基于变权的多目标物流网络流量分配问题研究
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摘要
物流网络的效率和效益直接取决于网络的拓扑结构以及网络中各物流节点和运输线路的流量分配情况。物流网络拓扑结构一旦确定,将在相当长的一段时间内不会发生变化,而物流网络中流量的分配则会受到供给、需求、网络能力等诸多因素的影响。在实际应用中,物流网络的每个物流节点和运输线路都与多个评价准则有关,在进行物流网络流量分配时,往往不仅需要考虑物流成本,还应考虑货物的运送时间、运送距离、网络的可靠性等其他因素。因此,如何在具有固定拓扑结构的物流网络中实现科学合理地流量分配,在满足货物从供应地到需求地的运输、存储和配送等物流需求的前提下获得多个目标整体最优的物流网络流量分配方案是一个值得深入研究的重要问题。
本论文在回顾总结已有的相关研究的基础上,对多对多二级物流网络的多目标流量分配问题进行了研究。本论文所做的主要工作如下：
1.物流网络变权方法。针对物流网络流量分配的目标多样性、决策过程中决策者偏好的局限性和不确定性,提出了物流网络变权方法,包括物流网络的因素(物流节点、运输线路、子路径和路径)表示方法以及它们的变权状态值计算方法。首先,通过隶属度函数对优化目标函数值进行评价；然后,利用基于决策者偏好的状态变权函数以及变权综合方法将目标评价值分阶段地集成为物流节点、运输线路、子路径和路径的状态值,路径的状态值是进行最优路径选择的依据；最后,提出了基于物流网络变权方法的流量分配方法。
2.中间节点无供应能力的多目标物流网络流量分配问题。针对具有固定拓扑结构的多对多二级物流网络,分别对运输线路的容量确定和随机变化两种情况,以物流节点和运输线路的容量为约束,以物流成本(考虑规模经济效应,将物流成本定义为流量的凹函数)最小、最长单程运送时间最短以及网络使用率(容量确定)或网络的容量可靠性(容量随机)最高为优化目标,寻求最优的物流网络流量分配方案。首先,建立了上述两种情况下问题的数学模型；然后,考虑到多目标物流网络流量分配问题属于NP-难问题,网络路径的数量会随着网络规模的扩大成指数增长,设计了基于物流网络变权方法的遗传算法作为问题模型的求解算法；最后,通过算例验证了求解方法的有效性。
3.中间节点有供应能力的多目标物流网络流量分配问题。在第2部分研究工作的基础上,增加了对物流网络中间节点供应能力的考虑。分别考虑物流节点和运输线路的容量确定以及运输线路、中间节点和供应节点的容量随机变化两种情况,以物流节点和运输线路容量为约束,以物流成本最小、最长单程运送时间最短以及网络使用率(容量确定)或网络的容量可靠性(容量随机)最高为优化目标,寻求最优的物流网络流量分配方案。首先,建立了上述两种情况下问题的数学模型；然后,提出了模型的求解方法,将物流网络分解为上下两级网络分别进行求解,每级物流网络再分解为若干个多对一子网络,每个子网络的流量分配通过基于物流网络变权方法的流量分配方法实现,再采用动态规划方法依次完成下级和上级物流网络的流量分配；最后,通过算例验证了求解方法的有效性。
The efficiency and effectiveness of logistics network are directly dependent on the network topology and the allocation method of flow in logistics nodes and transportation lines of the network. Once the logistics network topology is formed, it will not be changed in quite a long period of time. However, the flow allocation method for logistics network will be influenced by supply, demand, network capacity and many other factors. In practical application, every node or line of the logistics is related to many evaluation criterias. When allocating freight flow in logsitics network, cost is not the only consideration, other fators such as transport time, distance and reliability should be also considered. Therefore, in order to meet the need of freights'transportation, storage and delivery from suppliers to the customers and obtain the maximum efficiency and benefit of the logistics network, how to allocate the flow in the logistics networks with fixed topology scientifically and rationally is an important issue worthy of depth study.
On the basis of the review of existing researches, the problems of flow allocation in a tow level logistics network with many to many structure are studied in this dissertation, and the main contents of the dissertation are as follows:
1. Variable weight method for logistics network is proposed. Aiming at the diversity of optimization objective, the limitations and uncertainty of the decision makers'preferences about the problem of flow allocation in logistics network, a logistics network variable weight method is proposed, including representation for the factors of logistics network, such as logistics nodes, transportation lines, sub-paths and paths, and calculation method for their variable weight state values. First of all, values of optimization objective functions are evaluated by membership function; then, using state variable weight function which has considered the decision makers'preferences and variable weight sum method, the state values of logistics nodes, transportation lines, sub-paths and paths are obtained by integrating all of objective evaluations in stages, and operation of choosing the best path is in accordance with the state values of all paths; finally, the method for flow allocation which based on the logistics network variable weight method is proposed.
2. Multi-objective optimization problems for flow allocation in logistics network of which intermediate nodes has no supply capability are studied. For a two level logistics network with fixed many to many topology, aiming at the two situations that capacity of transportation lines are certain and stochastic, the problem of flow allocation is studied based on the constraints of transportation lines'and logistics nodes'capacity with the minimum logistics cost which is defined as a concave function because of the consideration of economics of scale, the minimum maximal delivery time for single path and the maximum logistics network's utilization ratio when capacity is certain or the maximum logistics network's reliability when capacity is stochastic as optimal objectives. Firstly, the mathematical models of the problem in both cases are built; and then, due to multi-objective optimization problem for flow allocation in logistics network is belong to NP-hard problem, the number of network paths will increase exponentially with the network scale growing. So, a Genetic Algorithm based on logistics network variable weight model is proposed to solve the problem; finally, a numerical example is given to verify the effectiveness of the algorithm.
3. Multi-objective optimization problems for flow allocation in logistics network of which intermediate nodes has supply capability are studied. Based on the work of section2, the supply capability of intermediate nodes is considered. Two situations are taken into account that capacity of both transportation lines and logistics nodes are certain and transport lines, stochastic. Aiming at the two situations that capacity of transportation lines and logistics nodes are certain and that of transportation lines, intermediate nodes and supply nodes are stochastic, the problem of flow allocation is studied based on the constraints of transportation lines'and logistics nodes'capacity with the minimum logistics cost, the minimum maximal delivery time for single path and the maximum logistics network's utilization ratio when capacity is certain or the maximum logistics network's reliability when capacity is stochastic as optimal objectives. Firstly, the mathematical models of the problem in both cases are built; then, the solution is proposed that logistics network is decomposed into lower and upper level network which are again decomposed into some many-to-one sub-network, and the problem of flow allocation for each sub-network can be solved by the method proposed in section1, and then the problems of lower and upper level network can be solved successively by the dynamic programming method; finally, a numerical example is given to verify the effectiveness of the solution.
本论文在回顾总结已有的相关研究的基础上,对多对多二级物流网络的多目标流量分配问题进行了研究。本论文所做的主要工作如下：
1.物流网络变权方法。针对物流网络流量分配的目标多样性、决策过程中决策者偏好的局限性和不确定性,提出了物流网络变权方法,包括物流网络的因素(物流节点、运输线路、子路径和路径)表示方法以及它们的变权状态值计算方法。首先,通过隶属度函数对优化目标函数值进行评价；然后,利用基于决策者偏好的状态变权函数以及变权综合方法将目标评价值分阶段地集成为物流节点、运输线路、子路径和路径的状态值,路径的状态值是进行最优路径选择的依据；最后,提出了基于物流网络变权方法的流量分配方法。
2.中间节点无供应能力的多目标物流网络流量分配问题。针对具有固定拓扑结构的多对多二级物流网络,分别对运输线路的容量确定和随机变化两种情况,以物流节点和运输线路的容量为约束,以物流成本(考虑规模经济效应,将物流成本定义为流量的凹函数)最小、最长单程运送时间最短以及网络使用率(容量确定)或网络的容量可靠性(容量随机)最高为优化目标,寻求最优的物流网络流量分配方案。首先,建立了上述两种情况下问题的数学模型；然后,考虑到多目标物流网络流量分配问题属于NP-难问题,网络路径的数量会随着网络规模的扩大成指数增长,设计了基于物流网络变权方法的遗传算法作为问题模型的求解算法；最后,通过算例验证了求解方法的有效性。
3.中间节点有供应能力的多目标物流网络流量分配问题。在第2部分研究工作的基础上,增加了对物流网络中间节点供应能力的考虑。分别考虑物流节点和运输线路的容量确定以及运输线路、中间节点和供应节点的容量随机变化两种情况,以物流节点和运输线路容量为约束,以物流成本最小、最长单程运送时间最短以及网络使用率(容量确定)或网络的容量可靠性(容量随机)最高为优化目标,寻求最优的物流网络流量分配方案。首先,建立了上述两种情况下问题的数学模型；然后,提出了模型的求解方法,将物流网络分解为上下两级网络分别进行求解,每级物流网络再分解为若干个多对一子网络,每个子网络的流量分配通过基于物流网络变权方法的流量分配方法实现,再采用动态规划方法依次完成下级和上级物流网络的流量分配；最后,通过算例验证了求解方法的有效性。
The efficiency and effectiveness of logistics network are directly dependent on the network topology and the allocation method of flow in logistics nodes and transportation lines of the network. Once the logistics network topology is formed, it will not be changed in quite a long period of time. However, the flow allocation method for logistics network will be influenced by supply, demand, network capacity and many other factors. In practical application, every node or line of the logistics is related to many evaluation criterias. When allocating freight flow in logsitics network, cost is not the only consideration, other fators such as transport time, distance and reliability should be also considered. Therefore, in order to meet the need of freights'transportation, storage and delivery from suppliers to the customers and obtain the maximum efficiency and benefit of the logistics network, how to allocate the flow in the logistics networks with fixed topology scientifically and rationally is an important issue worthy of depth study.
On the basis of the review of existing researches, the problems of flow allocation in a tow level logistics network with many to many structure are studied in this dissertation, and the main contents of the dissertation are as follows:
1. Variable weight method for logistics network is proposed. Aiming at the diversity of optimization objective, the limitations and uncertainty of the decision makers'preferences about the problem of flow allocation in logistics network, a logistics network variable weight method is proposed, including representation for the factors of logistics network, such as logistics nodes, transportation lines, sub-paths and paths, and calculation method for their variable weight state values. First of all, values of optimization objective functions are evaluated by membership function; then, using state variable weight function which has considered the decision makers'preferences and variable weight sum method, the state values of logistics nodes, transportation lines, sub-paths and paths are obtained by integrating all of objective evaluations in stages, and operation of choosing the best path is in accordance with the state values of all paths; finally, the method for flow allocation which based on the logistics network variable weight method is proposed.
2. Multi-objective optimization problems for flow allocation in logistics network of which intermediate nodes has no supply capability are studied. For a two level logistics network with fixed many to many topology, aiming at the two situations that capacity of transportation lines are certain and stochastic, the problem of flow allocation is studied based on the constraints of transportation lines'and logistics nodes'capacity with the minimum logistics cost which is defined as a concave function because of the consideration of economics of scale, the minimum maximal delivery time for single path and the maximum logistics network's utilization ratio when capacity is certain or the maximum logistics network's reliability when capacity is stochastic as optimal objectives. Firstly, the mathematical models of the problem in both cases are built; and then, due to multi-objective optimization problem for flow allocation in logistics network is belong to NP-hard problem, the number of network paths will increase exponentially with the network scale growing. So, a Genetic Algorithm based on logistics network variable weight model is proposed to solve the problem; finally, a numerical example is given to verify the effectiveness of the algorithm.
3. Multi-objective optimization problems for flow allocation in logistics network of which intermediate nodes has supply capability are studied. Based on the work of section2, the supply capability of intermediate nodes is considered. Two situations are taken into account that capacity of both transportation lines and logistics nodes are certain and transport lines, stochastic. Aiming at the two situations that capacity of transportation lines and logistics nodes are certain and that of transportation lines, intermediate nodes and supply nodes are stochastic, the problem of flow allocation is studied based on the constraints of transportation lines'and logistics nodes'capacity with the minimum logistics cost, the minimum maximal delivery time for single path and the maximum logistics network's utilization ratio when capacity is certain or the maximum logistics network's reliability when capacity is stochastic as optimal objectives. Firstly, the mathematical models of the problem in both cases are built; then, the solution is proposed that logistics network is decomposed into lower and upper level network which are again decomposed into some many-to-one sub-network, and the problem of flow allocation for each sub-network can be solved by the method proposed in section1, and then the problems of lower and upper level network can be solved successively by the dynamic programming method; finally, a numerical example is given to verify the effectiveness of the solution.
引文
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