摘要
目的安全检查在工业生产中不可或缺,是发现和消除事故隐患、落实安全措施、预防事故发生的重要手段。为提高巡检的效率,优化资源配置,通过建立数学模型以达到花费最短的时间和最少的人力完成巡检任务。方法通过对模型的假设及简化,建立目标规划模型,运用Kruskal算法找出连通图的最小生成树,运用Floyd算法找出最短路径,使用MATLAB、LINGO编程对建立的模型进行求解。结果在问题1中,运用Kruskal算法找出最小生成树后,经过分析计算,以调度中心XJ—0022为树根对最小生成树粗略划分为4个子图,运用Floyd算法找出每位工人的最短巡检路径,建立目标规划模型,再使用MATLAB及LINGO,确定每班4人为最优,并给出了最优巡检线路和巡检时间表。在问题2中,若增加休息和吃饭时间,经过分析讨论后每班应有6名工人。根据第一问的算法思想求出每位工人的最短巡检路径,经过软件求解,给出了最优巡检线路和巡检时间表。在问题3中,若要把问题1中的固定上班改为错时上班,反而会增加人力成本,不可取。对问题2,把上班时间进行如下调整3∶00-11∶30、11∶30-19∶00、19∶00-3∶00,这样每班5个人就可以完成工作,此种方法比固定上班可节省3人。结论通过建立数学模型,并对模型的求解,最终解决了问题,花费最短的时间和最少的人力完成巡检任务。
Objective Safety inspection is indispensable in industrial production.It is an important means to find and eliminate potential accidents,implement safety measures and prevent accidents.To improve the efficiency of inspection and optimize the allocation of resources,it is necessary to establish a mathematical model to complete inspection tasks with shortest time and minimum number of people.Methods Through the hypothesis and simplification of the model,the target planning model is established,the minimum spanning tree of the connecting graph is found by the Kruskal algorithm,the shortest path is found by using the Floyd algorithm,and the established model is solved by MATLAB and LINGO programming.Results In Question One,Kruskal algorithm is used to find out the minimum spanning tree.After analysis and calculation,the dispatching center XJ-0022 as the tree root,the minimum generation tree are roughly divided into 4 subplots.The Floyd algorithm is used to find out the shortest patrol path of each worker and establish the target planning model.MATLAB and LINGO programming are used to find out that 4 people per class are optimal.The optimal inspection lines and inspection schedules are given.In Question Two,if the rest time and meal time are increased,six workers per shift are needed according our analysis.Based on the algorithm idea of Question One,the shortest inspection path for each worker is derived,and the optimal inspection line and inspection schedule are given after the software solution.In Question Three,it is not advisable to change the fixed work in Question One to work at the wrong time,but it will increase the cost of manpower.For Question Two,the work hours can be adjusted into shifts:3∶00 to 11∶30,11∶30 to 19∶00,and 19∶00 to 3∶00,so that each shift of five people can complete their work,which there are three workers less than those needed in fixed work arrangement.Conclusion By establishment and sulution to the mathematical model,the three problems are finally solved,so as to spend the shortest time and the least workers to complete the inspection task.
作者
吕宁宁
潘娜娜
董慧
LV Ning-ning;PAN Na-na;DONG Hui(Anhui Technical College of Industry and Economy,Hefei,Anhui 230051,China;Anhui Xinhua University,Hefei,Anhui 230088,China)
出处
《河北北方学院学报（自然科学版）》
2020年第3期35-43,共9页
Journal of Hebei North University:Natural Science Edition
基金
安徽省自然科学基金重点项目:“关于磁流体方程组正则性的研究”(KJ2017A622)
安徽省教研一般项目:“以数学建模竞赛为依托深化高等数学课程改革”(2018jyxm0106)。
