基于成本的配送路线优化模型与算法研究
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摘要
物流业已经成为国民经济的重要产业，在社会经济发展中起着越来越重要的作用，配送是物流中的重要环节，配送路线的选择直接影响配送成本，进而影响了物流成本。物流配送路线优化研究，是配送系统优化中的重要一环。通过配送路线优化，可以提高企业的运作效率，降低配送成本，实现物流科学化。自从配送路径优化问题被提出以来，国内外的专家学者对其开展了广泛的研究。目前己经产生出多种成熟的模型和算法，为后人继续研究提供了基础。
通过阐述配送车辆路线优化问题及其构成要素，分析以往路线优化问题模型存在的不足，本文重新对配送车辆路线优化问题进行了必要的界定和约束，在建模过程中将拣选、加工、装卸等配送成本作为次要因素进行处理，以燃料费、人员费用、其它费用以及时间成本总和代替配送成本，在充分考虑车辆装载情况、配送线路的路面情况、车辆在各路段行驶平均速度情况以及各客户点不同时间窗需求的基础上，构建了以成本最低为优化目标的车辆路线优化问题数学模型。
粒子群算法被认为是求解组合优化问题的有效手段之一，本文所研究的问题属于组合优化问题，因此可采用粒子群算法来求解本文提出的成本最低配送车辆路线优化问题模型。本文提出的模型中存在车辆动态装载量和车辆到达客户时刻点两个动态变量，在求解过程中针对问题模型的特性构造全新的粒子编码方式，设计全新的动态求解配送车辆到达客户点的时刻点及车辆实时装载量的计算方法，有助于模型的求解及粒子群算法计算效率的提高。影响粒子群算法优化性能因素包括：惯性权重因子、学习因子、边界条件三种，本文在分析上述三种因子的基础上，设置适当的算法参数，确定粒子群算法的权重策略和边界策略，从而有效提高粒子群算法的解的质量。
通过对成本最低配送路线优化问题模型及粒子群算法的深入研究，本文形成了比较系统的配送路线优化理论和方法，能够为物流企业选择配送路线提供理论支持，具有实际应用价值。
本文的创新之处主要有以下几点：
1、在详细分析了配送成本及运输成本构成要素的基础上构建了以成本最低为优化目标的配送车辆路线优化模型。
2、根据本文所构建模型的特性，构造了全新的粒子编码方式，并给出了解码方式，设计了动态求解配送车辆到达客户点的时刻点以及车辆动态装载量的计算公式。
3、详细研究了影响粒子群算法优化性能的因素，并在此研究基础上选择了开口向上抛物线惯性权重变化策略及添加随机扰动项的边界策略，提高粒子群算法的算法性能。
Logistics, as the main industry in national economy, plays a very important role ineconomic development. Distribution is an important part of logistics. A fine distributionroute concerns the distribution cost, and then influence the logistics cost. Optimization ofdistribution route is a key part of the whole logistic system. By the optimization ofdistribution route, the enterprises can improve their nucleus competitiveness and achievescientific process of logistics. Since the VRP was put forward, many experts and scholarshave carried out extensive research. It has been many mature algorithm and model thatprovided basis for continuing the question.
By describing the Vehicle Routing Optimization Problem (VRP) and its constituentelements, also through analyzing the shortcomings of the VRP models in the past, it’snecessary to re-define and re-constrain the VRP model in this paper, By making somedistribution costs as secondary factor which contain selecting, processing, handling costsand so on, this paper uses fuel costs, personnel costs, other expenses and the total time costto replace the distribution costs, takes full account of vehicle loading conditions, roadconditions, the average speed of vehicles in various sections as well as different timewindow needs of customers, and establishes the VRP model with the lowest cost foroptimization objective.
The Particle swarm optimization (PSO) is considered to be an effective means of solvingcombinatorial optimization problems, the problem studied in this paper are combinatorialoptimization problems, so using PSO is effective in solving the VRP model proposed inthis paper. There are two dynamic variables exist in the proposed model, such as vehicledynamic loading and vehicle reach time. According to the characteristics of the VRP model,making a new particle encoding and decoding, designing a formula for vehicle reach time,as well as vehicle dynamic load, are helpful to solve the model and improve the efficiencyof the PSO. There are three factor affect the particle swarm optimization performance,including the inertia weight factor, learning factor, the boundary conditions. On the basis ofin-depth studies of the influencing factors of PSO, Setting the appropriate algorithmparameters and determining a decreasing inertia weight strategy and a boundary strategy, ishelpful to improve the quality of the solution of the PSO.
This paper studies the lowest cost VRP model and PSO, and establishes systematicVehicle Routing Optimization theory and method. It provides theory for company selectingthe distribution route which could be applied in practice.
The originality of this paper is as follows.
1、Establishing the VRP model with the lowest cost for optimization objective, throughanalysis the distribution costs and transport costs.
2、According to the characteristics of the VRP model, make a new particle encoding anddecoding, design a formula for vehicle reach time, as well as vehicle dynamic load.
3、On the basis of in-depth studies of the influencing factors of PSO, and select aparabola opening upwards decreasing inertia weight strategy and a random boundarystrategy to improve the performance of the PSO.
通过阐述配送车辆路线优化问题及其构成要素，分析以往路线优化问题模型存在的不足，本文重新对配送车辆路线优化问题进行了必要的界定和约束，在建模过程中将拣选、加工、装卸等配送成本作为次要因素进行处理，以燃料费、人员费用、其它费用以及时间成本总和代替配送成本，在充分考虑车辆装载情况、配送线路的路面情况、车辆在各路段行驶平均速度情况以及各客户点不同时间窗需求的基础上，构建了以成本最低为优化目标的车辆路线优化问题数学模型。
粒子群算法被认为是求解组合优化问题的有效手段之一，本文所研究的问题属于组合优化问题，因此可采用粒子群算法来求解本文提出的成本最低配送车辆路线优化问题模型。本文提出的模型中存在车辆动态装载量和车辆到达客户时刻点两个动态变量，在求解过程中针对问题模型的特性构造全新的粒子编码方式，设计全新的动态求解配送车辆到达客户点的时刻点及车辆实时装载量的计算方法，有助于模型的求解及粒子群算法计算效率的提高。影响粒子群算法优化性能因素包括：惯性权重因子、学习因子、边界条件三种，本文在分析上述三种因子的基础上，设置适当的算法参数，确定粒子群算法的权重策略和边界策略，从而有效提高粒子群算法的解的质量。
通过对成本最低配送路线优化问题模型及粒子群算法的深入研究，本文形成了比较系统的配送路线优化理论和方法，能够为物流企业选择配送路线提供理论支持，具有实际应用价值。
本文的创新之处主要有以下几点：
1、在详细分析了配送成本及运输成本构成要素的基础上构建了以成本最低为优化目标的配送车辆路线优化模型。
2、根据本文所构建模型的特性，构造了全新的粒子编码方式，并给出了解码方式，设计了动态求解配送车辆到达客户点的时刻点以及车辆动态装载量的计算公式。
3、详细研究了影响粒子群算法优化性能的因素，并在此研究基础上选择了开口向上抛物线惯性权重变化策略及添加随机扰动项的边界策略，提高粒子群算法的算法性能。
Logistics, as the main industry in national economy, plays a very important role ineconomic development. Distribution is an important part of logistics. A fine distributionroute concerns the distribution cost, and then influence the logistics cost. Optimization ofdistribution route is a key part of the whole logistic system. By the optimization ofdistribution route, the enterprises can improve their nucleus competitiveness and achievescientific process of logistics. Since the VRP was put forward, many experts and scholarshave carried out extensive research. It has been many mature algorithm and model thatprovided basis for continuing the question.
By describing the Vehicle Routing Optimization Problem (VRP) and its constituentelements, also through analyzing the shortcomings of the VRP models in the past, it’snecessary to re-define and re-constrain the VRP model in this paper, By making somedistribution costs as secondary factor which contain selecting, processing, handling costsand so on, this paper uses fuel costs, personnel costs, other expenses and the total time costto replace the distribution costs, takes full account of vehicle loading conditions, roadconditions, the average speed of vehicles in various sections as well as different timewindow needs of customers, and establishes the VRP model with the lowest cost foroptimization objective.
The Particle swarm optimization (PSO) is considered to be an effective means of solvingcombinatorial optimization problems, the problem studied in this paper are combinatorialoptimization problems, so using PSO is effective in solving the VRP model proposed inthis paper. There are two dynamic variables exist in the proposed model, such as vehicledynamic loading and vehicle reach time. According to the characteristics of the VRP model,making a new particle encoding and decoding, designing a formula for vehicle reach time,as well as vehicle dynamic load, are helpful to solve the model and improve the efficiencyof the PSO. There are three factor affect the particle swarm optimization performance,including the inertia weight factor, learning factor, the boundary conditions. On the basis ofin-depth studies of the influencing factors of PSO, Setting the appropriate algorithmparameters and determining a decreasing inertia weight strategy and a boundary strategy, ishelpful to improve the quality of the solution of the PSO.
This paper studies the lowest cost VRP model and PSO, and establishes systematicVehicle Routing Optimization theory and method. It provides theory for company selectingthe distribution route which could be applied in practice.
The originality of this paper is as follows.
1、Establishing the VRP model with the lowest cost for optimization objective, throughanalysis the distribution costs and transport costs.
2、According to the characteristics of the VRP model, make a new particle encoding anddecoding, design a formula for vehicle reach time, as well as vehicle dynamic load.
3、On the basis of in-depth studies of the influencing factors of PSO, and select aparabola opening upwards decreasing inertia weight strategy and a random boundarystrategy to improve the performance of the PSO.
引文
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[2] Ahmad Alshamrania, Kamlesh Mathurb, Ronald H Ballou. Reverse logistics:simultaneous design of delivery routes and returns strategies [J].Computers&Operations Research2007,vo1.34,No.2:595-619.
[3] Lu Quan, Dessouky, Maged M. A new insertion-based construction heuristicfor solving the pickup and delivery problem with time windows [J].EuropeanJournal of Operational Research2006,Vo1.175,No.2:672-687.
[4] Angelelli E, Speranza M G, et al. The periodic vehicle routingproblemwith intermediate facilities [J].European Journal ofOperational Research,2002,Vo1.137No.2:233-247.
[5] Francis, Peter Smilowitz, Karen.Modeling techniques for periodicvehicle routing problems [J].Transportation Research: Part B,2006,Vo1.40, No10:872-884.
[6] Jin M Z, Liu K, Royce O Bowden. A two-stage algorithm with valid inequalities forthe split delivery vehicle routing problem [J].International Journal ofProduction Economics,2006. Vo1.105,No.l:228-242.
[7] Archetti C, Speranza M, Hertz A. A Tabu Search Algorithm for the SplitDelivery Vehicle Routing Problem [J]. Transportation Science,2006,Vol.40,No.l:64-73.
[8] Benoit C, Jean F C, Gilbert Laporte. The mufti-depot vehicle routingproblem with inter-depot routes [J].European Journal of OperationalResearch,2007,Vo1.176,No.2:756-773.
[9] Lim, Andrew, Fan Wang. Mufti-Depot Vehicle Routing Problem: AOne-Stage Approach [J].IEEE Transactions on Automation Science&Engineering,2005,Vol.2,No4,397-402.
[10] Golden B, Assad A, Levy L. The fleet size and mix vehicle routing problem[J].Computers and Operations Research,1984,Vol.11:49-66.
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