基于匹配度的流线优化问题研究
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摘要
在宏观层面的城市及区域经济活动和微观层面的制造、贸易、消费等典型社会经济活动中,仓储、加工、运输、配送、包装、装卸搬运等物流活动的组织与需求方在物品数量、到达时间、物流费用等方面的需求构成了典型的物流供需网络,本论文将由若干特定的点、线和特定的权构成的物流供需网络称为流线网络.
区别于传统物流网络,流线网络具有嵌套、多层、多级、多维、多准则等典型的超网络结构,它不仅反映了物流服务供给网络和需求网络自身的特征,还表示了物流服务供给网络与需求网络之间的关系.根据各类物流需求的网络特征,对物流的供应网络(能力和服务)进行优化,可以揭示典型物流活动的一般规律与特征,进而优化物流组织方案,满足客户需求,从而实现物流服务的本质,即用恰当的费用,在恰当的时间把恰当数量的恰当物品,经恰当的路线送到恰当的地点.
首先,分别对制造、贸易、消费、城市及区域经济中存在的典型物流活动的特征、一般流线形式和流线的特点进行分析、归纳和总结,提炼流线网络的一般结构和数学描述,建立了流线网络的结构模型.在此基础上,分析了流线网络的基本结构、退化结构和矩阵描述以及统计特征、属性特征和权值复合等基本特征.
其次,通过对物流服务供给与需求在时间、数量、费用等特征方面的分析,借鉴广义费用函数将时间、数量和费用统一当量,并给出了流线网络中节点和弧上的供需匹配度定义和数学描述,构建了供需匹配度模型.利用向量函数,将点、弧上的供需匹配向流线网络供需匹配进行了扩展.基于供需匹配度模型,构建了流线评价与选择模型,以配送中心区域设施布置为案例进行了验证.
再次,建立了一般情形下以供需匹配度为目标函数、以能力和资源限制为约束条件的流线优化模型,以及考虑效益和效率等特殊情形下的流线优化模型.借鉴变分不等式模型与最优化问题的转换关系,分别给出了无约束和有约束两种情形下的变分不等式形式,并证明了解的存在性和唯一性.基于固定步长的Korpelevich投影算法,通过改进步长规则,设计了流线优化模型的求解算法.
最后,用两个案例分别验证了流线优化模型及求解算法的可行性.案例一针对城市物流节点布局规模优化问题,应用流线网络结构模型描述了物流节点空间布局的流线网络形态,应用流线优化模型与Korpelevich投影算法,求解给出了比经验比较法更优的布局方案；案例二针对钢铁厂内物流运输组织优化问题,应用流线网络结构模型描述了厂内物流运输组织的网络形态,应用流线优化模型建立了厂内物流运输组织优化问题的数学描述,分别应用ILOG CPLEX软件、Korpelevich投影算法和流线优化模型求解算法对模型进行了求解,并对三种方法的优劣进行了比较.
研究表明,流线网络是一类复杂的超网络,具有多级、多层、多属性的特征；流线网络供需匹配度可以较好地描述物流服务供给与需求的接近程度；流线优化模型是以供需匹配度为目标函数、以资源和能力限制为约束条件的非线性规划模型,其等价变分不等式形式存在唯一解；案例说明流线优化理论与方法可以解决典型物流优化问题.
本论文提出的流线网络的结构模型为典型物流活动的描述及其优化提供了通用结构和研究平台,为描述和分析典型物流问题提供了一种新方法；建立的供需匹配度模型为理清物流供需网络的复杂关系以及各因素对物流服务供需关系的影响程度提供了一种数学分析方法；基于变分不等式的流线优化模型和求解算法为物流优化领域提供了一种新的优化方法和途径.
本论文提出的流线优化理论与方法在解决典型物流优化问题的新方法方面进行了初步尝试与探索,有利于物流学科核心理论体系的构建和理论与方法的深入研究,有利于解决区域社会经济活动中的网络分配问题、生产制造活动中的流程优化问题以及贸易和消费活动中的复杂网络配送问题,具有重要的理论和实践指导意义.
There exists a typical social economic activity which includes urban and regional economic activities in macroscopic level; manufacture, trade and consumption in microcosmic level. It is called logistics. It includes the process of storage, manufacture, transportation, distribution, package, and assembling and disassembling. The claim of quantity, arriving time and cost of the goods from both the logistics organizer and the demander construct a typical logistics supply and demand network. In this thesis, this supply and demand network is called streamline network (SLN) which consists of some specific node, string and given weight.
Different from traditional logistics network, SLN has a complex structure, which is nested, multilayer, multi-level, multi-dimension and multi-criteria. It not only reflects the characteristic of logistic supply and demand network in logistics service, but also describes the relationship between the supply and demand network in logistics service. The logistics supply network (of its ability and service) can be optimized according to the network characteristics of varied logistics demands. This optimization can reveal general rules and characteristics of typical logistics activities, optimize logistics organization plan, satisfy the customer's demand, so to realize the essence of logistics service, that is to say taking right quantity of right goods to right place in right time by right route with right cost.
Firstly, it analyzed the typical logistics activities existed in manufacture, trade, consumption, urban and regional economy summarizes its characteristics, general streamline form and distinguish figures of streamline, so to find out the general structure and mathematical definition of SLN. And then, it analyzed basic structure, degenerate structure, matrix description and the characteristics of statistic, attribute and composite weight.
Secondly, by analyzing the time, quantity and cost of the logistics supply and demand, it can borrow the general cost function to unify time, quantity and cost, so to give a definition and mathematic description of the matching degree of supply and demand in node and arc among the streamline network. It can establish a model to show matching degree of supply and demand. Through introduced vector function to analyze the node, string and matching between supply and demand in all levels, it extended the calculation formula of supply and demand matching degree from node, arc to the whole network. It can also establish a model of streamline evaluation and selection based on the model of matching degree between supply and demand, and verified it in a case as the regional installation layout in a distribution center.
Thirdly, this thesis established an optimized streamline model, with the matching degree between supply and demand as the objective function, and capacities and resource as the constraint. In the meantime, the selection and evaluation models as well as the optimized streamline model mainly guided by benefit, weak benefit and efficiency were constructed. The model was converted to a variation inequality with or without constraint by the equivalence relation between variation inequality and optimizing model. It proved that the model has a unique way of solution. According to projection algorithm, the streamline model optimization algorithm is put forward.
At last, taking the spatial distribution of the logistics nodes in one city as a sample, by using the streamline optimization theory and method to explain the streamline network model of logistics nodes'spatial distribution, it established a streamline optimization model which takes the quantity matching degree as its objective function; also proved the effectiveness and feasibility of the model because found out a better distribution scheme than experience comparative method through mathematic-solving. Another sample was the organization optimization of logistic transportation in one steel factory. Based on the sample, established a streamline optimization no-linear plan model using the matching degree of supply and demand as the objective function, and then changed it into variation inequality. Then ILOG CPLEX software, fixed step iterative algorithms and variable step iterative algorithms was used to solve this model. Comparing those three methods, it can find out their advantages and disadvantages.
The research shows, streamline is a complex super network. It is multi-level, multi-layer and multi-attribute. The matching degree of supply and demand in streamline network can describe the approaching degree of supply and demand in logistic service better. Streamline optimization model is a no-linear plan model which uses matching degree of supply and demand as objective function, resource and capability limitation as constraint condition. Its equivalent form of variation inequality has only one solution. Improved variable step iterative algorithm can be solved to streamline optimization model in inequality form. This sample proves that this algorithm is better than fixed-step iterative algorithm.
The structure model and mathematical description of streamline network can offer a general structure and a research platform for typical logistics activities, it helps to reveal the nature and rules of logistics service. The matching degree model of supply and demand provides a mathematical analysis way to reveal the complex relationship between logistics supply and demand network, and factors influence them. The streamline optimization model and algorithm based on variation inequality provide a new optimization method in the area of logistics optimization.
This research is useful for both the construction of core theoretical system in logistics and the further study of theory and method in logistics. It can also help to settle the network distributional problem in regional social economic activities, optimize the process in manufacture activities, and solve the problem concerned with complex network distribution in trade and consumption. It is significant in theoretical and practical guidance.
区别于传统物流网络,流线网络具有嵌套、多层、多级、多维、多准则等典型的超网络结构,它不仅反映了物流服务供给网络和需求网络自身的特征,还表示了物流服务供给网络与需求网络之间的关系.根据各类物流需求的网络特征,对物流的供应网络(能力和服务)进行优化,可以揭示典型物流活动的一般规律与特征,进而优化物流组织方案,满足客户需求,从而实现物流服务的本质,即用恰当的费用,在恰当的时间把恰当数量的恰当物品,经恰当的路线送到恰当的地点.
首先,分别对制造、贸易、消费、城市及区域经济中存在的典型物流活动的特征、一般流线形式和流线的特点进行分析、归纳和总结,提炼流线网络的一般结构和数学描述,建立了流线网络的结构模型.在此基础上,分析了流线网络的基本结构、退化结构和矩阵描述以及统计特征、属性特征和权值复合等基本特征.
其次,通过对物流服务供给与需求在时间、数量、费用等特征方面的分析,借鉴广义费用函数将时间、数量和费用统一当量,并给出了流线网络中节点和弧上的供需匹配度定义和数学描述,构建了供需匹配度模型.利用向量函数,将点、弧上的供需匹配向流线网络供需匹配进行了扩展.基于供需匹配度模型,构建了流线评价与选择模型,以配送中心区域设施布置为案例进行了验证.
再次,建立了一般情形下以供需匹配度为目标函数、以能力和资源限制为约束条件的流线优化模型,以及考虑效益和效率等特殊情形下的流线优化模型.借鉴变分不等式模型与最优化问题的转换关系,分别给出了无约束和有约束两种情形下的变分不等式形式,并证明了解的存在性和唯一性.基于固定步长的Korpelevich投影算法,通过改进步长规则,设计了流线优化模型的求解算法.
最后,用两个案例分别验证了流线优化模型及求解算法的可行性.案例一针对城市物流节点布局规模优化问题,应用流线网络结构模型描述了物流节点空间布局的流线网络形态,应用流线优化模型与Korpelevich投影算法,求解给出了比经验比较法更优的布局方案；案例二针对钢铁厂内物流运输组织优化问题,应用流线网络结构模型描述了厂内物流运输组织的网络形态,应用流线优化模型建立了厂内物流运输组织优化问题的数学描述,分别应用ILOG CPLEX软件、Korpelevich投影算法和流线优化模型求解算法对模型进行了求解,并对三种方法的优劣进行了比较.
研究表明,流线网络是一类复杂的超网络,具有多级、多层、多属性的特征；流线网络供需匹配度可以较好地描述物流服务供给与需求的接近程度；流线优化模型是以供需匹配度为目标函数、以资源和能力限制为约束条件的非线性规划模型,其等价变分不等式形式存在唯一解；案例说明流线优化理论与方法可以解决典型物流优化问题.
本论文提出的流线网络的结构模型为典型物流活动的描述及其优化提供了通用结构和研究平台,为描述和分析典型物流问题提供了一种新方法；建立的供需匹配度模型为理清物流供需网络的复杂关系以及各因素对物流服务供需关系的影响程度提供了一种数学分析方法；基于变分不等式的流线优化模型和求解算法为物流优化领域提供了一种新的优化方法和途径.
本论文提出的流线优化理论与方法在解决典型物流优化问题的新方法方面进行了初步尝试与探索,有利于物流学科核心理论体系的构建和理论与方法的深入研究,有利于解决区域社会经济活动中的网络分配问题、生产制造活动中的流程优化问题以及贸易和消费活动中的复杂网络配送问题,具有重要的理论和实践指导意义.
There exists a typical social economic activity which includes urban and regional economic activities in macroscopic level; manufacture, trade and consumption in microcosmic level. It is called logistics. It includes the process of storage, manufacture, transportation, distribution, package, and assembling and disassembling. The claim of quantity, arriving time and cost of the goods from both the logistics organizer and the demander construct a typical logistics supply and demand network. In this thesis, this supply and demand network is called streamline network (SLN) which consists of some specific node, string and given weight.
Different from traditional logistics network, SLN has a complex structure, which is nested, multilayer, multi-level, multi-dimension and multi-criteria. It not only reflects the characteristic of logistic supply and demand network in logistics service, but also describes the relationship between the supply and demand network in logistics service. The logistics supply network (of its ability and service) can be optimized according to the network characteristics of varied logistics demands. This optimization can reveal general rules and characteristics of typical logistics activities, optimize logistics organization plan, satisfy the customer's demand, so to realize the essence of logistics service, that is to say taking right quantity of right goods to right place in right time by right route with right cost.
Firstly, it analyzed the typical logistics activities existed in manufacture, trade, consumption, urban and regional economy summarizes its characteristics, general streamline form and distinguish figures of streamline, so to find out the general structure and mathematical definition of SLN. And then, it analyzed basic structure, degenerate structure, matrix description and the characteristics of statistic, attribute and composite weight.
Secondly, by analyzing the time, quantity and cost of the logistics supply and demand, it can borrow the general cost function to unify time, quantity and cost, so to give a definition and mathematic description of the matching degree of supply and demand in node and arc among the streamline network. It can establish a model to show matching degree of supply and demand. Through introduced vector function to analyze the node, string and matching between supply and demand in all levels, it extended the calculation formula of supply and demand matching degree from node, arc to the whole network. It can also establish a model of streamline evaluation and selection based on the model of matching degree between supply and demand, and verified it in a case as the regional installation layout in a distribution center.
Thirdly, this thesis established an optimized streamline model, with the matching degree between supply and demand as the objective function, and capacities and resource as the constraint. In the meantime, the selection and evaluation models as well as the optimized streamline model mainly guided by benefit, weak benefit and efficiency were constructed. The model was converted to a variation inequality with or without constraint by the equivalence relation between variation inequality and optimizing model. It proved that the model has a unique way of solution. According to projection algorithm, the streamline model optimization algorithm is put forward.
At last, taking the spatial distribution of the logistics nodes in one city as a sample, by using the streamline optimization theory and method to explain the streamline network model of logistics nodes'spatial distribution, it established a streamline optimization model which takes the quantity matching degree as its objective function; also proved the effectiveness and feasibility of the model because found out a better distribution scheme than experience comparative method through mathematic-solving. Another sample was the organization optimization of logistic transportation in one steel factory. Based on the sample, established a streamline optimization no-linear plan model using the matching degree of supply and demand as the objective function, and then changed it into variation inequality. Then ILOG CPLEX software, fixed step iterative algorithms and variable step iterative algorithms was used to solve this model. Comparing those three methods, it can find out their advantages and disadvantages.
The research shows, streamline is a complex super network. It is multi-level, multi-layer and multi-attribute. The matching degree of supply and demand in streamline network can describe the approaching degree of supply and demand in logistic service better. Streamline optimization model is a no-linear plan model which uses matching degree of supply and demand as objective function, resource and capability limitation as constraint condition. Its equivalent form of variation inequality has only one solution. Improved variable step iterative algorithm can be solved to streamline optimization model in inequality form. This sample proves that this algorithm is better than fixed-step iterative algorithm.
The structure model and mathematical description of streamline network can offer a general structure and a research platform for typical logistics activities, it helps to reveal the nature and rules of logistics service. The matching degree model of supply and demand provides a mathematical analysis way to reveal the complex relationship between logistics supply and demand network, and factors influence them. The streamline optimization model and algorithm based on variation inequality provide a new optimization method in the area of logistics optimization.
This research is useful for both the construction of core theoretical system in logistics and the further study of theory and method in logistics. It can also help to settle the network distributional problem in regional social economic activities, optimize the process in manufacture activities, and solve the problem concerned with complex network distribution in trade and consumption. It is significant in theoretical and practical guidance.
引文
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