Application of Linear Programming Model to Refugee Migrating Problem

The refugee immigration problem can be considered as a special “transportation problem”. Linear Programming Model is built, where two objectives with weight in the objective function, for the shortest routes that the refugees go along and the minimum number of refugees stayed in each country. An example of EU is introduced and calculated on Lingo software. The results show that the model is available to solve the refugee immigration problem in different scale.

Managing Tourism Development in the Dutch City of Utrecht using a Linear Programming Model of the Tourist Carrying Capacity

As one part of the Landstad International Metropolitan Area,Utrecht has become known as one of the best tourist destinations in recent years,with the rapid growth of worldwide travel trends.In this paper,through the adaption of the linear programming model,the paper intends to not only quantify the optimum number of visitors to Utrecht but also formulate a number of policy recommendations based on the reconstruction of this optimum.The paper draws the following conclusions:(1) tourist carrying capacity of Utrecht is not yet exceeded;(2) restrictive accommodation policy does not currently seem necessary;(3) the cultural-historical attractions are not yet optimally used;(4) investing in strategic provisions is currently not necessary.And from the conclusion,the paper further puts forward the following suggestions on the city’s tourism development strategy:(1) to identify "tourist flood plains";(2) to encourage the tourist disclosure of these alternatives;(3) to invest even more explicitly in residential tourism and,where possible,curb day tourism;(4) to introduce a new business model.

A Weighted Goal Programming Model for the DASH Diet Problem: Comparison with the Linear Programming DASH Diet Model

A Linear Programming DASH diet model for persons with hypertension has previously been formulated and daily minimum cost diet plans that satisfy the DASH diets’ tolerable intake level of the nutrients for 1500 mg a day Sodium level and different daily calorie levels were obtained using sample foods from the DASH diet eating plan chart. But the limitation in the use of linear programming model in selecting diet plans to meet specific nutritional requirements which normally results in the oversupply of certain nutrients was evident in the linear programming DASH diet plan obtained as the nutrient level of the diet plans obtained had wide deviations of from the DASH diets’ tolerable upper and lower intake level for the given calorie and sodium levels. Hence the need for a model that gives diet plans with minimized nutrients’ level deviations from the DASH diets’ tolerable intake level for different daily calorie and sodium level at desired cost. A weighted Goal Programming DASH diet model that minimizes the daily cost of the DASH eating plan as well as deviations of the diets’ nutrients content from the DASH diet’s tolerable intake levels is hereby presented in this work. The formulated weighted goal programming DASH diet model is further illustrated using chosen sample foods from the DASH food chart as used in the work on the linear programming DASH diet model for a 1500 mg sodium level and 2000 calories a day diet plan as well as for 1800, 2200, 2400, 2600, 2800 and 3000 daily calorie levels. A comparison of the DASH nutrients’ composition of the weighted Goal Programming DASH diet plans and those of the linear programming DASH diet plans were carried out at this sodium level and the different daily calorie levels. It was evident from the results of the comparison that the weighted goal programming DASH diet plans has minimized deviations from the DASH diet’s tolerable intake levels than those of the linear programming DASH diet plans.

Approximate Solutions for a Class of Fractional-Order Model of HIV Infection via Linear Programming Problem

In this paper, we provide a new approach to solve approximately a system of fractional differential equations (FDEs). We extend this approach for approximately solving a fractional-order differential equation model of HIV infection of CD4+T cells with therapy effect. The fractional derivative in our approach is in the sense of Riemann-Liouville. To solve the problem, we reduce the system of FDE to a discrete optimization problem. By obtaining the optimal solutions of new problem by minimization the total errors, we obtain the approximate solution of the original problem. The numerical solutions obtained from the proposed approach indicate that our approximation is easy to implement and accurate when it is applied to a systems of FDEs.

Application of Linear Programming Algorithm in the Optimization of Financial Portfolio of Golden Guinea Breweries Plc, Nigeria

In this study, Simplex Method, a Linear Programming technique was used to create a mathematical model that optimized the financial portfolio of Golden Guinea Breweries Plc, Nigeria. This work was motivated by the observed and anticipated miscalculations which Golden Guinea Breweries was bound to face if appropriate linear programming techniques were not applied in determining the profit level. This study therefore aims at using Simplex Method to create a Mathematical Model that will optimize the production of brewed drinks for Golden Guinea Breweries Plc. The first methodology involved the collection of sample data from the company, analyzed and the relevant coefficients were deployed for the coding of the model. Secondly, the indices collected from the first method were deployed in the software model called PHP simplex, an online software for solving Linear Programming Problem to access the profitability of the organization. The study showed that Linear Programming Model would give a high profit coefficient of N9,190,862,833 when compared with the result obtained from the manual computation which gave a profit coefficient of N7,172,093,375. Also, Bergedoff Lager, Eagle Stout and Bergedoff Malta were found not to contribute to overall profitability of the company and it was therefore recommended that their productions should be discontinued. It also recommends that various quantities of Golden Guinea Lager (1 × 12) and Golden Guinea Lager (1 × 24) should be produced.

基于改进云模型和线性规划优化算法的山区泥石流危险性评价

泥石流是一种由暴雨或地震诱发常发生在山区的破坏力强大的地质灾害,为了提前预防和减少其破坏能力,使用特定算法评价其危险性十分必要。采用云模型雾化特性对各评价指标权重进行一致性检验后耦合,得到合理的权重阈值区间。以线性规划优化算法通过设定目标函数后对各评价指标在权重区间内动态取值,从而得到各个泥石流沟渠最危险评分。改进了单指标的云数字特征公式,构建覆盖更全面的综合云模型,输入最大危险评分对研究区泥石流沟渠进行危险性分级。将该研究应用在汶川地震后北川县产生的72条泥石流沟渠实例中,其评价结果显示与研究区实际地形环境情况相吻合,为相似类型泥石流灾害的预防提供了新思路。

梅钢转炉合金模型开发

为降低转炉合金成本,采用线性规划为核心算法,开发了转炉合金模型。模型通过设计碳冗余质量分数和磷冗余质量分数、确定合金收得率和LF增碳质量分数等主要参数、基于优先加足低价合金的原则分配转炉合金用量,在满足钢水成分的前提下降低了合金成本,可产生经济效益3.27元/t。

低轨星座传感器资源调度的自主任务规划建模方法

低轨星座传感器资源的优化调度是复杂多约束下的任务规划问题,为了满足多个运动目标全程跟踪与监视的资源实时优化调度需求,提出一种星上自主快速求解的规划模型.在对自主任务规划问题进行详细建模的基础上,考虑各项约束条件与优化因素,将原问题转化成简易的0-1线性整数规划模型,并构建多目标跟踪试验场景对所提方法进行了仿真验证.仿真结果表明,基于简易规划模型的资源调度可实现多目标的全程跟踪与监视.

基于CPM的多模式资源约束项目调度建模与复杂度分析

为有效降低多模式资源约束项目调度模型的复杂度和解空间,构建3类混合整数线性规划模型。运用紧上界TTUB缩减时间序列T的上界和关键路径法缩减各项活动结束时间的上下界,以降低模型复杂度和解空间。为验证改进模型的有效性,从MRCPSP标杆案例库中选取1106组规模不等的算例进行求解。结果表明,基于CPM的多模式资源约束项目调度模型解空间更小;决策变量同比缩小3~65倍,约束数同比缩小1~4倍;平均求解时间同比减少53%~112%,求解性能显著优于其他模型。为验证紧上界T_(TUB)的参数α性能,1106组算例结果表明,α越接近1,模型的复杂度越低,解空间越小。但随着算例规模增加,算例可行解探寻难度增加。因此,对大规模算例,α值应适当放宽。

基于换电的共享电动汽车调度与服务定价

为解决共享电动汽车出行模式车辆失衡与电能补给问题,基于集充统配换电模式,考虑共享电动汽车电能补给、换电站选址与电池配送路径间的耦合关系,基于时空网络构建以最大化利润为目标的共享电动汽车调度与服务定价优化模型,并通过共享电动汽车需求-价格函数逆变换,将非线性非凸模型转换成更易求解的非线性凸模型。数值试验结果表明:协同决策换电站位置、电池配送路径、共享电动汽车调度方案与服务价格,可提高共享电动汽车出行服务商利润;基于割线的外逼近算法比基于切线的外逼近算法和拉格朗日松弛算法更适于求解所提出的模型。参数敏感度分析结果显示,潜在共享电动汽车出行需求与电能可得性都是影响共享电动汽车出行服务商利润的重要因素。

基于线性规划模型的电极头更换方法研究

为解决电极头更换需要停线,直接影响自动生产线设备综合效率和单车制造成本的问题,通过对电极头更换时间和更换频率进行分析,使用线性规划模型搭建出电极头分组集中更换数据分析模型,并根据实践经验总结出不同情况下电极头更换的风险级别,同时推广定人、定时、定工位的标准化实施方式,多次迭代调整后确定最终方案,根据此策略进行分组电极头更换,降低了自动岛的点焊电极头更换频率及整体更换时间,设备综合效率指数明显提高,同时单车辅料成本得到优化。

Unmanned Aerial Vehicle Inspection Routing and Scheduling for Engineering Management

Technological advancements in unmanned aerial vehicles(UAVs)have revolutionized various industries,enabling the widespread adoption of UAV-based solutions.In engineering management,UAV-based inspection has emerged as a highly efficient method for identifying hidden risks in high-risk construction environments,surpassing traditional inspection techniques.Building on this foundation,this paper delves into the optimization of UAV inspection routing and scheduling,addressing the complexity introduced by factors such as no-fly zones,monitoring-interval time windows,and multiple monitoring rounds.To tackle this challenging problem,we propose a mixed-integer linear programming(MILP)model that optimizes inspection task assignments,monitoring sequence schedules,and charging decisions.The comprehensive consideration of these factors differentiates our problem from conventional vehicle routing problem(VRP),leading to a mathematically intractable model for commercial solvers in the case of large-scale instances.To overcome this limitation,we design a tailored variable neighborhood search(VNS)metaheuristic,customizing the algorithm to efficiently solve our model.Extensive numerical experiments are conducted to validate the efficacy of our proposed algorithm,demonstrating its scalability for both large-scale and real-scale instances.Sensitivity experiments and a case study based on an actual engineering project are also conducted,providing valuable insights for engineering managers to enhance inspection work efficiency.

水库供水调节计算优化模型研究与应用

水库供水调节计算是实现河流水资源时空合理分配的重要技术手段。常规水库供水调节计算方法流程清晰、操作简单,但计算所得供水量并非最优值。针对常规水库供水调节计算方法难以充分发挥水库供水效益的问题,以调节计算期内水库总供水量最大为目标,以各供水对象供水保证率和最大破坏深度为约束条件,构建水库供水调节计算优化模型;基于等价变换原理,将模型中供水对象供水保证率非线性约束条件进行线性化处理,采用Cplex线性求解器对模型进行求解。张峰水库供水工程实例分析结果表明:优化模型计算所得张峰水库多年平均供水量较常规方法增加948万m^(3),增加比例为7.5%,供水效益明显增加;水库多年平均水位较常规方法降低6 m,水库蓄泄变化次数更多,充分发挥了张峰水库多年调节作用;供水对象的最大破坏月份数量大于常规方法,但仍满足各供水对象的设计供水保证率要求,说明优化模型是通过增加最大破坏月份数量的方式,来到达减小最大破坏深度的目的;水库多年平均出库流量较常规方法减小0.2 m^(3)/s,但可保证长系列所有月份均满足河道内生态流量要求;1997-2002年、2008-2010年两个沁河流域典型的连续枯水时段缺水量及缺水过程与常规方法结果相似,符合实际情况,验证了模型的合理性;优化模型可根据实际需要修改优化目标和约束条件,能够精准控制各供水对象的供水保证率和最大破坏深度,且具备可移植性,使用更加灵活。

基于均衡性和能力利用的高速铁路标杆车运行图编制方法研究

高速铁路标杆车的服务品质对于提高铁路客运产品的竞争力具有重要意义,在现场实际编图过程中,高速铁路标杆车须优先铺画,因此标杆车运行图的编制结果决定了整个列车运行图的框架。为了提高高速铁路标杆车的服务品质,考虑标杆车区间运行时分约束、交路接续时间约束等编图基本约束,结合标杆车始发时间约束、成组约束等特殊约束,基于事件活动网络构建以OD服务均衡性和能力利用为目标的整数线性规划模型。设计分阶段迭代求解算法框架,嵌套商业求解器进行求解,第1阶段为不考虑安全间隔时间约束的标杆车分组问题,以OD服务均衡性为目标进行求解;第2阶段以求解得到的标杆车分组为输入,增加安全间隔时间约束,以能力利用为目标进行求解。最后以京广高速铁路为案例,使用实际编图参数,运用优化求解器ILOG CPLEX进行求解,验证模型的有效性和可行性。实验结果表明:优化模型可以在较短时间内高效求解,与实际图对比,上下行OD服务均衡性分别提升38.2%和51.7%,能力损失降低50%,针对不同规模的算例,在200 s内均能得到最优解。针对不同交路接续时间,得出限制标杆车在北京西站的交路接续时间在45 min以内,不会对OD服务均衡性和能力利用造成较大影响。研究结果可为高速铁路标杆车运行图编制及优化提供参考。

基于规划模型的运输网络最大流问题的分析研究

当今,世界经济形成命运共同体,各国各地的贸易往来非常频繁。物流产业作为供应链的重要组成部分,也迎来快速发展。研究运输网络最大流问题成为许多学者关注的焦点。现实生产生活中,某地区有一公司需将货物从配送中心运送至仓库储存,在运输过程中,物流车会遇到若干个路口,因为每段路程的车辆承载量和目前平均通过量各有不同,因此,文章通过建立规划建模求解,得出货物运输效率最大的研究结果,以期在实际物流运输环节中节约大量的成本。

考虑路径关系的干线多路径绿波优化模型

针对协调路径数目增加后绿波带宽变窄问题,本文提出一种考虑路径关系的多路径协调控制优化模型。分析路径的相关关系,构建上下行分区和路径分解模型;引入子区划分参数,改进经典多路径模型,构建子区内部协调约束;分析路径在相邻子区之间的衔接特征,构建子区间连接性约束条件;综合考虑子路径长度和流量构建权重系数,以各子路径绿波带宽加权和最大为优化目标,建立多路径协调控制优化模型。为验证模型的有效性,选取南京市典型干道为研究对象开展案例分析。实验结果表明,本文提出的模型可以有效增大绿波带宽,相较于对比模型,加权绿波带宽和提高49.44%。利用VISSIM验证了方案的应用效果,仿真结果表明,本文模型方案可以获得更高的通行效益。相较于对比方案,关键路径车均延误和车均停车次数明显降低,干道车均延误和车均停车次数分别降低了20%和27%,车辆平均速度提高了17%。本文模型可为城市道路干线协调控制提供理论基础。

基于线性规划优化小精细化工企业的生产措施

由于小精细化工企业生产灵活、工艺复杂、对成本和利润控制严格,因此,对生产工艺的优化,就成为小精细化工企业生产措施改进的主要内容之一。文章结合小精细化工企业的生产状况以及在该状况条件下相应的约束因素等,采用运筹学线性规划法构建最优计划数学模型,利用计算软件就具体数据进行求解,得到生产计划的最优解。

延误条件下高速铁路列车运行时刻表混合调整策略研究

高速铁路列车在运行过程中受各种外部干扰可能导致列车延误。为提升调度员面对复杂延误情况的应急处置效率,研究针对列车轻微延误、严重延误情况下的自动调整方法,提出考虑列车到发时刻、发车顺序、计划外停车、限制列车被越行次数、取消列车的混合调整策略,建立符合列车实际运行状态的混合整数规划模型。以所有列车总延误时间最小为调整目标,设计改进遗传算法求解,并采用京沪高铁部分线路数据验证混合调整策略的有效性。实验表明,在轻微延误、严重延误场景下,采用混合调整策略比常用的先来先服务策略分别减少总延误时间16%、10.7%以上,能够有效减少列车晚点情况的发生,快速恢复行车秩序。

含抽水蓄能电站与分布式能源的输电网联合规划多阶段模型

虽然能源消耗量仍在增加,但由于电力系统的管制放松、需求响应方案的应用、微电网和智能电网的实施等,系统峰值负荷正在下降,作为公共实体的输电系统运营商必须加强输电系统以保持电力系统的可靠性。为此,提出了一种含抽水蓄能电站与分布式能源的输电网联合规划双层模型。其中,上层从输电系统运营商的角度出发,最大限度地降低线路投资成本和从传统发电机和配电系统购买能源的成本,同时确保分布式能源投资的给定回报率;下层模拟市场清算以找到节点价格,用于计算配电商的利润和购买能源的成本。通过强对偶技术、big-M方法和互补松弛条件,将所提出的模型转化为一个单层混合整数线性规划问题,并在IEEE RTS-24母线测试系统中验证了其有效性。