environments, decision-making problems of fleet planning under uncertainty are researched. by introducing the robust optimization approach based on scenario analysis and by using a scenario set with given probability to describe the uncertainty of market demands, a robust optimization model for fleet planning under demand uncertainty is established. The effectiveness of this robust model is demonstrated by a calculation example.
(4) A large shipping company is used as an example to make an empirical analysis. The large-scale, multi-route, multi-ship fleet planning problem in complex situations is solved by using of Benders decomposition algorithm to test and verify the application effect of the new proposed models and algorithms to large-scale practical problems.
(1)建立了复杂市场环境下多种类型投资的船队规划数学模型,将船舶投资、更新、配线和运用规模等决策同时进行优化。在此基础上,考虑了船舶航速变化对规划决策产生的非线性影响,建立了船队规划的非线性模型,并设计了求解此类问题的混合粒子群优化算法。
(2)研究了多港口挂靠直达航线和干、支线结合分程运输航线的班轮船队规划问题,建立了同一航线上配置相同船型和同一航线上配置多种船型两种情况下的船队规划数学模型。考虑到模型的求解复杂性,提出了原模型的改进模型,同时设计了拉格朗日松弛启发式混合求解算法。
(3)针对变动的实际营运环境,研究了不确定条件下的船队规划决策问题。通过引入基于情景分析的鲁棒优化方法,采用具有已知概率的情景集合描述市场需求的不确定性,建立了需求不确定条件下船队规划的鲁棒优化模型。通过算例分析,证明了鲁棒优化模型的有效性。
(4)以某大型航运企业船队为例进行分析,利用Benders分解算法对在多航线复杂情况下,由多种类型船舶构成的大规模船队规划问题进行求解,验证所提出的模型及算法对于大规模实际问题的应用效果。
The fleet planning, as an important decision in the development strategies, determines the survival and the long-term development of the shipping companies. With the constant expansion of the world's shipping scale, importance of the research on the fleet planning is becoming more and more obvious. Through reviewing and summarying lots of literature on fleet planning, we found that the solutions to the large-scale, multi-route, multi-ship fleet planning problems in complex situation is still not very satisfying, relatively little work has been done in the liner fleet planning, and the research on fleet planning under uncertainty has taken the initial step at present. So the research on fleet planning needs to be further improved. Based on the above problems, the main studies in this paper are as follows:
(1) A mathematical model of fleet planning with multimode investment in complex market environments is established, which can optimize the decisions on ship investment, updating, routing and fleet size simultaneously. In consideration of the nonlinear influence to the decision-making caused by the ship speed changing on this basis, a nonlinear model for fleet planning is established, and a hybrid particle swarm optimization algorithm is developed to solve the nonlinear model.
(2) Two type of fleet planning problems of multi-call liners and trunk line and feeder system are researched. Mathematical models are presented respectively to optimize liner fleet planning problems in the two cases that the same type or variety types of ships are deployed on the same route. Taking the complexity of solving these models into account, the original model is further improved and a Lagrangian relaxation heuristic algorithm is designed.
(3) In view of the varying actual operating environments, decision-making problems of fleet planning under uncertainty are researched. by introducing the robust optimization approach based on scenario analysis and by using a scenario set with given probability to describe the uncertainty of market demands, a robust optimization model for fleet planning under demand uncertainty is established. The effectiveness of this robust model is demonstrated by a calculation example.
(4) A large shipping company is used as an example to make an empirical analysis. The large-scale, multi-route, multi-ship fleet planning problem in complex situations is solved by using of Benders decomposition algorithm to test and verify the application effect of the new proposed models and algorithms to large-scale practical problems.
引文
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