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双语推荐：线性规划的数学模型

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本文尝试运用运筹学中线性规划理论的数学模型，结合SWOT分析决策房地产开发最高最佳使用方式，为开发商或土地估价师提供一条可供参考的技术路线。
This paper tries to combine the mathematical model in the linear programming of operations research with SWOT analysis to determine the best operation method for the development of real estate to provide a technical route of the reference for developers and land valuers.

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提出一种服装缝纫流水线负荷平衡的编排方法。利用工序分析表，得到各个工序的工作时间、所使用的机械种类以及各个工序之间加工的优先逻辑关系。建立相应的数学模型，依据数学模型编辑相应程序。利用线性规划软件Lingo求解，得到最优化的工位数、生产节拍以及各个工序之间的编组。
A scheduling method about the garment sewing assembly line load balancing is proposed. The work time, mechanical type and priority logic relationship of the processing between each working procedure are obtained by using process analysis table. We create the corresponding mathematical model, and edit the program based on a mathematical model. By using linear programming software Lingo, we obtained the optimum working median, production rhythm and the marshalling between each working procedure.

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利用线性规划理论建立物流运输调度的数学模型，研究一个开放的、动态的现代化物流运输调度问题，然后通过匈牙利算法来求解物流运输调度的最优方案，并通过实例分析了这种算法在求解物流运输调度问题中的有效性。
In this paper, we built the mathematical model for the open-ended and dyanamics logistics dispatching problem using the linear programming theory, then solved it using the Hungarian algorithm to obtain the optimal logistics dispatching plan, and at the end, through an empirical analysis, demonstrated the validity of the algorithm in the solution of such problems.

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引入并改进NSGA-II算法，用于解决GM PLS光网络的流量工程问题。首先给出流量工程问题数学模型；然后提出一个基于线性规划和NSGA-II的混合启发性算法；最后对算法进行仿真，将结果与车比雪夫精确算法所得结果进行比较，验证了本算法的有效性。
In this paper ,we introduce and devise Non-dominated Sorting Genetic Algorithm (NSGA-II) for solving the constrained multipath traffic engineering problem in GM PLS optical networks .A formulation of this problem as a multiobjective constrained optimization is first extended .Then ,we develop a hybrid heuristic algorithm based on linear programming .We also compare the performance of the proposed heuristic using a similar problem adopted from the literature with the exact solutions generated using a lexicographic Chebyshev method .

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以响应灾害事件发生后应急冷链物流资源调度时间最短为目标，构建了应急冷链物流调度的数学模型，并基于网络优化和线性规划优化思想，运用启发式算法对应急冷链物流调度模型进行求解，再采用 MATLAB 算法语言设计了冷链物流的仿真程序，最后提出相应的对策建议。
In order to response to the disaster event as shortly as possible,the paper builds a mathematical model of the emergency cold chain logistics scheduling,and uses a heuristic algorithm to solve the mode based on the network optimization and linear programming optimization,and then designs the cold chain logistics simulation program by MATLAB.Finally,it puts forward corresponding counter-measures.

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为了提高天然肠衣的原料使用率和生产效率，运用分类分析法建立了肠衣原料搭配的线性规划数学模型。基于该模型和所给数据，使用Lingo软件编程得到了原料搭配的最大成品捆数，并在此基础上使用C语言编程得出了最佳原料搭配方案，提高了肠衣的原料使用率和生产效率。该模型也可应用于不同批次的肠衣原料搭配，可解决与长度有关的材料分配等问题。
The usage and the production rate have been improved of in the natural casing.This process can be carried out through building linear programming mathematic models, using classification analysis meth-od of collocation in the natural casing. Based on the models and the given data,the most problems of the matching number of bundles in the raw materials collocation have been solved using Lingo software.With the addition of C language programming,a set of optimum matching scheme can be obtained.This result can improve the usage and the production rate of the natural casing raw materials. The models can be used in different batches and also solve the problem of the material distribution of length.

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针对以往国内外农机装备配备的研究存在的不足,提出了改进型整数线性规划的一般数学模型.模型适合作业面积及收获作业天数可变情况下的农机装备结构优化问题,综合考虑农机装备工作效率、人工配备、燃油消耗等影响参数,并结合实例运行运筹学软件Lingo进行分析计算,证明了该模型的有效性及经济性,可为农场、种植大户、农业合作社、各级农机主管部门提供区域内农机装备最优配置的决策支持.
@@@@Considering the shortcomings of domestic and foreign research for farm machinery and equipment, we propose the general mathematical model of the improved integer linear programming. The model is suitable for the optimization problem of farm machinery and equipment allocation with variable operating area and operating days. It considers the impact parameter of the efficiency of farm machinery and equipment, number of workers and fuel consumption. We give examples and use software Lingo to calculate and prove the validity and the economics of the model. Our model can provide decision support for optimal allocation of farm machinery and equipment in the region for the farm, grower, agricultural cooperatives, and agricultural departments.

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针对工件具有位置退化效应,机器具有多个维修区间的单机调度问题。工件的加工时间为位置相关的函数。每次机器维修后回到初始的水平。目标函数为总的提前费用,误工费用,共同交货期的窗时费用和开始时间费用。对于共同交货期分为包括维修区间和不包括维修区间两种情形进行讨论,采用线性规划建立指派问题的数学模型,并分别提出最优序列的一些最优性质和相应的多项式时间算法。
This paper deals with single-machine scheduling with rate-modify activities and position-dependent deteriorated job. The machine can be performed multiple rate-modify activities to change the processing times of the jobs scheduled after the activity. The objective is to find a common due window for all the jobs and a location of the rate-modifying activ-ities for each job to minimize the sum of earliness, tardiness and the cost and the starting time of common due window. The common due window is divided into two cases:in maintenance interval or out maintenance interval. Some properties of the optimal schedule are provided for the problem and present polynomial algorithms, respectively.

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将下层带多目标函数的二层线性规划与灰色理论相结合,提出了一类灰色二层线性多目标规划问题,给出了该问题的数学模型和相关概念。在约束域为非空紧集的条件下,证明了漂移型灰色二层线性多目标规划问题的最优解一定可以在约束域的极点达到,并提出了一个基于k次最好法的求解算法,证明了该算法具有全局收敛性,算例分析验证了所提算法是有效的。
Based on the bilevel linear multi-objective programming problem with multiple objectives at the lower level and the characteristic of the grey system, a grey bilevel linear multi-objective programming problem is put forward, and its model and theorem are given. Under the assumption of the constraint region of the proposed model nonempty and compactness, it is shown that the optimal solution of the drifting grey bilevel linear multi-objective programming prob- lem can be reached on the extreme point of the constraint region. Finally, an algorithm based on the k-th best method is developed and its global convergence is proven. Numerical examples show that the proposed algorithm is effective.

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峰谷电价制是我国今年来采取的一种有效经济手段，峰谷分时电价不仅能具有调节电力供需矛盾，还能起到减少资源消耗与保护环境的作用。就某管网基于峰谷电价体制下的运行现状，建立了线性规划数学模型，提出了日输气计划优化问题。并以该线为例进行分析，初步揭示了峰谷电价体制下日输气计划方式的一些基本规律，表明在该体制下该管网具有一定的节能降耗潜力。
TOU system is an effective economic means which our country has take this year,TOU pricing not only can regulate electricity supply and demand, but also reduce the consumption of resources and protect the environment. In this paper, a linear programming model for a network-based system running under TOU current situation was established to optimize the daily gas transportation plan. Taking the pipeline as an example, some basic laws of the daily gas transportation plan based on TOU price were revealed, which indicated that this system had a certain energy saving potential.

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