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对小规模MTSP问题,建立了可精确求解方案的0-1规划模型,并在满足邮政运输需求的前提下给出了最佳方案.问题一首先以县支局、县局为顶点构建无向赋权图,通过Floyd算法求解各局间的最短距离;然后以Fijk为决策变量,以邮车工作时间、车辆运载能力为主要约束,建立以总空载损失费用最小为目标的0-1非线性规划模型,运用规划软件Lingo求解.问题二考虑到市邮路成本,我们采用分层规划策略,首先以市支局、县局为顶点构建无向赋权图,求解出最短路矩阵,建立以邮路运行成本最小为目标的0-1非线性规划模型IIA求解;然后,建立各县区的最短路矩阵,同样建立规划模型IIB求解各县运输方案.问题三由于县局地理位置不变,对区邮路无影响,故以全市各县支局为中心采用逐步最优方法对所有县区支局重新划分;然后采用模型IIB求解.第四问中考虑县局迁移,我们建立近似的启发式算法完成县局选址,并运用规划模型II求解的到新方案.最后,我们对两种区域划分调整方法还进行了定量的分析.
For the small-scale MTSP problem, a 0-1 programming model that can accurately solve the problem is established, and the best solution is given on the premise of meeting the postal transportation requirements.Question 1 Firstly, construct the undirected endowment with county branch and county bureau as the vertex And the Floyd algorithm is used to solve the shortest distance between the offices. Then, based on Fijk as the decision variable and the main constraints of the working hours of the mailing vehicle and the carrying capacity of the vehicle, a 0-1 nonlinear programming with the goal of minimizing the total no-load loss is established Model, the use of programming software Lingo solution.Question two city postal costs, we use a hierarchical planning strategy, first city branch, county office as the top to construct the undirected weighted graph, the shortest path to solve the matrix to establish the postal route The minimum running cost is the target 0-1 nonlinear programming model IIA solution; then, the establishment of the shortest path matrix of each county area, also establish planning model IIB to solve the transportation scheme of each county.Question 3 Because of the geographical location of the county bureau, Postal no effect, so the city’s county branch as the center step by step optimization method for all county branch to re-divide; then use the model IIB solution .In the fourth question to consider the relocation of county, we establish a similar inspiration Type algorithm to complete the county site selection, and use the planning model II to solve the new program.Finally, we also carried out a quantitative analysis of the two regional adjustment methods.