公交车调度问题的数学模型

对2001年全国大学生数学建模竞赛的B题－公交车调度问题进行了分析，建立了调度的目标规划模型及0－1规划模型。在假设各站上、下车人数服从均匀分布的条件下，通过对模型的求解，求出了公交公司的最小运行车辆数52辆，并给出了发车时刻表，其中上行方向运行225班次，下行方向运行220班次，该模型简单，求解容易，能较好地考虑各方利益。     

一类或决策模型及其应用

提出了一类特殊类型的数学规划模型并给出了一种新的分枝定界算法.这类数学模型尽管可以转化为0-1规划模型,但它相对于转化后的0-1规划模型:①决策意义明确,表达形式相对简单;②不需要引入参数M并在求解前确定其上界;③相对于求解转化后的0-1规划模型的分枝定界法,新分枝定界算法在最好情形下计算量最多为原算法的八分之一.作为本模型的一个应用,可以用来解决一些要么不实施要么有一定数量下限限制才可以实施的决策问题.     

基于正弦型光滑打磨函数对0-1规划问题的连续化求解方法

传统的求解0-1规划问题方法大多属于直接离散的解法.现提出一个包含严格转换和近似逼近三个步骤的连续化解法:(1)借助阶跃函数把0-1离散变量转化为[0,1]区间上的连续变量;(2)对目标函数采用逼近折中阶跃函数近光滑打磨函数,约束条件采用线性打磨函数逼近折中阶跃函数,把0-1规划问题由离散问题转化为连续优化模型;(3)利用高阶光滑的解法求解优化模型.该方法打破了特定求解方法仅适用于特定类型0-1规划问题惯例,使求解0-1规划问题的方法更加一般化.在具体求解时,采用正弦型光滑打磨函数来逼近折中阶跃函数,计算效果很好.     

用LINGO6.0求解大型数学规划

LINGO6.0的特出功能是求解大型数学规划 ,它提供的内部建模语言能够自然地描述各种规划问题 ,使大规模数学规划的求解不再困难 .本文以 2 0 0 0年全国大学生数学建模竞赛 B题——钢管订购和运输计划的模型求解为例 ,介绍最新版本 LINGO建模语言和它的用法 .     

考虑乘客时间成本与换乘感受的中转航班登机口分配问题研究

针对2018年"华为杯"第十五届中国研究生数学建模竞赛F题展开研究对考虑乘客时间成本与换乘感受的中转航班登机口分配调度问题(Airport Gate Assignment Problem,AGAP)进行研究,建立了多目标0-1整数线性规划的中转航班登机口分配模型.根据不同的实际应用条件,对该模型进行相应改进,并使用Lingo求解,得出在最大化航班分配数量的基础上,最小化乘客换乘成本,同时尽量减少登机口使用数量的最优中转航班登机口分配方案,最后对分配结果进行分析.模型亮点在于:1)创新性地引入了乘客换乘成本惩罚因子,令模型对实际问题考虑更加全面.2)模型在时间离散化的基础上,将航班间隔时间纳入航班占用时间,建立了0-1整数线性规划模型求最优解,求解结果更加可靠.3)模型通过线性加权的方法,将多目标规划问题简化为单目标问题进行建模.     

航线优化的随机动态规划模型

航空公司在给定的运力和机队配置条件下,如何适应航线需求的不断变化而合理地分配运力,使航空公司的经营效益最大化是我国航空经营管理的一个重大课题.根据航班效益分析,在一定的经营时间,航行班次的条件下,建立一个航线贡献最大化的含有随机变量的动态规划模型.求解方法是先用M ON TE C ARLO方法计算机仿真把模型转化为非线性的整数规划.再用动态规划中资源分配算法求出模型的最优解,编排最优各航线规划.     

多气源天然气管网运行优化问题的混合整数规划模型及其算法

对于多气源天然气管网运行优化问题,文章首先引入了刻画压缩机开关的0-1整数变量,并对非线性的管道压降方程进行了合理的松弛化处理,建立了更符合实际的非线性混合整数规划模型.其次,基于序列线性化的思想,设计了一种求解该模型的序列混合整数线性化算法.最后,在不同规模的天然气管网系统中进行了多方面的对比实验.实验结果表明,新模型及求解算法能够有效降低成本、减少压缩机能耗,并且所需求解时间大大减少.     

呼叫中心坐席人员排班问题优化模型与算法研究

国内呼叫企业在保证每个坐席人员周内当值相同班次情况下,通过灵活安排周内当班日期与班次来制定排班方案。针对该实际排班场景,构建问题整数规划模型。通过对问题数据特征及优化性质分析,以及对班次人力有效满足区段电话服务需求的量化指标表征,分别提出两个构造性启发式算法。使用企业实例数据对模型算法进行计算实验。实验结果显示,整数规划模型适合于求解小规模排班问题最优解,而启发式算法能够以小计算成本获得大规模排班问题优化解。最后讨论保证员工上班规律性的同班次用工制度对企业人力成本控制的影响。     

高层电梯系统运行方案的建模与求解

随着社会的发展,运用垂直交通系统的高层建筑和智能化建筑不断出现。而有效的电梯交通配置,是垂直交通系统高效运行的基本保证。本文针对高层商务建筑中的电梯运行管理方案设计问题,分析了影响电梯耗能和用户满意度的主要因素。分别建立了电梯数目已知和电梯数目未知情况下的电梯调度优化模型,并设计相应动态规划算法和遗传算法。结合算例,求解算例中的电梯优化调度方案,以验证模型的合理性。最后根据我们建立的电梯调度模型,借助VC++作出可视化的电梯调度示意界面,将本文的研究结果用于实际的电梯调度中。     

邮政运输网络中的邮路规划和邮车调度研究

邮政运输网络是邮政企业运营的重要保障,而邮路规划和邮车调度设计是决定邮政运输网络效率的关键因素,问题1的邮路规划问题归结为带返程货的车辆路由问题,该问题是NP-难的,采用改进蚁群算法,通过对单环路旅行商问题进行断环分析,将运行线路的好坏反馈给蚁群算法的目标函数,求取最终的优化路径.第二问邮路规划扩展到了全区,采用有优先级的分县优化途径寻求最佳邮路.最后,给出模型的评价及改进方向.     

Dispatch planning using newsvendor dual problems and occupation times: Application to hydropower

We consider price-driven dispatch planning under price uncertainty: A storable commodity is optimally sold and purchased over time. First, we consider models where the storage level is constrained in expectation. The dual of the corresponding optimization problem is related to the newsvendor problem. Exact solutions of bang-bang type are given. The second methodology is for high-frequency dispatch decisions in multistage stochastic programming models: To overcome the curse of dimensionality, prices are modeled by occupation times at price levels. In a case study, we consider a pumped-storage hydropower plant: Numerical solutions are given, which have similar patterns as for the first, exactly solvable problems.     

A stochastic manpower planning model under varying class sizes

Solution related to different types of manpower planning problems arising in different industries and organizations are very much helpful for proper planning and implementation of different objectives. Previously those type of problems are mostly solved under the deterministic set up. Gradually several scientists have developed different types of stochastic models appropriate for solving such types of problems. The present study is an attempt to develop a stochastic manpower planning model under the set up where the classes are of varying sizes and promotion occurs only on the basis of seniority. The work of second author was supported by a research fellowship from Council of Scientific and Industrial Research (Sanction No. 9/28(611)/2003-EMR-I), India.     

Optimizing base station location and configuration in UMTS networks

Radio planning and coverage optimization are critical issues when deploying and expanding third generation cellular systems. We investigate mixed integer programming models for locating and configuring base stations in UMTS networks so as to maximize coverage and minimize installation costs. The overall model considers both uplink and downlink directions, that we studied separately in Amaldi et al. (2002, 2003b). The two-stage Tabu Search algorithm we propose exploits solutions of a simplified model for the uplink direction to drastically reduce the computational time required to find good approximate solutions of the overall uplink and downlink model.Computational results obtained for realistic instances %with voice as well as data traffic are reported and discussed. Research carried out within the national project “Optimization, simulation and complexity in the design and management of telecommunication networks”funded by the Italian Ministry of Education, University and Scientific Research (MIUR).     

Reoptimization gaps versus model errors in online-dispatching of service units for ADAC

Under high load, the automated dispatching of service vehicles for the German Automobile Association (ADAC) must reoptimize a dispatch for 100-150 vehicles and 400 requests in about 10 s to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within 10 s. One way out are simplified reoptimization models. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new models ShadowPrice and ZIBDIP_dummy can keep up with ZIBDIP.     

The Application of Preprocessing and Cutting Plane Techniques for a Class of Production Planning Problems

This paper investigates properties of integer programming models for a class of production planning problems. The models are developed within a decision support system to advise a sales team of the products on which to focus their efforts in gaining new orders in the short term. The products generally require processing on several manufacturing cells and involve precedence relationships. The cells are already (partially) committed with products for stock and to satisfy existing orders and therefore only the residual capacities of each cell in each time period of the planning horizon are considered. The determination of production recommendations to the sales team that make use of residual capacities is a nontrivial optimization problem. Solving such models is computationally demanding and techniques for speeding up solution times are highly desirable. An integer programming model is developed and various preprocessing techniques are investigated and evaluated. In addition, a number of cutting plane approaches have been applied. The performance of these approaches which are both general and application specific is examined.     

面向集团供应链的大宗物资采购计划研究

针对集团大宗物资采购的特性,研究集团采购计划的编制与调整,将集中采购计划方法应用于集团供应链中,并重点研究了需求计划变动以及集团内物资平衡引发的采购计划调整模型。模型的构建依据三个权衡准则:获取数量折扣、准时采购、降低库存,以达到计划期内采购总成本最低的目的,所建模型经转化为一般非线性模型,应用优化软件求解。最后通过算例说明所建模型的有效性。     

Modelling heterogeneity in manpower planning: dividing the personnel system into more homogeneous subgroups

Manpower planning is very useful for human resource management in large organizations. Most manpower models are concerned with the prediction of the future behaviour of the staff: they might leave the organization, get promoted or acquire more and new skills. This behaviour can vary a lot among different employees, what makes prediction difficult. It is common to tackle this problem by dividing the whole heterogeneous personnel system in several more homogeneous subgroups. This approach is often used to develop manpower planning models for prediction, control or optimization. Although the division in homogeneous subcategories is a fundamental and important step in the application of the models, up till now literature neglects to discuss a procedure to deal with this in practice. This paper suggests a general framework to find the distinguished homogeneous subcategories by determining and considering observable sources of personnel heterogeneity. Copyright © 2006 John Wiley & Sons, Ltd.     

Reoptimization Gaps versus Model Errors in Online-Dispatching of Service Units for ADAC

Under high load, the automated dispatching of service vehicles for the German Automobile As- sociation (ADAC) must reoptimize a dispatch for 100–150 vehicles and 400 requests in about ten seconds to near optimality. In the presence of service contractors, this can be achieved by the column generation algorithm ZIBDIP. In metropolitan areas, however, service contractors cannot be dispatched automatically because they may decline. The problem: a model without contractors yields larger optimality gaps within ten seconds. One way-out are simplified reoptimization mod- els. These compute a short-term dispatch containing only some of the requests: unknown future requests will influence future service anyway. The simpler the models the better the gaps, but also the larger the model error. What is more significant: reoptimization gap or reoptimization model error? We answer this question in simulations on real-world ADAC data: only the new model ZIBDIP_dummy can keep up with ZIBDIP.     

基于复杂项目群优化选择的水电经济效益计算

针对目前已运行水电站经济效益计算存在的问题,本文提出了基于大系统分解协调模型选择水电站在不同运行时间的最优等效替代运行位置.考虑目前电力系统中正在逐步推行的两部制电价（容量电价与电量电价）,研究中分别计算了已运行水电站最优等效替代位置的边际容量成本和边际电量成本,并将其分别作为已运行水电站优化运行中各时段（刻）经济效益计算的容量价格与电量价格.以运行水电站经济效益最大作为优化准则,采用动态规划方法对其进行实时调度,从而实现其经济运行调度.文章给出的实例计算表明,本文提出的方法与模型是可行的.     

突发事件情景下串联式需求系统应急物资协同调度研究

针对突发事件情景下串联式需求系统遭受破坏问题,分析了突发事件情景下串联式需求系统应急物资协同调度的特征。在对系统提供应急物资进行修复的基础上,以串联式需求系统修复的时间最短及成本最小为目标,分别构建了纵向配送的应急物资调度模型和纵向配送与横向转运相结合的应急物资协同调度模型,并设计一种遗传算法对两种模型进行求解。最后通过算例分析,求解得到两种模式下串联式需求系统应急物资调度的最优配送方案,比较解的结果,得出纵向配送与横向转运相结合的应急物资协同调度模式优于一般的应急物资纵向配送模式的结论,验证了该应急物资协同调度模式的有效性和可行性。