Solving linear programming problems under fuzziness and randomness environment using attainment values

In this paper, the author presents a model to measure attainment values of fuzzy numbers/fuzzy stochastic variables. These new measures are then used to convert the fuzzy linear programming problem or the fuzzy stochastic linear programming problem into the corresponding deterministic linear programming problem. Numerical comparisons are provided to illustrate the effectiveness of the proposed method.     

一类直觉模糊线性规划的求解及其应用

研究一类直觉模糊线性规划及其应用.首先,定义直觉模糊不等式,给出直觉模糊线性规划模型;然后,提出一种基于总精确函数的直觉模糊线性规划求解方法,并给出其求解步骤;最后,建立证劵投资组合的直觉模糊线性规划模型.数值算例表明了所提出理论是合理有效的.     

A geometric view of parametric linear programming

We present a new definition of optimality intervals for the parametric right-hand side linear programming (parametric RHS LP) Problem () = min{c ^t x¦Ax =b + ¯b,x 0}. We then show that an optimality interval consists either of a breakpoint or the open interval between two consecutive breakpoints of the continuous piecewise linear convex function (). As a consequence, the optimality intervals form a partition of the closed interval {; ¦()¦ < }. Based on these optimality intervals, we also introduce an algorithm for solving the parametric RHS LP problem which requires an LP solver as a subroutine. If a polynomial-time LP solver is used to implement this subroutine, we obtain a substantial improvement on the complexity of those parametric RHS LP instances which exhibit degeneracy. When the number of breakpoints of () is polynomial in terms of the size of the parametric problem, we show that the latter can be solved in polynomial time.This research was partially funded by the United States Navy-Office of Naval Research under Contract N00014-87-K-0202. Its financial support is gratefully acknowledged.     

Leveraging technological knowledge transfer by using fuzzy linear programming technique for multiattribute group decision making with fuzzy decision variables

Despite the importance of knowledge transfer for firms involved in foreign direct investment activities, this area has not received appropriate attention from the perspectives of both the knowledge transferor (i.e., MNC parent) and the knowledge recipient. To fill in the gap in the current literature we propose a model to understand the links between criteria complicating the transfer of knowledge and preferences that the company has to focus. This model is based on both the existing literature as well as views of company representatives and provides a useful methodology for identifying decision making problems on the transfer of knowledge. In this paper, we investigate the fuzzy linear programming technique (FLP) to analyze these links and for multiple attribute group decision making (MAGDM) problems with preference information on criteria. To reflect the decision maker’s subjective preference information and to determine the weight vector of attributes, the technique for order preference by similarity to ideal solution (TOPSIS) developed by Hwang and Yoon (1995) and the linear programming technique for multidimensional analysis of preference (LINMAP) developed by Sirinivasan and Shocker (Psychometrica 38:337–369, 1973) are used.     

An experimental comparison of the new goal programming and the linear programming approaches in the two-group discriminant problems

The aim of this article is to consider a new linear programming and two goal programming models for two-group classification problems. When these approaches are applied to the data of real life or of simulation, our proposed new models perform well both in separating the groups and the group–membership predictions of new objects. In discriminant analysis some linear programming models determine the attribute weights and the cut-off value in two steps, but our models determine simultaneously all of these values in one step. Moreover, the results of simulation experiments show that our proposed models outperform significantly than existing linear programming and statistical approaches in attaining higher average hit-ratios.     

A new mixed-integer linear programming model for rescue path planning in uncertain adversarial environment

Efficient vehicle path planning in hostile environment to carry out rescue or tactical logistic missions remains very challenging. Most approaches reported so far rely on key assumptions and heuristic procedures to reduce problem complexity. In this paper, a new model is proposed to solve the discrete rescue path planning problem for a single agent navigating in uncertain adversarial environment. It relies on a novel and simplified mathematical mixed-integer linear programming formulation aimed at minimizing traveled distance and threat exposure. Exploiting a user-defined survivability function approximation and survivability threshold, the approximate model allows constructing a solution providing an adjustable optimality gap interval on the optimal solution. Experimental results show the value of the proposed approach in computing near optimal solutions reasonably fast for various problem instances.     

一类区间系数线性双层规划问题的遗传算法

针对一类上层目标函数带区间系数的线性双层规划问题,提出了一种基于双适应度函数评估的遗传算法(GA)。该算法的特点是在一次运算中同时获得最好最优解和最差最优解。首先,利用双层规划约束域的顶点进行个体编码,以上层目标函数中系数的上下端点构造两个适应度函数;其次,利用适应度函数排序种群中的个体,并按从好到差的次序验证个体的下层最优性,直到找到一个可行个体;最后,在算法运行中更新找到的可行个体。通过对4个算例的仿真实验,表明算法是可行且有效的。     

A cost benefit analysis for industry 4.0 in a job shop environment using a mixed integer linear programming model

As the manufacturing industry is approaching implementation of the 4th industrial revolution, changes will be required in terms of scheduling, production planning and control as well as cost-accounting departments. Industry 4.0 promotes decentralized production and hence, cost models are required to capture costs of products and jobs within the production network considering the utilized manufacturing system paradigm A new mathematical cost model is proposed for assessing the cost-benefit analysis of introducing Industry 4.0 elements to the manufacturing facility, specifically, integrating and connecting external suppliers as strategic partners and establishing an infrastructure for communicating information between the manufacturing company and its strategic suppliers. The mathematical model takes into consideration the bi-directional relationship between hourly rates and total hours assigned to workcentres/activities in a certain production period. A case study, from a multinational machine builder, is developed and solved using the proposed model. Results suggest that though an additional cost is required to establish infrastructure to connect suppliers, the responsiveness and agility achieved resulting from uncertainty outweighs the additional cost.     

Adaptive dynamic programming for finite-horizon optimal control of linear time-varying discrete-time systems

This paper studies data-driven learning-based methods for the finite-horizon optimal control of linear time-varying discrete-time systems. First, a novel finite-horizon Policy Iteration (PI) method for linear time-varying discrete-time systems is presented. Its connections with existing infinite-horizon PI methods are discussed. Then, both data-driven off-policy PI and Value Iteration (VI) algorithms are derived to find approximate optimal controllers when the system dynamics is completely unknown. Under mild conditions, the proposed data-driven off-policy algorithms converge to the optimal solution. Finally, the effectiveness and feasibility of the developed methods are validated by a practical example of spacecraft attitude control.     

An exact algorithm for the bilevel mixed integer linear programming problem under three simplifying assumptions

We present an exact algorithm for the bilevel mixed integer linear programming (BMILP) problem under three simplifying assumptions. Although BMILP has been studied for decades and widely applied to various real world problems, there are only a few BMILP algorithms. Compared to these existing ones, our new algorithm relies on fewer and weaker assumptions, explicitly considers finite optimal, infeasible, and unbounded cases, and is proved to terminate finitely and correctly. We report results of our computational experiments on a small library of BMILP test instances, which we created and made publicly available online.     

The scheduling of maintenance. A resource-constraints mixed integer linear programming model

The scheduling of preventive maintenance is crucial in reliability and maintenance engineering. Hundreds of parts compose complex machines that require replacement and/or repairing. Maintenance involves the machine vendor (1), the machine user (2) and the service maintenance provider (3). The vendor and the maintenance service provider have to guarantee a high level of availability and productivity of the machines and maintain their down-time at a minimum even though they are installed worldwide and usually far from the vendor’s headquarters and/or the locations of the provider’s regional service offices. Moreover, many companies have great profits from maintenance and spare parts management.This study aims to illustrate an original mixed integer linear programming (MILP) model for the cost-based, reliability-based and resource-constraints scheduling of preventive maintenance actions. The model minimizes the total cost function made of spare parts contributions, the cost of the execution of the preventive actions and the cost of the additional repair activity in case of unplanned failure. The cost of the personnel of the producer and/or the maintenance service provider is also included. Finally, the paper presents a case study in a what-if environment demonstrating the effectiveness and the novelty of this study in real and complex applications.     

GeoVISTA Studio: a codeless visual programming environment for geoscientific data analysis and visualization

The fundamental goal of the GeoVISTA Studio project is to improve geoscientific analysis by providing an environment that operationally integrates a wide range of analysis activities, including those both computationally and visually based. Improving the infrastructure used in analysis has far-reaching potential to better integrate human-based and computationally based expertise, and so ultimately improve scientific outcomes. To address these challenges, some difficult system design and software engineering problems must be overcome.This paper illustrates the design of a component-oriented system, GeoVISTA Studio, as a means to overcome such difficulties by using state-of-the-art component-based software engineering techniques. Advantages described include: ease of program construction (visual programming), an open (non-proprietary) architecture, simple component-based integration and advanced deployment methods. This versatility has the potential to change the nature of systems development for the geosciences, providing better mechanisms to coordinate complex functionality, and as a consequence, to improve analysis by closer integration of software tools and better engagement of the human expert. Two example applications are presented to illustrate the potential of the Studio environment for exploring and better understanding large, complex geographical datasets and for supporting complex visual and computational analysis.     

Sequence of linear programming for transmission of fine-scalable coded content in bandwidth-limited environments

In this paper, we propose an optimal peer assignment algorithm on peer-to-peer networks. This algorithm is designed to maximize the quality of transmitting fine-scalable coded content by exploiting the embedding property of scalable coding. To be more realistic, we assume that the requesting peer has a delay constraint to display the content within a certain delay bound, and it also has limited incoming bandwidth. We first use a simple example to illustrate the peer assignment problem, and then formulate this problem as a linear programming problem, followed by a nonlinear programming problem. To efficiently solve the second nonlinear problem, we transform it into a sequence of linear programming problems. Finally, we apply our proposed algorithm to both image and video transmissions in bandwidth-limited environments. Extensive experiments have been carried out to evaluate the complexity and performance of our approach by comparing it with both nonlinear formulation and two heuristic schemes. The results have verified the superior performance of our proposed algorithm.     

基于线性规划和遗传–粒子群算法的烧结配料多目标综合优化方法

针对钢铁企业二次配料工艺,本文采用将硫含量折算为可比成本,兼顾节能减排目标和配料成本,建立了二次配料多目标优化模型;提出了一种基于线性规划和遗传–粒子群算法（GA–PSO）的钢铁烧结配料优化方法.首先采用线性规划算法进行求解,若线性规划方法无法求得最优解,则采用GA–PSO算法进行搜索.该方法应用于某钢铁企业360m2生产线的＂配料优化与决策支持系统＂中,实际运行结果表明,该算法在保证烧结矿质量的前提下,能够有效地减少二氧化硫排放,降低配料成本.     

基于线性规划的移动数据库广播调度算法研究

阐述了移动计算通用模型和移动数据库广播技术及发展状况,介绍了移动广播领域中经典的多盘广播调度算法。在多盘广播调度算法的基础上,运用统筹学的线性规划对所要广播的数据进行最优规划,并通过调度算法优化调度。     

求解线性规划的单纯形法的直接方法

通过对单纯形求解法的实质的分析和认识,提出了基于矩阵初等变换初始可行基的获得方法,进而得到基于单纯形法的求解线性规划模型的直接方法,省略了以往为选择解法而进行的分析判断,使单纯形法的运用简便明了。     

Applying software engineering techniques in the development and management of linear and integer programming applications

This work addresses characteristics of software environments for mathematical modeling and proposes a system for developing and managing models of linear and integer programming (IP) problems. The main features of this modeling environment are: version control of models and data; client‐server architecture, which allows the interaction among modelers and decision makers; the use of a database to store information about the models and data scenarios; and the use of remote servers of optimization, which allows the optimization problems to be solved on different machines. The modeling environment proposed in this work was validated using mathematical programming models that exploit different characteristics, such as the treatment of conditions for generating variables and constraints, the use of calculated parameters derived from other parameters, and the use of integer and continuous variables in mixed IP models among others. This validation showed that the proposed environment is able to treat models found in various application areas of operations research and to solve problems with tens of thousands of variables and constraints.     

Alternative mixed integer linear programming models for identifying the most efficient decision making unit in data envelopment analysis

A mixed integer linear model for selecting the best decision making unit (DMU) in data envelopment analysis (DEA) has recently been proposed by Foroughi [Foroughi, A. A. (2011a). A new mixed integer linear model for selecting the best decision making units in data envelopment analysis. Computers and Industrial Engineering, 60(4), 550–554], which involves many unnecessary constraints and requires specifying an assurance region (AR) for input weights and output weights, respectively. Its selection of the best DMU is easy to be affected by outliers and may sometimes be incorrect. To avoid these drawbacks, this paper proposes three alternative mixed integer linear programming (MILP) models for identifying the most efficient DMU under different returns to scales, which contain only essential constraints and decision variables and are much simpler and more succinct than Foroughi’s. The proposed alternative MILP models can make full use of input and output information without the need of specifying any assurance regions for input and output weights to avoid zero weights, can make correct selections without being affected by outliers, and are of significant importance to the decision makers whose concerns are not DMU ranking, but the correct selection of the most efficient DMU. The potential applications of the proposed alternative MILP models and their effectiveness are illustrated with four numerical examples.