运输调度联合产能分配的约束规划模型
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摘要
目的针对优化运输方案,解决如何在已知销地安排情况和交通路网情况下,合理分配有限产能并为产地指定生产方案。方法以某市区92个建筑工地与20个混凝土搅拌站设置情况与水泥运输路网相关情况为对象,先采用Floyd算法求解出销地之间的最短路邻接矩阵,再通过引入0-1整数变量来指派每个产地的生产方案,据此设计出以运输距离最小为目标函数的混合整数规划模型,为了求解产地分配和生产方案都未知的混合整数规划模型,通过聚类降维的方法将混合整数规划模型转化为已知产地分配的整数非线性规划模型。结果利用LINGO求解得到该模型最短总运输距离和产地生产方案,并与原指定的20个产地下求解得到的最短总运输距离相比,可明显得到更优运输方案。将其应用到如何为建筑工地设计搅拌站产能分配方案且为其指定运输调度方案的实际问题,并给出求解算法及结果分析。结论该数学模型可以推广到在城市交通路网确定的和当地生产力水平有限的情况下,根据销地的分布情况来解决产地的位置安排以及确定产地的生产方案等问题。
Objective To optimize the transportation scheme,the problem of how to allocate the limited capacity reasonably and assign the production scheme for the production area is solved under the condition of only known distribution arrangement and transportation network.Methods With the setting of 92 construction sites and 20 concrete mixing stations in an urban area as the object of study,the shortest path adjacency matrix was solved by Floyd algorithm,and then the production plan of each producing area was assigned by introducing 0-1 integer variable.Based on this plan,a mixed integer programming model with the objective function of minimizing transportation distance was designed.To solve the mixed integer programming model with unknown origin allocation and production plan,the mixed integer programming model is transformed into the integer non-linear programming model with known origin allocation by clustering dimension reduction method.Results The shortest total transportation distance of the model and the production plan of the production area was obtained by the use of LINGO solution.Compared with the shortest total transportation distance obtained from the original 20 production and underground solutions,the transportation scheme was obviously better.This paper also applied it to the practical problem of how to design the capacity allocation scheme of mixing station for construction site and assign the transportation scheduling scheme for it,and gave the solving algorithm and result analysis.Conclusion The mathematical model can be extended to solve the problems of location arrangement and production plan determination of the origin according to the distribution of the selling area under the condition of the determination of urban traffic network and the limitation of local productivity level.
Objective To optimize the transportation scheme,the problem of how to allocate the limited capacity reasonably and assign the production scheme for the production area is solved under the condition of only known distribution arrangement and transportation network.Methods With the setting of 92 construction sites and 20 concrete mixing stations in an urban area as the object of study,the shortest path adjacency matrix was solved by Floyd algorithm,and then the production plan of each producing area was assigned by introducing 0-1 integer variable.Based on this plan,a mixed integer programming model with the objective function of minimizing transportation distance was designed.To solve the mixed integer programming model with unknown origin allocation and production plan,the mixed integer programming model is transformed into the integer non-linear programming model with known origin allocation by clustering dimension reduction method.Results The shortest total transportation distance of the model and the production plan of the production area was obtained by the use of LINGO solution.Compared with the shortest total transportation distance obtained from the original 20 production and underground solutions,the transportation scheme was obviously better.This paper also applied it to the practical problem of how to design the capacity allocation scheme of mixing station for construction site and assign the transportation scheduling scheme for it,and gave the solving algorithm and result analysis.Conclusion The mathematical model can be extended to solve the problems of location arrangement and production plan determination of the origin according to the distribution of the selling area under the condition of the determination of urban traffic network and the limitation of local productivity level.
引文
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[2]MILIA H,HICHAM C,FAROUK Y,et al.Availability optimization of a redundant dependent system using genetic algorithm[J].IFAC Papers OnLine,2016,49(12):82-86.
[3]谢金星,薛毅.优化建模与LINDO/LINGO软件[M].北京:清华大学出版社,2006:11-78.
[4]姜启源,谢金星,叶俊.数学模型[M].3版.北京:高等教育出版社,2003:20-130.
[5]周建兴.Matlab从入门到精通[M].北京:人民邮电出版社,2012:1-92.
[6]王广民,马林茂,李兰兰.运筹学中运输问题求解算法及其扩展研究[J].长江大学学报(自然科学版),2011,08(10):1-5.
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