An operational mathematical programming model for the planning of economic activities in relation to the environment

The model described in this article is a mathematical programming model to assess the economic implications of different industrialization policies. It consists of input-output relationships connected with an environmental quality model converting emission data into expected distribution over space.     

A university admissions system

This paper presents a mathematical programming model that will make admit/reject decisions for applicants to a university freshman class.The model is intended to aid (rather than replace) reviewers and will help produce better and more consistent decisions. It also provides a university administration with some control over “balance” in the composition of the student body and allows investigation of the consequences of alternative admission policies.The nature of the problem suggests an integer programming formulation, however it is shown that a linear programming formulation will provide an efficient and practical solution for all but a very small set of applicants (no more than 19).     

Inventory policies for humanitarian aid during hurricanes

In this work we present a stochastic programming model minimizing costs, to support the decision process of inventory policy which best satisfies the demand for food in shelters when hurricane winds are about to impact a town. In this model we consider perishable products as well as the first in first out (FIFO) system for their consumption. In order to make the model closer to reality ordering cost is time-varying and we add a penalty cost in case the shortage exceeds a known limit for two days in a row. Finally the cost to dispose of expired food is greater than the purchase cost of the product since throwing away food has ethical implications. Starting from a stochastic programming model, we present a procedure to transform it to a deterministic mixed integer programming model (MIP) with non-convex objective function over its entire domain, which closely states the situation in reality. Preliminary computational results and discussion are presented.     

A goal programming model for achieving racial balance in public schools

This paper develops a goal programming model for achieving racial balance in segregated public schools. The model is illustrated and offered as an improvement upon linear programming, a model previously applied in the literature which allows a single objective function only and, in comparison with goal programming, requires more variables and constraints. Goal programming, a member of the general multiple objective linear programming (MOLP) model, improves upon these among other disadvantages thereby emerging as a more efficient tool for student assignment problems.     

顾客需求变化对供应商选择影响的一种量化方法

本文在零部件供应商参与产品设计的背景下,根据顾客需求权重的变化,利用QFD技术中的产品规划质量屋、部件配置质量屋及两者之间的关系,以客户满意度最大化为尺度,建立整数数学规划模型,求解各部件的变化情况,实现了从顾客需求变化到外包给供应商部件变化的转换,从而为供应商的动态选择提供依据,并给出了数值实例。     

Goal programming solutions to transportation problems with variable supply and demand requirements

This article deals with goal programming as an aid to resolving transportation problems. The objective of this study is to demonstrate the use of goal programming as an approach to reducing total cost in transportation problems that possess variable supply and demand requirements. A generalized goal programming model is formulated and applied to a series of transportation problem situations based on the empirical data provided by a medium-size trucking firm. Comparison of the results demonstrates the cost advantage of using the goal programming model in place of the transportation method and integer interval linear programming.     

天然肠衣搭配的优化模型

首先,采用假设检验法,建立双目标整数规划模型;其次,通过引入权重,将双目标整数规划转换为单目标整数规划;最后利用Lingo软件进行求解,对给定的肠衣原料进行搭配,得到总捆数为191捆,剩余肠衣25根。     

带有模糊参数的城市生活垃圾逆向物流网络设计

在垃圾回收逆向物流网络中,回收的数量具有不确定性,根据这一特点,将各消费区域垃圾回收量看成模糊参数,提出了逆向物流网络的模糊约束机会规划模型,通过把模型中模糊机会约束清晰化,将模型转化为确定性的0—1整数规划模型,通过算例,针对不同的置信水平对模型进行了求解,为逆向物流网络设计提供了依据。     

考虑费用函数约束的物流配送中心选址双层规划模型

针对现有物流配送中心双层规划选址模型的不足,建立了考虑下层规划费用函数约束的物流配送中心选址双层规划模型,并用算例对比验证了此模型的有效性。     

Two-stage stochastic integer programming: a survey

Stochastic integer programming is more complicated than stochastic linear programming, as will be explained for the case of the two-stage stochastic programming model. A survey of the results accomplished in this recent field of research is given.     

A priority-based multi-objective framework for water resources diversion and allocation in the middle route of the South-to-North Water Diversion Project

Because of the degradation of the social-ecological-economic-environmental (SEEE) system, water scarcity has been a growing source of conflicts over the globe. Further, the uncertainty arising from complex water resource scenarios increases the conflicts between the different water users and destabilizes water allocation systems. In this study, a priority-based multi-objective programming (MOP) model (quantitative path) with fuzzy random variables (FRVs) is established for a water resource diversion and allocation (WRDA) problem. To determine the priorities of the multiple objectives, a priority-determination approach (qualitative path) is designed, comprising of a pressure-state-response (PSR) multiple attribute assessment system and a technique for order preference by similarity to an ideal solution (TOPSIS)-based evaluation method. Then the MOP model is transformed into a solvable goal programming (GP)-based model. Because of the inclusion of FRVs, the obtained results can be adjusted to local conditions in view of social, economic, environmental and ecological objective priorities. Therefore, they are more applicable than traditional weight sum or Pareto multi-objective WRDA methodologies. A case study from the middle route of the South-to-North Water Diversion Project (SNWDP-MRP) in China is given to demonstrate the practicability and rationality of the proposed methodology in obtaining scientific WRDA plans.     

供水管网模糊优化设计数学模型研究

供水管网优化设计通常具有模糊性，即影响管网优化设计的某些因素难以准确确定。针对这一特点，建立了供水管网模糊优化设计数学模型。通过变换，将模糊线性规划问题转化成一般线性规划问题，用单纯形法求解。根据所建立的管网模糊优化设计模型，可确定模糊环境下供水管网优化设计方案，与普通线性规划问题相比，该方法使设计结果更为经济合理。     

基于动态规划改进求解VRP问题节约法的DSM模型及其拓展分析

提出了改进求解VRP问题节约法的DSM模型(动态规划节约法),将代表启发式算法的节约法与代表精确算法的动态规划相结合,建立不断增加节约量的动态规划数学模型,使其得到全局最优解。该法计算过程平稳收敛,对增加约束条件的情况更易接受。     

A logistics model for emergency supply of critical items in the aftermath of a disaster

This paper proposes a logistics model for delivery of prioritized items in disaster relief operations. It considers multi-items, multi-vehicles, multi-periods, soft time windows, and a split delivery strategy scenario, and is formulated as a multi-objective integer programming model. To effectively solve this model we limit the number of available tours. Two heuristic approaches are introduced for this purpose. The first approach is based on a genetic algorithm, while the second approach is developed by decomposing the original problem. We compare these two approaches via a computational study. The multi-objective problem is converted to a single-objective problem by the weighted sum method. A case study is presented to illustrate the potential applicability of our model. Also, presented is a comparison of our model with that proposed in a recent paper by Balcik et al. [6]. The results show that our proposed model outperforms theirs in terms of delivering prioritized items over several time periods.     

多目标线性规划在广深城际列车组合中的应用

利用多目标线性规划的方法,以广深城际列车组合产品为研究对象。经过建立数学模型并采用LINGO软件分析,可以达到对多目标线性规划问题较易求解的目标,从而较好的利用多目标线性规划解决实际问题。     

A mathematical programming model for planning training opportunities in relation to manpower targets for development

One major obstacle to the implementation of development projects in many developing countries is the inadequate supply of skilled manpower. Thus efficient planning of training opportunities to supply the requisite quantity and quality of skills in phase with project implementation is an important problem. This paper develops a mathematical programming model for planning training opportunities in relation to manpower targets determined for development projects. The projects are assumed to have been selected according to some criteria of desirability deriving either from social cost-benefit analysis or national goals. The model permits alternative avenues of developing skilled manpower to be investigated with a view to ensuring the availability of qualified personnel given a stated work/task schedule, over a period of time, while attempting to minimize costs to the manpower supply system.     

对立交桥选址建模的初步探讨

本文提出了立交桥选址问题的0－1规划模型。该模型以平均车速和对路网交通均衡的作用为目标函数，考虑了立交桥选址的各项约束条件。考虑由计算机实现隐枚举法求解。在解的过程中该规模规划与交通流量分配模型不断相互作用。     

Jackknife model averaging

We consider the problem of obtaining appropriate weights for averaging M approximate (misspecified) models for improved estimation of an unknown conditional mean in the face of non-nested model uncertainty in heteroskedastic error settings. We propose a “jackknife model averaging” (JMA) estimator which selects the weights by minimizing a cross-validation criterion. This criterion is quadratic in the weights, so computation is a simple application of quadratic programming. We show that our estimator is asymptotically optimal in the sense of achieving the lowest possible expected squared error. Monte Carlo simulations and an illustrative application show that JMA can achieve significant efficiency gains over existing model selection and averaging methods in the presence of heteroskedasticity.     

Planning in an uncertain environment: Stochastic goal programming using the versatility criterion

This article presents a planning model that applies the versatility criterion to goal programming problems with uncertainty about the constraints which define the set of feasible decisions. Some of the constraint parameters are assumed to be stochastic variables with a joint normal distribution. The solution sought maximizes the probability of satisfying all the constraints. A nonlinear programming model is set out which can be solved by using numerical integration at every step. An illustrative example is provided which shows the possible application of the versatility model to land-use planning.     

面向对象的编程方式在网络神经元算法中的应用

网络神经元算法是一个建立非线性模型的算法,在自动化控制领域得到了较高的评价。但同时应用起来较为困难的算法。在建立一个实际的自动化控制模型时,必须根据控制对象采用合适的网络及合适训练方法,因此在研发过程中需要不断的调整程序和算法。在这个繁琐的过程中,一个好的设计和编程方法是非常重要的。该文章通过一个实践中网络神经元算法开发过程的案例,对比采用面向对象方法编程的过程,分析了这种编程方式的得失。